Analysis of the seismic coherence attribute with respect to subsurface fault geometry

The objective of this study was to analyze the behavior of the seismic coherence attribute, particularly its relationship to subsurface fault geometry. Using data from the seismic survey of the Kuparuk River Field of the North Slope of Alaska as well as model data, a Monte Carlo method was applied to test the sensitivity of the coherence attribute in both settings. In the model setting the study tested coherence response to single faults, fault intersections, and master-minor fault geometries. The number of statistical experiments conducted for the Monte Carlo technique was restricted due to significant College of Engineering; times required to generate coherence volumes. The study concluded that the coherence attribute responds differently to different fault geometries. The ability of this attribute to resolve fault geometry depends on the selection of input parameters within the software suite used to compute it and on the frequency of sampling performed on the resulting coherence volumes. It was confirmed that the coherence attribute is affected significantly by the choice of migration methodology. Random noise of up to 50% of the absolute value of the maximum amplitude, on the other hand, has a negligible effect on how faults are imaged with the coherence attribute. Analyzing a composite result of several statistical coherence extractions is an improvement over mapping a single coherence volume on an interpreted fault surface. This study related a geophysical attribute to a geologic property, a relationship that can be used for detailed interpretations of fault geometry from coherence attribute volumes in the future.

COHERENCE by in ANALYSIS OF THE SEISMIC COHERENCE ATTRIBUTE WITH RESPECT TO ~ . - - SUBSURFACE FAULT GEOMETRY by Anastasia Mironova A thesis submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Master of Science m Geophysics Department of Geology and Geophysics The University of Utah May 2009 Copyright © Anastasia Mironova 2009 All Rights Reserved © T H E U N I V E R S I T Y U T A H G R A D U A T E S C H O OL majority vote has been found to be satisfactory. Chair: Ronald L. Bruhn Christopher R. Johnson David S. Chapman \ THE UNIVERSITY OF UTAH GRADUATE SCHOOL SUPERVISORY COMMITTEE APPROVAL of a thesis submitted by Anastasia Mironova This thesis has been read by each member of the following supervisory committee and by satisfactory. 7 I Christophe~on THE U N I V E R S I T Y OF U T A H G R A D U A T E SCHOOL APPROVAL To the Graduate Council of the University of Utah: I have read the thesis of Anastasia Mironova jn i t s f i n a i f o rm and have found that (1) its format, citations, and bibliographic style are consistent and acceptable; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the supervisory committee and is ready for submission to The Graduate School. Date Konald L. Bruhn Chair: Supervisory Committee Approved for the Major Department Marjorie A. Chan Chair/Dean Approved for the Graduate Council David S. Chapman^ Dean of The Graduate School UNIVERSITY UTAH GRADUATE SCHOOL FINAL READING APPROVAL in its final form ~~ tZA---- Chapman attribute, particularly its relationship to subsurface fault geometry. Using data from the seismic survey of the Kuparuk River Field of the North Slope of Alaska as well as model data, a Monte Carlo method was applied to test the sensitivity of the coherence attribute in both settings. In the model setting the study tested coherence response to single faults, fault intersections, and master-minor fault geometries. The number of statistical experiments conducted for the Monte Carlo technique was restricted due to significant computing times required to generate coherence volumes. The study concluded that the coherence attribute responds differently to different fault geometries. The ability of this attribute to resolve fault geometry depends on the selection of input parameters within the software suite used to compute it and on the frequency of sampling performed on the resulting coherence volumes. It was confirmed that the coherence attribute is affected significantly by the choice of migration methodology. Random noise of up to 50% of the absolute value of the maximum amplitude, on the other hand, has a negligible effect on how faults are imaged with the coherence attribute. Analyzing a composite result of several statistical coherence extractions is an improvement over mapping a single coherence volume on an interpreted fault surface. This study related a geophysical attribute to a geologic property, a relationship that can be used for detailed interpretations of fault geometry from coherence attribute volumes in the future. ABSTRACT The objective of this study was to analyze the behavior of the seismic coherence ~orth future. To ZZooyyaa VV.. MMiirroonnoovvaa 1 5 Attribute Geosciences 11 Seismic Attribute 3.2.2 Behavior of the Coherence Statistical Experiments 45 50 Coherence Coherence 93 95 CONTENTS ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. iv ACKNOWLEDGEMENTS .. ............... . .... . .. .. .............. vii CHAPTERS 1. INTRODUCTION ......... . ................................... 2. BACKGROUND ............... . ................ . .... . ........ 2.1 The Seismic Coherence Attribute. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Monte Carlo Methods in Geosciences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Kuparuk River Field .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3. RESEARCH METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.1 Forward Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Fault Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 3.1.2 Model to Seismic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20 3.2 Coherence Statistical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 Sampling of the Coherence Attribute. . . . . . . . . . . . . . . . . . . . . . . . . 41 ... . .......... 4. RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Migration Versus Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50 4.2 Noise Versus Coherence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54 4.3 Resolution Versus Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62 4.4 Model Fault Geometry Versus Coherence. . . . . . . . . . . . . . . . . . . . . . . . .. 65 4.5 Real Fault Geometry Versus Coherence ........................... 78 5. CONCLUSIONS AND FUTURE WORK ........................ 93 REFERENCES . ............ ... .... . ... . .. . ..... .. ............ . ... 95 Bruhn, and David Chapman. This work would not have been possible without the generous financial support, technical guidance, and data from the ConocoPhillips Company's Subsurface Technology group as well as its Alaska Business Unit. In the Subsurface Technology group my most sincere gratitude goes to Jenny Thompson, Randy McKnight, Peter Hennings, Bob Krantz, and John Sinton and in the Alaska Business Unit to Dominique VanNostrand and Lisa Isaacson. Also, many thanks to the Partners of ConocoPhillips Alaska: BP, Chevron, and ExxonMobil for supporting data release for publication. ACKNOWLEDGEMENTS I am most grateful to my understanding advisors Christopher Johnson, Ronald Bruhn, Efficient development of modern subsurface hydrocarbon reserves requires a thorough knowledge of reservoir structure. Determining how faulting alters hydraulic properties in the subsurface environment poses a major challenge. Faults can act as barriers, baffles, or conduits to flow, characteristics that relate directly to production, particularly when applying secondary recovery methods such as water and gas injections. Optimizing a faulted reservoir's performance relies on an accurate interpretation of the spatial location of faults, their geologic properties, and the associated uncertainties. in unfortunate co­herence attribute and subsurface fault geometry by discovering whether the coherence attribute responds differently to different fault geometries. The study also examines how seismic and computational processes affect the outcome of the coherence attribute response. Explanation. This study addressed the three major shortcomings of modern fault in­terpretation techniques: 1) the limited ability of interpreted surfaces to carry information about geologic properties of faults; 2) the biases arising from the selection of a version of the coherence attribute to be used for interpretation; 3) the biases involved in placement of fault picks by individual interpreters. CHAPTER 1 INTRODUCTION uncertainties. Typically, geophysicists interpret faults from seismic data as surfaces m three di­mensions. A recent article noted that the excess number of geophysical attributes over­whelms the process of advanced seismic interpretation and points out the unfortunate circumstance of these attributes lacking direct links to the geological properties of the studied subsurface [38]. This study targets the discovery of a connection between the seismic coherence attribute, one of the most frequently used geophysical attributes, and the geometric properties of faults. Thesis statement. This study investigates the relationship between the seismic co­herence 1) The limited ability of interpreted surfaces to carry information about geologic properties of faults. Modern interpretation methods that represent fault geometry as surfaces lack information about the changing dimensions of the associated fault zone, intensity of deformation, and possibly other geometry complications occurring along faults. Moreover, picking faults from seismic images introduces additional complications to the interpretation process in the form of numerous uncertainties. Even if it were possible to represent faults in three dimensions in a more accurate way that could capture this sort of geologic information, an extensive interpretation of geologic properties would still rely primarily on geophysical data, especially geophysical attributes. This depen­dency necessitates the discovery of any relationship between geophysical attributes and geological properties. The unsuitability of fault representation and lack of an established relationship between fault geometry and geophysical data hinder the ability to produce detailed geologic interpretations. routine choices during the process of computing a coherence attribute volume for a given seismic survey. The choices, which can alter the resulting coherence volume significantly, include the selection of the algorithm and software suite to be used for the computations and the selection of input parameters available within the selected software package. Further complexity arises from software availability, the interpreter's experience working with the coherence attribute, and the amount of testing an interpreter carries out with respect to the individual input parameters. Coherence volumes computed via the different algorithms and/or different input parameters differ greatly in their ability to display fault continuity, extent, and image clarity. 3) The biases involved in placement of fault picks by individual interpreters. Different interpreters working with the same three-dimensional fault surfaces derived from the same seismic and coherence volumes may obtain fault surfaces of different placement and connectivity. For example, some individuals may choose to do a detailed interpretation and pick several faults where others would outline only one. The exact placement of fault picks also may vary depending upon how sharply a particular fault is imaged in seismic data. geometry. Second, it addresses the issue of uncertain and biased fault placement by introducing a special sampling methodology that allows the inclusion of information about 2 ·capture interpretations. 2) The biases arising from the selection of a version of the coherence attribute to be used for interpretation. Interpreters introduce placement biases when they make fault This study addresses each of these shortcomings. First, it investigates the relation­ship between the geophysical coherence attribute and the geologic characteristic of fault of using a single coherence volume for fault interpretation by analyzing an existing fault interpretation with respect to several coherence volumes.' The latter two efforts enhance the value of the first contribution because they remove two significant biases involved in the typical fault interpretation process. space around the picks. The sampling methodology placed linear segments normally to interpreted fault surfaces, extending a set length from these surfaces. The analysis probed the shape of the coherence envelope around the interpreted surfaces by computing the statistical measures of mean, standard deviation, skewness, and kurtosis of the sampled coherence along the linear segments. applied both the special sampling and the statistical coherence extraction techniques to the model data as well as to the Kuparuk River Field data. fault coherence attribute. Next, the study analyzed the realistic domain of the Kuparuk River Field. By comparing two sets of Kuparuk River Field faults that were visibly different in their geometry styles, the study found a difference in the corresponding coherence responses to their geometries, strengthening the theory of a relationship between fault geometry and the coherence attribute. Even though other factors, such as throw and 3 the volume space around an interpreter's fault picks. This approach limits the impact of the fault's location on the analysis of its properties. Third, the study explores the issue volumes: Methodology. To reduce the bias caused by the interpreted location of faults, the analysis of the coherence attribute response included sampling the coherence volume In order to examine the coherence response more consistently, the study investigated the response of several coherence attributes. A Monte Carlo sensitivity analysis-based methodology generated multiple statistical coherence extractions to be evaluated to­gether. The chosen methodology used two major approaches to study the response of the coherence attribute to fault geometry. The analysis first focused on analyzing the response of the seismic coherence attribute to fault geometry in a modeled setting. The model setting made it possible to study the response of the coherence attribute given a set of specific fault geometries. Second, the study compared real seismic coherence attribute data from the Kuparuk River Field with the field's different fault styles. The study Validation. The following procedures validated the results. The study examined the modeled setting and noted differences in the coherence responses for different fault geometries. The results confirmed that different fault geometries cause differences in the different stratigraphy variations, could contribute to changes in coherence response, the study diminished their impact by selecting fault surfaces across the entire area of study. Ad­ditional confidence in these results came from the use of several statistical coherence extractions rather than relying on a single coherence volume. Other factors studied included the choice of a migration methodology, random noise, and resolution capabilities. Migration methodology has a significant impact on the coherence attribute. On the other hand, random noise has a negligible effect on the coherence envelopes surrounding faults. Analysis verified that the resolution capabilities were adequate for analyzing fault geometries of interest and their variability. As its most significant finding, this work determined that the seismic coherence attribute responds differently to different fault geometries in both model and real data. The study also found that the coherence attribute's ability to resolve differences in fault geometries depends on the input parameters selected in the process of computing this attribute. chapter coherence attribute. The second section specifies the choice of methodology for the coherence statistical experiments. The third section gives an overview of the Kuparuk River Field. The Research Methods chapter describes the techniques used for the forward modeling part of the project as well as the details of extracting and sampling statistical coherence volumes. The Results and Discussion chapter describes significant findings. The Conclusions and Future Work chapter summarizes the results and suggests future investigations. 4 vciluine. Thesis Structure. The thesis consists of the following elements. A background chapter conveys a general overview of the different aspects of the research previously studied in the literature. The sections in the background chapter address three major parts of this project. The first section offers a review of literature with respect to the seismic Kuparuk findings. of the study. The first section defines the seismic coherence attribute and reports its this attribute. The second section describes the background of the methodology chosen to carry out the proposed coherence statistical experiments. includes a brief history of the Monte Carlo and sensitivity analysis methods as well as their relation to geosciences. The work in this study is centered on a particular oil reservoir, the Kuparuk River Field, so the last section of this chapter covers some of the basic characteristics of this field, including structural and stratigraphic aspects. 2.1 The Seismic Coherence Attribute key tool used for seismic interpretation of faults today. of multiple traces, implemented by Marfurt and Kirlin [26], and the second was based on examining the eigenstructure of covariance matrices constructed from windowed seismic traces [16]. Aside from these major changes, researchers have developed several other improvements on the coherence algorithm [15, 24]. CHAPTER 2 BACKGROUND This chapter presents detailed background information about the major components history of development. It also notes the lack of research relating to the sensitivity of It geosciences. The seismic coherence attribute is a volume derived from seismic data that highlights areas of discontinuity of seismic reflectors. High coherence indicates continuity of seismic reflectors and low coherence indicates lack thereof, potentially implying the presence of faults, stratigraphic changes, and noise. Introduced by Bahorich and Farmer [8], this attribute offered a major breakthrough in fault interpretation. Arguably, it remains the Scientists made several major improvements on the original "Coherence Cube" algo­rithm in the years following its introduction. The original implementation of the coherence attribute relied on normalized cross-correlation [8]. Afterwards, two fundamentally dif­ferent approaches arose for calculating this attribute. The first was based on semblance 24]. This research set investigating the sensitivity of the coherence attribute as a major 6' different algorithms and/or input parameters given the same seismic volume. Researchers commonly recognize the sensitivity of the coherence attribute with respect to the algo­rithm or the set of input parameters chosen and that they must consider this variability in the process of fault interpretation. However, the field lacks formal studies to investigate such sensitivity for this or other seismic attributes. Experiments relied on a single software suite, Paradigm's Coherence Cube[l]. The use of a single software suite eliminated the complication of examining multiple im­plementations. Also, because one of the industry's most commonly used packages was chosen, the applicability of this research became more immediate and direct. Restricting computations to one program limited the variability of the coherence attribute to this specific version of the coherence attribute computation suite and its input parameters. 2.2 Monte Carlo Methods in Geosciences The output volume of coherence algorithms varies substantially with respect to chosen input parameters. fact, software documentation for coherence attribute computations often recommends generating several coherence volumes with different input parameters and selecting the one that best highlights features of interest. The temporal aperture parameter has been found to have a significant effect on coherence [25]. Variability of output with respect to input parameters exists for other attributes as well. For example, the curvature attribute shows great sensitivity to the wavelength parameter embedded in the extraction process [14]. Although researchers recognize the importance and necessity of analyzing uncertainty in geophysical data [31], especially for fault interpretation [37], the field lacks formal studies to properly address this deficiency. This project addresses the issue of nommiqueness of the coherence attribute volume by applying a technique analogous to the Monte Carlo sensitivity analysis but with many fewer realizations. Because of the significant difference in the number of realizations, this study refers to the sensitivity analysis carried out here as statistical experiments rather than Monte Carlo experiments. numbers" [18]. Sambridge and Mosegaard provided a more modern definition: "experi- 6 objective. In the context of this study, the sensitivity of the coherence attribute refers to the variability of the coherence image that results when generating this attribute with thc I]. parameters. In parameters [37], nonuniqueness During its early development, researchers defined the Monte Carlo method as "the branch of experimental mathematics that is concerned with experiments on random ments making use of random numbers to solve problems that are either probabilistic or deterministic in nature" [32]. So, Monte Carlo experiments involve inputting some form of random numbers into a system of interest and analyzing the generated set of results. commonly applying them to problems in geophysical inversion [32]. This study deals with the specific application of the Monte Carlo method to sensitivity analysis, the procedure modeling results [13]. Monte Carlo sensitivity analysis involves assigning a probability distribution for each input parameter, drawing a set of those parameters, and repeating the computations for multiple sets of parameters [17]. This work restricted the statistical experiments of the coherence attribute to analyzing the effect of input parameters. The procedure of coherence extraction itself remained unchanged. models multiple times in order to compute a single value. Under such circumstances the required data come from the variability of this single resulting value. The Monte Carlo techniques plot the results of the executions as a statistical distribution, then evaluate the summaries of this distribution for variability [36]. However, in the case of coherence sensitivity assessment, each time a coherence computation employs a different set of parameters, a new three-dimensional volume is produced. The variation in parameters generates a separate distribution with its own characteristics at every point in this three-dimensional space. This complexity does not lend itself to expression as a single-variable distribution on a two-dimensional plot. In order to facilitate an effective assessment, this work introduced a more sophisticated approach for presenting variability among the resulting coherence volumes. 2.3 The Kuparuk River Field billion barrels of recoverable oil [27]. Production began in 1981. Currently, the mature Kuparuk River Field uses water and gas injections as the primary means of recovering its remaining oil. ConocoPhillips Company is the majority owner and operator of this field. 7 The geosciences have practiced Monte Carlo methods for more than 30 years, most that determines the effect of input parameters or the structure of a model upon the statistical Commonly, Monte Carlo uncertainty estimation techniques execute the deterministic corne surmnaries of parameters three­dimensional The Kuparuk River Field is located on the North Slope of the State of Alaska (see Figure 2.1). Discovered in 1969, the Kuparuk River Field contained an estimated 1.8 Company is the majority owner and operator of this field. An anticline that plunges gently to the southeast traps the oil in the Kuparuk River Field (see Figure 2.2). The formation of the anticline is thought to be associated with 8 Wl A Aia&a Wl N | Wl NWESchrader Midnight Sun Figure 2.1. The Kuparuk River Field is located on the North Slope of the State of Alaska. eastward tilting of the beds during the Eocene epoch. During this tilting process, the difference in subsidence between the western and eastern flanks of the field may have created the anticline. [27] The Kuparuk River Formation, a clastic sequence deposited during the Early Creta­ceous epoch, contains divisions into upper and lower members separated by a regional unconformity. The lower member consists of interbedded marine sandstones, siltstones, and mudstones, and is subdivided into units A and B. The A unit contains the reservoir rocks, which are further divided into six units, A-l to A-6. The upper member, which contains units C and D, consists of a sequence of bioturbated marine sandstones, silt-stones, and mudstones. The C unit is subdivided into four units, C-l to C-4. (see Figure 2.3). [27] Normal faulting provides the main reservoir heterogeneity in the Kuparuk River Field. These faults number in the thousands and contain significant variances in hydraulic 78% WI Western North Slope ~ 55% WI Greater Kuparuk Area 36% WI Greater Prudhoe Area ,.., ( J r0- t , \ ( 1 0 I~ 2~ , i , I ri a / I • 8 r 'JD£')2 ( \ 2 .1. differ ence [Creta­t.: eous (;Ontains memb ers unconformity, rocks , I 5. member , silt­stones, nnits, I Fignre [9 Figure 2.2. Structure map of the top of the Kuparuk River Formation, after Masterson and Eggert, 1992. [27]. The area of study, pad 1A, is marked with a cyan square. properties, posing a great challenge for the production of oil (especially with water and gas injections). Faults in this field can act as barriers, baffles, or conduits to fluid flow [20]. Moreover, a single fault may have varying permeability along strike. The effectiveness of a fault seal lies in its fault geometry [37], underlining the importance of understanding fault geometry in order to discern hydraulic properties. Two main fault sets exist in the Kuparuk reservoir, and they differ in strike and age. The earlier fault set strikes WNW and the latter due north. Evidence from core studies suggests that the WNW-striking fault set formed when the C unit was being deposited at the surface and the second fault set developed much later, after the Kuparuk strata were buried. The WNW-striking faults typically show more offset at the base of the Kuparuk interval than at the top, where these faults tend to "exhibit a component of folding or distributed faulting" [23]. The opposite holds true for the north-striking faults, with greater offset at the top of the reservoir and few faults with smaller offset or a fold KUPARUK RIVER UNIT : ' I I ,,,1,. ._____________ -6400' ,.- 1 I ,1 1 1 1 I \ FAULTS I 5 MILES 5 km I Egger t, lA, wit h Moreover , st rike. scal understanding hydra ulic proper ties. set s reservoir , lat ter la ter, aft er Kllparuk top , striking faults , great er t he 10 2.3. and Eggert, 1992. [27]. The area of study, pad 1A, is marked with a cyan rectangle. at the base [23]. Successful prediction of fault properties relies on a detailed fault interpretation. The current approach of the team developing the Kuparuk River Field largely depends on fault geometry and fault throw. The distinction between faulting and folding changes property prediction, making such a distinction critical to the outcome. The overwhelming amount of detail of the faults in the subsurface rocks of the Kuparuk River Field makes interpretation very difficult and time consuming. Due to the extremely large size of this field, this investigation limited its research to a smaller area of the field. The study refers to this area as pad 1A within the Central Production Facility 1 (CPF-1). Figures 2.2 and 2.3 illustrate the location of this area. A WEST -5500' -6000' SUBSEA DEPTH (FEET) -6500' -7000' STRATIGRAPHIC UNITS lA 5 MILES 5 KM V.E.= 35x A' EAST Figure Structural cross section through the Kuparuk River Field after Masterson Eggert , l A, [23]. t hrow. t his Central t he t his CHAPTER 3 RESEARCH METHODS This chapter describes the methods applied during the course of this research project. The first section outlines the forward modeling procedures used to investigate the sen­sitivity of the coherence attribute to known fault geometry along with the procedures used for constructing geologic models and subsequently obtaining their synthetic seismic images. The rest of this chapter describes the coherence statistical experiments and the special sampling technique for the analysis of statistical coherence extraction results. 3.1 Forward Modeling This research created the modeling aspect to investigate the behavior of the coherence attribute with respect to known fault geometry. The modeling consisted of five fault models defined with dimensions and displacement relationships similar to those observed in the Kuparuk River Field. The methodology adopted for analyzing the coherence response to modeled fault ge­ometry incorporated the following: 1) defining a set of fault geometry models; 2) deriving a one-dimensional profile of velocity and density from well log data from the Kuparuk River Field; 3) creating three-dimensional reflectivity volumes by combining the fault models with the density /velocity profile; and 4) transforming and the reflectivity volumes into the time domain via the exploding reflector modeling technique and migrating them. Figure 3.1 contains a diagram of these steps. Finally, the research carried out coherence statistical experiments to test the sensitivity of the results. Models This section describes the five fault models created for this study in terms of their relation to the fault geometries of interest in the Kuparuk River Field. They are then described in detail in terms of their dimensions and scaling relationships. density/3.1.1 Fault Models 12 Kuparuk River field geological observations / fault model as geologic surfaces fin well logs \ IP density/ velocity profile (hi depth) reflectivity (in depth) demipration Figure 3.1. A diagram of the entire forward modeling process. t'ault geolo~ic (in depth) reHecti ity dep[h) demi~ration 1 mi~ratjoll ' ~ IU densit. ' ill depth process, 13 Figures 3.2, 3.3, 3.4, 3.5, and 3.6 diagram the five fault models as if viewed from the top Kuparuk horizon. Fault Model 1 consists of a single fault with maximum throw in the center that decreases linearly toward both ends. Fault Model 2 represents an intersection of two faults of constant throw. Fault Model 3 contains a single fault of constant throw with two faults of smaller throw alongside it, offsetting only the C sands of the Kuparuk interval. Fault Model 4 incorporates a single fault of constant throw with two faults of smaller throw alongside it, which offset only the A sands of the Kuparuk interval. Fault Model 5 consists of a horizontal relay of two faults. The study used Model 1 to investigate the relationship of the coherence attribute to throw, targeting the smallest resolvable throw because it reflected the vertical resolution capabilities of the attribute. The second fault model represented a typical intersection of two faults in the Kuparuk River Field. The angle between these two faults corresponded to the angle of intersection between the main fault sets in the oil field. The proximity of the actual fault intersec­tion to the fault intersection observed in the coherence attribute reveals the horizontal resolution capabilities of the coherence attribute. Fault Model 3 described the typical fault geometry of the WNW-trending fault set, and Model 4 described that of the North-trending set. Both models sought to examine the coherence attribute's ability to detect the presence of small faults. The resolutions experiments on models 1 and 2 formed the basis of the dimensions of smaller faults in models 3 and 4 (see Section 4.3). The smaller faults were set to have the smallest resolvable throw and their horizontal distance from the larger fault corresponded to the measured horizontal resolution. The study then compared the coherence response between the areas where small faults were present and those where they were absent. The fifth fault geometry model represented a horizontal fault relay zone where two faults overlap. The ability to distinguish a small-scale relay zone from a continuous fault of constant throw is useful in determining regions of different permeability along faults. Specifications of the first model consist of the following. The only fault of this model had a NS strike with linearly decreasing throw along strike away from the center point. The maximum throw was 250 ft, approximating the maximum throw observed in the Kuparuk River Field. The throw was distributed unevenly between the footwall and the hanging wall, with 80% displacement from the horizontal plane in the hanging wall and 20% in the footwall. The total length of the fault along strike was 7500 ft, consistent Modell a Model 5 consists of a horizontal relay of two faults. field. l30th land 14 Fault K 11000 ft H A 6000 ft 0 f: i i 250 f- T 1750 ft J T 750 1 Oft 0 I': 1 [>ft f 5500 ft 1 175 -J T Legend: Horizon Depth 6200 ft i 5950 ft 6000 * ft - throw X 0 fault dip X ft - horizontal distance F i g u r e Model 1. through entire section. this faults jo'awl Geometry Model 1: Top Kuparuk Horizon ft ~ t 6000 ft N I 4000 ft HorizOl1 Deptll 6200 ~ I ft Or: Of: I - normal fault X ft fault thro~ X 0, - fau lt dip ft 14 ,- Figure 3.2. A diagram of fault ModelL This is a single fault tear t hrough the ent ire Kuparuk section . The maximum throw on t his fault is comparable to the maximum throw observed in fa ults at the Kuparuk River Field. 15 Fault Geometry Model 2: Top Kuparuk Horizon k II000 ft Legend: Horizon Depth i l l 6100 ft I 6000 ft 6030 ft ^ J ^ ^ - - normal fault X it - fault throw • angle of intersection ° - fault X horizontal distance W i n . amMmmi.mmM..i. . n i i . i . u .mipii um of between North-trending trending "ault I.e I HXXHt t 6000 it ,(I r: N I ~5° Legend : HorizoJl • 6 100 fa It x :1 fa It _ t - inter ection X 0 fau lt dip ft - di. tance 15 Figure 3.3. A diagram of fault Model 2. This is an intersection of two faults of constant throw. The angle bet.ween these two faults is similar to the angle between the Nor th-t rending and WNW-t rending fault sets of the Kuparuk River Field. 16 Fault h 11000 ft H Legend: Horizon Depth 6100 ft 6000 mmmmmmmLm^^^ ' tUXtJial X ft fault throw ° -fault X ft » horizontal distance F i g u r e . }'autt Geometry Model 3: Top Kuparuk Horizon t 6000ft N I Le~elld : Ho rizoJl • 6 100 ft ft - normal fault ft - thro~ X 0 - fault dip ft - dir.tallce 16 Figure 3.4. A diagram of fault Model 3. This is a single fault of constant throw that is accompanied by two smaller faults which offset the top of the Kuparuk section and terminate within the B shale. 17 Geometry Model 4: 1KKX) it t 6000 ft 4 ( ) t l N Of: ^ 120 ft a 3750 ft 40 5500ft 60 ft 750 ft 3750 fi 5500 ft Legend: Depth 1 1 ft 6000 1 - normal fault normal fault at A interval. invisible at top Kuparuk X ft - fault throw ° - dip X ft horizontal distance the Fault (Teometr):.~todeI4: Top Kuparuk Horizon t I u gend: Horizon • 6040 ft .1. - inter al. in isible ~t fau It X 0 _ fault d ip It - ho izooral dist3Jlce 17 Figure 3.5. A diagram of fault Model 4. This is a single fault of constant throw that is accompanied by two smaller faults which offset t he A sands and terminate at the base of the Kuparuk section. Fault Model 5: Us 11000 ft Legend: Horizon 6080 f t l ~ ~ ~ ~ ~ 5980 6000 ft I it fault throw ° distance Model rawl Geometry ModelS: Top Kuparuk Horizon loE t N I Le~end: HorizoJl Depth OOtlO ft I fl 59tlO ft - normal fault X t - fa It thro\ X 0 - fault dip X ft - horizontal d.istance Figure 3.6. A diagram of fault YIodel 5. This is a horizontal relay of two faults. 18 19 with the typically observed ratio of 1:30 for throw to strike length in normal faults [33, 39). The fault dipped 55 degrees, which is approximately the average fault dip in the Kuparuk River Field. Vertical displacement of the hanging wall and footwall dropped to zero 2000 ft away from the fault surface. The second fault model portrayed two faults of constant throw that offset the entire Kuparuk section. The throw of the NS striking fault was 30 ft, and the throw of the WNW-striking fault was 100 ft, decreasing to 70 ft at the point where the two faults met. The fault dip was 55 degrees. The angle of intersection between the faults was 70 degrees, which approximates the angle between NS and WNW faults in the Kuparuk River Field. which were 60 ft apart, offset only the part of the Kuparuk interval above the B shale. Both of the small faults had variable throw, decreasing linearly away from the center of the model at length to throw ratios of 30:1 and 150:1 toward the two tips of each. See Figure 3.4 for a detailed illustration. The smaller faults shown in the fourth model occupied opposite sides of the main fault. The smaller fault on the hanging wall was 60 ft away from the main fault, and the smaller fault on the footwall was 120 ft away from the main fault. The maximum throw on both faults was 30 ft. The throw changes were similar to those of the smaller faults in the third model. See Figure 3.5 for the detailed specifications. The smaller faults in the fourth model only offset the A sands of the Kuparuk section. The smaller faults in both models 3 and 4 dipped at 55 degrees with a NS strike, and had hanging wall and footwall throw distributions as specified for the fault in the first model. The fifth fault model encompassed two NS striking faults, one of which passed through the center of the model space with the second fault 60 ft from the first. The maximum throw on both faults was 100 ft. The throw was constant away from the center of the model space on both faults, with the relay zone located in the center. The length of the entire relay zone was set to 900 ft and the throw along both faults decreased linearly to zero within this distance. The dip of both faults was 55 degrees and the ratio of displacement between the hanging wall and the footwall was the same as that of the fault in the first model. 39]. Wl'\W-The third and fourth fault models both enclosed the same NS striking fault at the center with a dip of 55 degrees to the east. The throw of the NS fault was 100 ft in Model 3 and 40 ft in Model 4. The smaller faults in the third model were located in the hanging wall of the main fault, the closest being 60 ft from the main fault. The smaller faults, illustration. faults The fault model specifications as described above were transformed into three-dimensio­nal space in order to be useful for the forward modeling procedures. To carry out this transformation, the study defined a set of geological surfaces that complied with the diagrammed fault geometry. In detail, this procedure consisted of first computing points within the model space of 11000 ft x 11000 ft x 7000 ft that defined the geologic surfaces of interest in Mathematica [2]. The next phase then triangulating those points into surfaces in the GoCAD [3] software. Figure 3.7 illustrates the surfaces constructed for the second fault model. This subsection describes the process of obtaining seismic images of the five geologic models described above. The process combined the fault models with a density/velocity profile derived from the well logs of the Kuparuk River Field and subsequently trans­formed the models into reflectivity models and their respective seismic images. The description began with the derivation of the one-dimensional density/velocity profiles, followed by a description of the process of combining them with the geologic surfaces into three-dimensional reflectivity volumes. The section concludes with a description of the seismic imaging. The study required the greatest detail in the density/ velocity profile of the Kuparuk interval, the location of the relevant faults. The velocity/density model for the intervals above and below the Kuparuk were simplified to piecewise linear functions based on the Figure 3.7. A triangulated geologic surface representation of Model 3 in three dimen­sions. The visible surfaces are the top Kuparuk horizon, the base Kuparuk horizon, and the faults. N W E S 20 transform~d three:"dimensio­nal transformation , detail , consisteu tha t surfaces 3.1.2 Model to Seismic ahove. procetiti dimentiional volumeti. tiection seismIc Imaging. velocity Kuparuk faults . faults. 21 The study used the density function from a linearly approximated bulk density log 1A-08, Figure ,3.8 for location). Figure 3.9 illustrates this linear function along with the bulk density log. D = 1.99565 + 0.00007 x d . where D is the model density and d is total vertical depth. The study extrapolated density to the surface to cover the depth interval where no density was recorded. The study computed velocity function as a linear fit to the sonic velocity log. To capture the effect of the permafrost, which exists at approximately 1400 feet of depth, the study generated two piecewise linear functions. Figure 3.10 illustrates the p-wave velocity function resulting from this calculation alongside the recorded sonic velocity log of 1A-08. V = 9978.81 - 1.22 x d, if d < 1400 and V = 5491.45 + 0.71 x d, if 1400 d 6000, where in both cases V is the p-wave velocity and d is the total vertical depth. The interval below the Kuparuk section was described with constant velocity and density set to those of the Miluveach shale at the base of the Kuparuk section, 10168 ft/s 3.8. Time slice through the coherence attribute at the top of the Kuparuk River Formation. The area illustrated corresponds to the area of study, pad 1A. Two well penetration locations are marked with maroon circles and labeled. original density and velocity log data. from one of the wells with the most extensive logged 'interval above Kuparuk (lA-OS , see 3.8 ilfustrates = + , functions . alongsidn = :::; = + < < ft/,•. I. ' Nt ,. I It ( ) l I ( ~A'10 I , ) I , -l.~J " Figure lA. Depth (ft) Figure 3.9. bulk density recorded 1A-08 its function (in red), which was adopted as the density function in the first version of the model for the interval above Kuparuk. 22 2.6 2.8 Density (g/cc) 4000 5000 The b1llk oensity log recoroed in well lA-OB (in green) and it.s linear fit Kuparuk. well 1A-23 Velocity (ftls) 6000 8000 10000 12000 2000 3000 4000 5000 6000 Depth (ft) Figure 3.10. The p-wave velocity log computed from a sonic log in we111A-08 (in blue) and its linear fit functions (in red), which were adopted as the velocity function in the first version of model for the interval above Kuparuk. 24 and 2.4 g/cc, respectively. The study generated more detailed models of velocity and density in the Kuparuk interval. The additional detail supported the objective to include enough vertical vari­ability of velocity and density to enable observation of faults offsetting only parts of the Kuparuk strata through a reflectivity contrast. Velocity and density comparisons also revealed a resemblance between the modeled velocity and density functions and the seismic signature of the Kuparuk interval observed in the seismic survey of the area. Correspondence to seismic data. To compute normal incidence synthetic seismograrns, the study used Well Seismic Fusion [4] for wells in the area of interest (pad 1A) that contained both bulk density and sonic slowness logs. These synthetic seismograrns were compared to the seismic traces from the collected survey at the locations of the selected wells (see Figure 3.11). This procedure resulted in the selection of a well with a normal incidence synthetic seismogram that best matched the real seismic trace, well 1A-10 (see Figure 3.8 for location). For reflectivity modeling, the study transformed the density and velocity logs into piecewise linear curves for use by the GoCAD software package. The Backus averaging technique [7] was applied to the log curves with a sampling interval of 5 ft (see Figure 3.12). Acoustic impedance, the primary factor influencing the shape of the seismic wavelet, was the control curve. By combining the resulting density and velocity curves with the piecewise linear functions of these measures for the intervals above and below the Kuparuk River Formation, a single velocity and a single density profile emerged. The study used the software program GoCAD to combine the velocity/density profile with the previously created three-dimensional geological surfaces. The study first defined a volume space in which the modeled faults would reside. The model volume measured 11000 ft along the first horizontal axis (x), 11000 ft along the second horizontal axis (y), and 7000 ft deep along the depth axis (z). The sampling interval of 55 ft in both horizontal directions matched the horizontal sampling interval in the seismic survey of the Kuparuk River Field. Vertical sampling of 5 ft allowed detailed modeling of the strata within the Kuparuk interval. Vertical interval of 5 feet also matched the same interval spacing used in the Backus averaging procedure. glee, seismograms, 4J seismograms 1O 7J velocity I Total Vertical* Depth ft . -5700 •5750 - - 5800 - - 5850 - -5900 - • 5950 - 6000 - - 6050 " Seismogram from Normal Incidence Seismogram from Location 3.11. seismograrns 1A-10 j700 j850 5900 Normal Incidence Synthetic Seismogram from Approximated Logs Normal Incidence Synthetic Seismogram from Original Logs Recorded Seismic Trace at the Well Location 25 Figure The normal incidence synthetic seismograms of the original density and velocity logs (left) and the normal incidence synthetic seismogram of the Backus averaged density and velocity logs (center) compared with the seismic trace from the collected seismic survey at the well lA-lO (right). 26 1A-10. of I Thtal l Vertical Depth ft i"'" j700 • j7jO j800 jBjO j900 j950 • {)()()() 6OjO '- Approximated B~ Density I glee • 0ri2ina1 BJI!k Density 18 28 . ! ':' ,.- 'V •.•.. f. .~ "~r:.: .'. '. :'rl '.- r~' .T rop Kupa 11k " .".. •: 1i. . - f' I pick --='! ~-= I> '? ""'"'""'!!: ~~ ~ ~~ ~ ~7 ~ "'S <:: f> ~ ~ ? ~ .> i~ 1;.. ~~ ~~ ..oC~ l=- « po. ~--- ~[-. .-.. .. > ;? ~=-. :? F-- base Kupa 11k ..; .. picJc r: . - I .... !:.: ... f .. . ! ' .. ~ I - I - - ApproximaJed p·wa'le Velocity Ws Original p-wave Velocity:; ;:;:;;:;:w 4000 Ws 30000 ~i ~ I ~ . I -t:-::-= I 2 . i <=::: <: ~ - r =-' ~ 1 I 1--' -i f' ~ i". "'" ~ ~ I- I - _ i 1- - 26 Figure 3.12. Density (left) and velocity (right) logs of well lA-lO. The red curves are the original versions of the logs and the pink curves are the Backus averaged versions of the original curves. The fault surfaces were embedded in the volume along with the top and base of the Kuparuk River Formation horizons. Density and velocity values were distributed according to the density and velocity profile derived from well data. A cross section through the three-dimensional Model 1 (see Figure 3.13) shows the proper distributions of the density (see Figure 3.14) and velocity (see Figure 3.15) properties. The study ignored lateral variability in density and velocity properties because the one-dimensional velocity and density profiles were distributed throughout the entire Fault Geometry Model 1: U 11000 ft 6000 ft 4000 ft , 250 ft 0 ft 1750 It 7500 rt 1750 V 6200 ft 1 5950 ft > • normal fault X ft - fault throw X ° fault dip ft Figure 3.13. A diagram of the cross section A-A' through the center of Model 1, perpendicular to the fault strike. 27 Il1 of distributed "from Modef1 distributions t'ault Geometr)' Modell: Top Kuparuk Horizon I~ l"1 t 6OOOf't N I ft i ft .::: § 4000 ft A' A 5500 ft ft Legend: Horizon Depth 6200 ~ I I 5950 ft 6000 ft - normal faul t x :·1 - fault thrm X 0 _ t"ault dip X It - horizontal distance Modell, 2H Figure 3.14. A cross section of the density volume of Model 1. Cross section location model. Vertical reflectivity was computed on the entire volume using [29] = P2V2 - PiVj p\V\ + P2V2' Iii this formula reflectivity R is computed from the densities of the media, p\ and P2 , and the p-wave velocities of the media, V\ and . A cross section of the reflectivity volume for Model 1 is presented in Figure 3.16. When experimenting with migration methodologies, it became necessary to introduce additional reflectivity above and below the Kuparuk section because of the significant noise and edge effects caused by the sharp contrast between the detailed model of the Kuparuk section and the large volumes above and below the section with no reflectivity. Because of the similarities between the seismic signature of the Kuparuk section and the intervals above and below (see Figure 3.17 ), the study repeated the reflectivity layering of the Kuparuk section above and below the formation (see Figure 3.18). 28 3 .14. ModelL displayed in Figure 3.13. ent ire volmllc In densit ie:; (! I VI V2 . experiment ing migrat ion refl ectivity b elow significant contra..'lt bet.ween det ailed modd similari ties signa ture b elow Figure 3.15. A cross section of the velocity volume of Model 1. Cross section location displayed in Figure 3.13. The CPS [5] software package created seismic images of the reflectivity models. After using the exploding reflector modeling technique [22] to transform the data into the time domain, three migration methods were tested (referred to as Cases 1-3). 1. reflectivity data into the time domain using the exploding reflector modeling procedure [22] and to then migrate the resulting time traces using Kirchhoff time migration [10] (see Figure 3.19). The velocity was assumed to be constant throughout the entire volume and equal to the average velocity value for the section above the Kuparuk interval (7950 ft/s). The study utilized an existing Kirchhoff time migration routine that was embedded in the CPS software. This methodology provided the most precise focusing of the time-migrated image. Case 2. this case the study used the exact three-dimensional interval velocity 29 p-wave Velocity (xlOA3 flIs) 8 9 10 11 12 t he Case This workflow applied the same constant velocity value to first convert the llsing 3. 19) . ft/s). t ime-In Figure 3.17. A sample cross section of the seismic survey over the Kuparuk River Field A' -0.06 -0 .04 -0.02 Refte!;tivity o 0.02 30 A base Kuparut 0.04 0.06 Figure 3.16. A cross section of the reflectivity volume of YIodell. Cross section location displayed in Figure 3.13. East West - top Kuparuk - Kuparuk __ Amplitude 10 8 6 4 2 0 -2 -4 -6 -8 -10 ..................l oL!l: ll l ll, 1 1 1 III1IIII1I I , .!l:o:::!:::!. ......... within the area of interest, pad 1A. 3.18. A cross section of the adjusted reflectivity volume of Model 1. Cross VRMS ) f ° r velocities the migrated transforming information into a corresponding relationship between velocity and time. The interval velocities were adopted from the velocity modeling described above (see Figure 3.21). This interval velocity function excluded fine variations within the Kuparuk section for three reasons. First, velocity in the models was dominated by the 6,000 foot layer above the Kuparuk section, where velocity does not vary rapidly. Second, the exact velocity function was not critical for time migration. Third, the coherence attribute was not expected to be affected by this assumption because those variations in velocity would not change the nature of the discontinuity; they would only stretch or compress it. A' ~.06 ~ .04 Reflectivity o 0.02 31 A 0.04 0.06 Figure t he adjust ed refl ectivity section location displayed in Figure 3.13. model for the demigration step and a computed root mean square velocity ( VRMS ) for the Kirchhoff time migration step (see Figure 3.20). This methodology provided the most accurate velocit ies in t he time migrat ed image. The root mean square velocity computations involved t ransforming interval velocity t ime. wer e adop ted describ ed F igure 3. 21) . exeluded t hree First , dominat ed migra tion. Third , at tribute t o assumpt ion b ecause varia tions it . 32 reflectivity velocity ( in depth) (in depth) 7950 ft/s image f in time) Vrms ,. " 3D reHecth'ity ;'ll.iL·pthj 3D nlocit)' il1 deplh) ...• .. '''Plod i., ""r"' onod,li •• '--------> 7~ti'.ooO " 3D ima~e (iJl time) constant: tt's , interval \reJoc ity Figure 3.19. A diagram of the forward modeling procedure labeled as 'Case 1.' 32 fault model surfaces (in depth) ID velocity/ density profile (in depth) 3D reflectivity 3D velocity fin depth) f in depth) i exactly exploding reflector modeling computed <T interval velocity N r - - ~ Figure 2.' Vrms geologic !>urf~ces fill d.eprh) JU imaRe (ill rimt·) 3U reHecti~'ity (ill de/Jlhj 31) {(leplh) " . used ~)(ilctly Figure 3.20. A diagram of the forward modeling procedure labeled as 'Case 2. ' 33 34 Interval Velocity (ft/s) 10000 Depth (it) 1000 2000 3000 4000 5000 6000 7000 Figure 3.21. 9000 8000 Interval velocity function from model. 34 (ft) 35 t o VRMS '• lyNv2At, VRMS - \ T^.v 1-- > where Ati is vertical two-way travel time through the i th layer, and V{ is the interval velocity of the ith layer. Two-way travel times are then computed using the known interval velocities and depths within the model to produce a time-depth curve (see Figure 3.22). Next, the VRMS velocity is computed using the above formula given the known interval velocities Vj and two-way travel times At{ just computed. The result of this procedure, sampled at every 0.2 milliseconds is illustrated in Figure 3.23. Case 3. The process of depth migration with exact velocity is illustrated in Figure 3.24. Here, the exploding reflector modeling step used the exact three-dimensional velocity information that corresponded to the model being considered. At the step of Kirchhoff time migration that same three-dimensional velocity was used again to obtain the seismic image in depth. This method gave the most precise image of the original model. The seismic images computed using the three different cases are reviewed and com­pared in Section 4.1. The impact on the coherence attribute is discussed there as well. Time (s) 1.5 1.25 I 0.75 0.5 0.25 Depth (ft) 1000 2000 3000 6000 7000 Figure 3.22. Computed veloci­ties. 35 The interval velocity function is sampled every 5 ft to calculate VRM8 : VRMS = ~;::r:tti;' where 6.ti is vertic~l two-way travel time through the ith layer, and Vi is the interval velocity of the ith layer. Two-way travel times are then computed - - nsing the known interval velocities and depths within the model to prodnce a time-depth curvc (sec Figure 3.22). Next, the VRMS velocity is computed u~ing the above forIllula given the known interval velocities V; and two-way travel times 6.ti just compu ted. The result of this procedure, sampled at every 0.2 milliseconds is illustrated in Figure 3.23. Case 3. The process of depth migration with exact velocity is illustrated in Figure 3.24. Here, the exploding reflector modeling step used the exact three-dimensional velocity information that corre~pond ed to t he model being cOl1~idered. At the step of Kirchhoff time migration that same three-dimensional velocity was used again to obtain the seismic image in depth. This method gave the most precise image of the original model. The seismic images computed using the three different cases are reviewed and com­pared in Section 4.1. The impact on the coherence attribute is discussed there as well. / 025 4000 5000 Compnted time-depth curve for known model depths and interval veloci­t ies. ft/s) . 9000 0.25 0.75 1.25 1.5 (s) Figure 3.23. RMS Velocity (ftls) 10000 • 9500 8500 . . . . . • . . 025 .. . . .. .. .... .' .' .. .' ..... .... .. .... .. ..... . 0.5 0.75 , ••••••••• t 1.25 1.5 .' .' .' Time 36 The computed root mean square velocity function plotted against two-way travel time. 3D reflectivity 3D velocity fin depth} 1in depth) 3D image ' f'/r depth) the 3D retlecti vity ( in J<'pIJr) . 3D ~·eloc[t)· (ill deplll) depth 31) image (in t1tplh) used exactly used exactly imerval velocity Figure 3.24. A diagram of t he forward modeling procedure labeled as 'Case 3.' 37 38 for each coherence algorithm parameter that was being evaluated for sensitivity. It then randomly picked a set of parameters from the previously defined distributions and ran the deterministic computation for many such trials. The resulting set of coherence volumes generated a statistical sample on which to perform the variability assessment. the software used to extract coherence attributes. The section goes into detail about narrowing the list of parameters to those deemed most critical for the sensitivity analysis, because the process of carrying out this analysis for all of the parameters involved would have become intractable. Finally, it outlines the assignment of appropriate statistical distributions for each of the selected input parameters. The Paradigm software suite's documentation describes their version of the coherence attribute extraction in the following mariner. "The Coherence Cube quantifies the mea­surement of local waveform similarity within a 'global' aperture defined in space and time, utilizing dip and azimuth calculations." It claims that the generated coherence volumes can be used to map spatial change in the seismic waveform, which is associated with geologic features such as faults, fracture systems, channels, onlap depositional patterns, turbidite sequences, and so on. The documentation highlights the importance of choosing optimal input parameters. Paradigm's Coherence Cube algorithm provides multiple categories of input param­eters. The categories include 1) parameter choices associated with dip methods; 2) temporal aperture window; 3) spatial aperture; 4) a set of scaling methodologies that can be applied to the resulting coherence; 5) adaptive smoothing and sampling of the coherence; 6) advanced parameters that allow fine-tuning of the previously described parts of the procedure; and 7) the choice of algorithm, which is provided at the last stage of parameter selection. The selection of dip methods controls the coherence attribute's sensitivity to rapidly changing dip. The study kept the default selection of the FX Dip methodology because the dip parameter was not critical for coherence evaluation. The FX Dip methodology reduces the banding effect that can be generated by other methods and is optimal for cases when true dip does not change rapidly. Choosing the default was particularly appropriate for the Kuparuk River Field's seismic survey, as the dip within the reservoir 3.2 Coherence Statistical Experiments The coherence statistical experiments applied in this study defined probability distri­butions The section first describes the input parameters for Paradigm's Coherence Cube, parameters. manner. IIlap parameters. pararn­eters. fine-t.he methodology particularly does not change rapidly except where faults are located. Paradigm documentation cites the Temporal Aperture parameter as the most critical for the procedure of coherence extraction. Larger temporal aperture may allow suppress­ing noise; shorter temporal aperture reveals small-scale features. The study applied three methods to compute the optimal ranges for the Temporal Aperture parameter(i): 1) based on the recommendation in documentation for the Paradigm Coherence Cube; 2) based on the period of the wavelet; and 3) based on the thickness of the stratigraphic section of interest. Aperture parameter: "about one-half wavelength of the highest frequency to about one times wavelength of the lower frequency of the reflection data." This option creates a range of temporal apertures using the velocity information and the frequency filter applied in the processing of seismic data (see Figure 3.25). The final range of temporal aperture selected for the study was > 1 samples. The upper limit in this case was too high to provide a meaningful boundary (it was t < 1 second). The study used the seismic wavelet to drive the second reasonable range of choices for the Temporal Aperture parameter. The study filtered a single spike in the time domain with the frequency filter of Figure 3.25 then transformed it back into the time domain to derive an appropriate range of temporal apertures based on the period of the resulting wavelet: 3 < < 25 samples. The research also took into account the thickness of the Kuparuk section when select­ing temporal aperture. Hence, the third limitation on the temporal aperture parameter was imposed by the condition that should be less than the number of samples that span the Kuparuk section. The appropriate computations resulted in < 8 samples. Based on the above computations and experimental testing of the temporal aperture parameter on the Kuparuk River Field's seismic survey, the temporal aperture was assigned a Gamma distribution with the shape parameter of 2 and the scale parameter of 3 (Figure 3.26). This distribution allowed lower temporal apertures to be chosen more frequently (2 < t < 8); the use of higher temporal apertures less frequently (8 t < 25); and almost never those greater than 25. The Spatial Aperture parameter specifies the number and location of neighboring traces to use in the coherence estimation. For the purposes of the coherence statistical experiments, the study ranked equally likely the two available options: a five-point 39 t): Paradigm's documentation recommends the following range of choices for the Tem­poral t 2': :::; resulting :::; t :::; parameter t t :::; parameter :::; t:::; < :::; number' usc I . 1 . r-T L_ I I I i i 1 0 40 60 Frequency IIz) +conducted. Resolution 40 0.8 \ ..g3 0.6 \\ 0.. \ E -< '\ 0.4 \ \ 0.2 \ \ 0 20 80 100 (lIz) Figure 3.25. Filter applied in the frequency domain for processing both collected and modeled seismic data. neighborhood or a nine-point neighborhood. The Coherence Scaling parameter rescales the range of coherence values from the original 0.0 to 1.0 to a user-defined range. Coherence Scaling has no impact on the variability of the coherence computations as long as as the range remains consistent for all calculations. As a result, the study ignored the parameter in the statistical coherence extractions and rescaled the range of values consistently to -128 to + 127. Due to the high quality of the Kuparuk River Field's seismic survey, the study also ignored the adaptive eigen suite of selections for the statistical experiments conducted. Coherence extraction produces clean coherence images that did not suffer from noise artifacts, making the eigen suite unnecessary. The study limited advanced input parameters to include only the "High Resolution Method." Typically, high-resolution sharpening is performed on Horizontal traces. Reset­ting the method to "Vertical" enabled the method for inline traces. The study limited the 41 3), aperture this parameter consisted of "Eigen," [16] "High Resolution Eigen," "Semblance," [26] and "High Resolution Semblance." Paradigm based the versions of these algorithms on the previously referenced eigenstructure and semblance approaches; see Section 2.1. four 2,3]; neighbor­hood"; 3 . 2 . 1 t h e C o h e r e n c e A t t r i b u te Probability 0.12 0.10 0.08 0.06 0.04 0.02 5 10 15 20 Temporal Aperture (samples) 25 30 Figure 3.26. Gamma(2, 3) , the statistical distribution selected for the temporal aperture coherence input parameter. distribution for this parameter to two equally likely choices: "Horizontal" and "Vertical." The fourth and final parameter in the coherence statistical experiments involved selection of the specific algorithm implementation. The equally probable choices for 16J 26J In summary, the study tested the sensitivity of the coherence attribute through four input parameters: Temporal Aperture, Spatial Aperture, High Resolution Method, and Coherence Algorithm. The input parameters featured the following options: Temporal Aperture: discrete Gamma[2,3J; Spatial Aperture: equally likely between "5-pt neighborhood" and "9-pt neighbor-hood"; High Resolution Method: equally likely between "Vertical" and "Horizontal"; Coherence Algorithm: equally likely between "Eigen," "High Resolution Eigen," "Sem­blance," "High Resolution Semblance." 3.2.1 Sampling of the Coherence Attribute Establishing a relationship between coherence sensitivity and fault structure relies on comparisons between coherence sensitivity and the changing shape and structure of 42 coherence envelopes surrounding expert-interpreted faults. In order to investigate the changes, the study introduced a sampling technique that focused on t h e areas of coherence in t h e vicinity of expert-interpreted faults. The study selected a set of points on the faults' surfaces and sampled the surrounding coherence volume "at these points in the direction normal to these fault surfaces. This sampling produced a distribution of coherence values at each point along the faults' surfaces. Figure 3.27 illustrates a two-dimensional version of this approach. Figure 3.28 illustrates the sampling of the coherence attribute in relation to the statistical experiments. This figure shows three executions of the coherence algorithm where parameters were selected randomly from previously specified distributions. The coherence time slices corresponding to each of the respective coherence volumes illustrate the same fault interpretation in green. The coherence envelope surrounding that fault was sampled normally to the interpreted fault surface and the different shapes the coherence envelope assumed in the three cases were then compared relative t o each other. expert interpreted fault surface Figure 3.27. An illustration of sampling of the coherence a t t r i b u t e along an interpreted the the surrounding-· t hese faults ' illust rates t his illust.rat.es interprded to To assess variability, the study compared the structures of the different coherence runs that resulted from the sample distributions. Figure 3.28 illustrates such a comparison for three different shapes of the sampled coherence envelope. Statistical methods described and compared these sample distributions quantitatively. The distribution properties normals to interpreted faull's. su rfaoc / urfaoc attribute fault surface on a coherence time slice. time window = 10 neighbors = 4 high res. - no etc. f p v time window 11 res. = etc. I r interpreted fault f surface time window= 15 neighbors • 4 high res. yes etc. interpreted fault surface 1 interpreted fault surface Coherence Run 1 = = = interpreted fault surface 7 coherence distribution normal Coherence Run 2 = neighbors = 8 high res . = yes etc. coherence distribution Coherence Run 3 lime window = = = coherence distribution 43 Figure 3.28. The process of carrying out statistical experiments on the coherence attribute. t o these variability in shape of coherence envelopes that result from changing algorithm input parameters. A short description of these parameters follows. function distribution. shapes. coherence corresponding < ^ mean I range of means interpreted fault surface 44 targeted for computation included: mean, standard deviation, skewness, and kurtosis. The study chose these values because of their ability to describe shapes of single-valued distributions. By examining the changes in these' measures, the study assessed the from- A statistical mean measures the center of the associated probability distribution, an arithmetic mean [9]. Skewness measures the asymmetry of a probability density function [9]. Standard deviation measures the variability or the amount of spread in the distribu­tion of a random variable [9]. Kurtosis measures peakedness of a probability distribution. Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent, modestly sized deviations [19]. Computing these parameters for coherence envelope curves (see Figure 3.29) enabled quantitative comparison of their 128 range of coherence values o Coherence Run 1 Coherence Run 2 normal Figure 3.29. An example of computing the range of means for three coherence statistical experiments. This section outlines the procedure used to analyze the behavior of the coherence statistical experiments. When generating multiple coherence volumes, it was important to consider the amount of variability introduced with each additional coherence volume. The high dimensionality of the problem at hand demanded a careful approach. The study first applied the methodology for this analysis to a single linear sample through a coherence volume, then extended the methodology to an entire fault surface. 10 that sampled these coherence volumes in the same location produced 10 values for each statistical parameter of interest: 10 means, 10 standard deviations, 10 skewnesses, and 10 kurtosis values. The study performed the analysis for just one of these and later applied the analysis to the rest of the measures. greatest and the least statistical mean of the 10) changes when more coherence volumes decreased, then the behavior of the coherence statistical experiments for that particular linear segment was considered convergent. In order to assess quickly whether the general trend of the change in the range of means was decreasing or increasing, a line was fit to the points of the graph of Figure 3.32 (see Figure 3.33). The sign of the slope of the linear fit determined the decreasing or increasing trend of the change in range of means. This methodology allowed a single value to characterize convergence for each linear segment sampling the statistical coherence extractions. A positive value meant the statistical experiments' behavior was overall divergent at that linear segment. A negative value indicated convergent behavior. clearly distribution of convergent and divergent statistical means. The linear segments with convergence estimate values above the x-axis represent those for which the statistical experiments 45 3.2.2 Behavior of the Coherence Statistical Experiments important Consider the case of statistical coherence extractions. A single linear segment A single linear segment contains 10 different means across it for the 10 different coher­ence volumes (see Figure 3.30). The range of statistical means (the difference between the are added (see Figure 3.31). The study computed the extent of change for each additional coherence volume by taking the difference successively (see Figure 3.32). This change then successively increases, decreases, or remains stable. If the change in range of means particular Using all the sampled linear segments, the convergence estimates were plotted for an entire fault surface. For example, for a surface with 400 linear segments sampling the surrounding coherence space, the convergence estimates as described above might look like the values depicted in Figure 3.34. The graph dearly shows the distribution convergence 46 Meats Along the Normal 1 5 Number of • * ^ i Monte Carlo 2 | 5 s Id Simulations Mean Along the NonIa! .. I. ' o. " • .. -I Number of .. • .. MomeCarlo 6 H III Simulations Figure 3.30. 10 values of statistical mean across a single linear segment sampling the corresponding 10 different coherence volumes. Mean 12 a 6 4 Number 6 1( ) Simulations Figure 3.31. Range of statistical means is the difference between the greatest and the least statistical mean measured for a given number of coherence volumes. The range of means is different given one, two, and up to 10 coherence volumes. Range of Mean Values 12 10 .. • • • 4 .. • • 6 • 47 • r-.'umber of Monte Carlo 10 st atistical Change in 5 \ 2 I « Monte Carlo number Figure 3.33. The amount of change in range of statistical means as more coherence volumes are added to the sample set. A linear fit to these values allows the assessment Change in range of means 4 "2 • • 2 • • 4 • • 6 • ' . 8 48 • simulation Figure 3.32. The amount of change in range of statistical means as more coherence volumes are added to the sample set. Change in range of means 5 4 2 2 4 . 6 8 Monte Carlo simulation number ]0 of the overall behavior trend of the change in range of means. Convergence Estimate 0.5 * % * » • * * • • • « * * t" ii i ^ -« ** ^ M ** ^5^' ^ * « i »»i *• «• *» • j6j£]iififSLia.Li3f ' ' . v * 1 «* >WV'* * 200 * t 6 ;'«.,\% 4 0 0 Numbered ." *\ •'• ' "\ * • Segments -0.5 1 . 0 Figure 3.34. Plotting convergence estimates for all 400 linear segments sampling a single fault surface. Convergence estimates are the slopes of the linear fit to change in range of means. the slope value is positive, the coherence statistical experiments is considered divergent and if it is negative, it is considered convergent. In this case about half of the linear segments show convergent behavior. diverged and the linear segments with convergence estimates below the x-axis are those for which the behavior of the coherence statistical experiments converged. The study used several other plots to analyze and visualize this basic convergence estimation. A more visual representation of the plot shown in Figure 3.34 was generated by rendering the same convergence estimates directly onto the interpreted fault surface with values appropriately color mapped. Such a plot permits visual examination of convergence relative to the location in the interpreted fault surface. Convergence Estjmate 1.0 .' ... ' , . .. .. . ... , # .. ., -. I· .. .. .. . .". ... ".... .. ....... ... I, ,., ... " ." "., •••• • "'.. ......_ I. ........ \ ...... '!,. •• ;.: •• ~ •• :. III . ..,...." "...." ..... I' .. ·. --: .......... .. ,. ..;.... '" Sequenuall>' .' ..•• ".. ... ;,. ·I ?~"':.· •• • 2M " ",.' ' .l.:b .":' '.:-... 400 Nun1bere.d ~ •• 'f! •• _ "\ ..... . , t! .:. l' ..: w:: .. ~ . '. ' .... "" ... : " Linear Segnlents '. .~.. .. _ ,.". • 1. ..... '-' -0 .5 . !' - . ...".. • - 1.0 . . 49 of If convergent . converged . convergence mapped . methods. Second, the study evaluated the attribute's sensitivity to random noise. The third experiment examined the resolution capabilities of the coherence attribute. Fourth, the coherence attribute was extracted on the five fault geometry models. The last set of experiments involved performing coherence extractions on the Kuparuk River Field seismic data. velocity computations could also have contributed to this disadvantage. The seismic image migrated using the procedure of Case 2, however, has a realistic correspondence of layer thicknesses according to their respective velocities. In this study, the image obtained through the methodology of Case 3 (see Figure 4.3) offered better focus compared to both of the time migration images, an expected outcome because the velocity information used in both dernigration and migration steps was three-dimensional and exact. Under CHAPTER 4 RESULTS AND DISCUSSION This chapter presents the results of the experiments conducted with the coherence at­tribute. The study first tested the coherence attribute with respect to different migration 4.1 Migration Versus Coherence This section discusses the analysis of the influence of migration procedures on the coherence attribute response. Using data from the first model only, the analysis generated three seismic images with the different migration procedures (Cases 1-3) reviewed in Subsection 3.1.2. The coherence attribute was then extracted on the three volumes using the same software, the same algorithm, and the same set of input parameters. The study then compared the resulting coherence images of the modeled fault and drew conclusions about the influence of migration methods. The seismic image of Case 1 methodology (Figure 4.1) provides better focus than that of Case 2 methodology (Figure 4.2). A relative lack of clarity in the image of Case 2 is a result of velocity mismatches caused by not taking into account the offsets in the reflectors caused by the fault. The discretization steps in the root mean square of Case 3 (see Figure 4.3) offered better focus compared to both demigration top Kuparuk base Kuparuk 10 8 6 4 2 0 -2 -4 -6 -8 -10 W t W W M ^ 1 " ' A " I I I I I I Figure 4.1. An East-West cross section through the center of the seismic image of Model 1 obtained through Kirchhoff time migration with constant velocity (Case 1). A' Kuparuk base Kuparuk 6 4 2 0 -4 -6 -8 -10 , . , , . i Figure 4.2. An East-West cross section through the center of the seismic image of Model 1 obtained through Kirchhoff time migration with exact velocity (Case 2). A' op Kuparuk base Kuparuk 10 6 4 2 0 -2 -4 -6 -8 -10 i T i i i i l . wmim Figure 4.3. An East-West cross section through the center of the seismic image of Model 1 obtained through depth migration with exact velocity (Case 3). 51 A A' - A top A top .1.0. ...8.. .....6. . .....4" "'" , t " ,,? ,,,1,,,, 1,, -respective Cube suite and a single set of coherence parameters. Figures 4.4, 4.5, and 4.6 illustrate the result of extracting the coherence attribute on the seismic image of Model 1, which were processed using the procedures of Cases 1 through 3, respectively. The location of the cross section is the same in all figures and corresponds to cross section locations in Figures 4.1, 4.2, and 4.3 in the seismic domain. time-1 depth-i,a ••in« i ii • l i m n top Kuparuk base Kuparuk 1256 240 220 200 18C ^ ^ ^ ^ ^ ^ ^ ^ | J U • • 160 140 120 100 80 60 40 0 Figure Model 1, 52 real-world conditions, velocity information cannot be determined . this well, so this last migration method produced the best possible image of the original model. The test extracted the coherence attribute on each of the three migrated volumes. In order to assure an appropriate comparison among the · respecti ve coherence images, the test employed the same extraction method in all three cases using Paradigm's Coherence Modell, The coherence cross sections show visible differences. Although the two time-migration images look similar (Cases and 2), the coherence extracted on the depth-migrated image (Case 3) is sensitive to small discontinuities in the model. The coherence of the depth-migrated seismic image was even sensitive to the stair-step discretization of the model domain that occurred along the dip of the hanging wall. Such high resolution in the depth migration confirmed that this technique was the most prized and focused, given accurate velocity information. This experiment verified that migration methodology does have a profound influence on the coherence attribute. For further experiments with the coherence attribute, this study selected a single migration methodology from the three above. This restriction resulted from the fact that F igure 4.4. An East-West cross section through the center of seismic coherence volume of Modell, originally obtained through Kirchhoff time migration with constant velocity. 53 Figure 4.5. An East-West cross section through the center of seismic coherence volume of Model 1, originally obtained through Kirchhoff time migration with exact velocity. Figure 4.6. West volume of Model 1, originally obtained through depth migration with exact velocity. performing the statistical experiments for each different migration method or for multiple sets of model parameters would quickly become intractable. Those experiments could, perhaps, lend themselves to future research into the coherence attribute. result, Demigrating and migrating with a constant velocity value offered a more focused image than that of Case 2, where root mean square computations had limited accuracy compared to the original interval velocity model. Despite the fact that depth migration (Case 3) 53 Modell, F igure An East-West cross section through the center of the seismic coherence Modell, As a result , the study justified the procedure of Case 1 as the methodology of choice. fo cused provided the most precise image, having the exact three-dimensional velocity model is unusual and conclusions drawn from such experiments would be difficult to relate to real data. The coherence of the seismic image time-migrated with constant velocity did appear to have more artifacts; however, the additional reflectivity above and below the Kuparuk section made this result insignificant for the purposes of analyzing the interval of interest. Another benefit of using constant velocity was the ability to carry out time-depth conversion with a single velocity value. Using time migration with constant velocity eliminated the necessity of modeling density and velocity above the Kuparuk interval as piecewise linear functions. Hence, for further experiments, the study assumed the density and velocity above and below the Kuparuk interval to be constant based on the average values of the density and velocity log data. The interval above the Kuparuk was described with the velocity value of 7905 ft/s and density of 2.3 g/cc. The velocity of the interval below Kuparuk was set to 10168 ft/s and the density in that interval was set to 2.4 g/cc, representative of the average value of the underlying Miluveach shale. 4.2 Noise Versus Coherence This section describes the effect of adding noise to model data. Because it was expected that the effect of noise would be the same regardless of the fault geometry, experiments were conducted only on a single model, the first of the fault geometry models. Figure 4.7 illustrates a center cross section of the noiseless seismic image of this model. The noise present in collected seismic data typically falls into two categories: random noise and coherent noise. This study considered only the addition of random noise because the presence of coherent noise (e.g., multiple reflections, air waves, surface waves, tube waves, and converted waves [28]) can be recognized easily and its influence on coherence taken into account by interpreters. On the other hand, random noise is difficult to estimate in seismic surveys and its influence on the resolution capabilities of the coherence attribute is not well known. Due to the inherent difficulty of estimating noise levels in seismic data and, hence, in the Kuparuk River Fields survey, the study introduced several random noise levels and compared their corresponding coherence attribute volumes. The procedure used the CPS software to add noise with percentages of the maximum absolute value of the amplitudes contained in the seismic volume: 10%, 20%, 30%, 40%, and 50%. 54 time-ftls glee. 10168 ftls glcc, Illodel amplitudes 50%. 55 random Gaussian noise added after time migration. Note that migration, as expected, significantly reduced the contribution of Gaussian random noise. The effect of noise on the coherence attribute is examined further. and very low coherence compared to the coherence image of the cross section of Figure 4.11. On the other hand, areas of continuous reflectivity preserved their character well in both of the coherence images with high noise levels. 55 A ,- A' top Kuparuk - base-K"Uparu ~------------------ 10 8 6 4 2 0 -2 -4 -6 -8 -10 J I I I I I I I I I I I I I I I I I t I I I I I I Figure 4.7. A cross section of the seismic image of fault geometry Model 1. The cross section illustrated is through the center of the model, perpendicular to the fault (Figure 3.13). The workflow created for generating synthetic seismic images provided several points where noise could be introduced. Figure 4.8 illustrates the selected workflow of time migration with constant velocity and possible insertion points. Possibility 1 would add noise to the three-dimensional reflectivity model; possibility 2 would add noise to the time traces prior to time migration; and possibility 3 would add noise to the time-migrated image. The study rejected possibility 1 as unrealistic because it essentially implied perturbations within the original geological model. Figure 4.9 shows a volume with random Gaussian noise added to the time traces. Figure 4.10 displays a volume with In both cases, the coherence attribute experienced significant effects from the added noise. A comparison of the images in Figures 4.11, Figures 4.12, and 4.13 illustrates coherence of the noiseless seismic images and those with the random noise components, respectively. The comparison shows significant disturbances in the areas of no reflectivity This study concentrated on the key comparison showing the effect of the random 56 4.8. migration with constant velocity. Three possible locations are noted within this process where noise can be added. 3D image (in time) 3D reflectivity (in depth) 3D velocity (in depth) .. .. . . .. ' .. . ' ". , ­56 co slant: 7950 IVs , inleNal 'Velocity Figure A diagram of the process of generating a seismic image of a model with time 57 base Kuparuk 10 8 6 4 2 0 -2 -4 f -8 -10 Model 1 50% Model 1, top Kuparuk 10 8 6 4 2 0 -2 ^ - 6 - 8 -10 i i i , i i i i i I , , , 1 4.10. Model 1 Model 1, A A' top Kuparuk 10 8 6 4 2 0 -2 -4 -6 ............ ~~~' I I I I I I I I I I I I I I I I I I I I I I I~I ==~ ...... -8 -10 Figure 4.9. A cross section of the seismic image of fault geometry Modell with 50% noise added to the time traces before they were migrated. The cross section is through the center of Modell, perpendicular to the fault (Figure 3.13). A' 10 8 -4 -6 -8 -10 _ ............e :!::!:...'!.1 t tllllll l llll lll ll, I , !I,:!:::!::!. ...._ _ Figure A cross section of the seismic image of fault geometry Modell with 50% noise added to the time traces after they were migrated. The cross section is through the center of Modell, perpendicular to the fault (Figure 3.13). 58 Model 1 extracted Model 1, Model 1 extracted to the time migration procedure. The cross section is through the center of Model 1, Figure 4.11. A cross section of the coherence image of fault geometry Modell extracted from noiseless seismic volume. The cross section is through the center of Modell, perpendicular to the fault (Figure 3.13). Figure 4.12. A cross section of the coherence image of fault geometry Modell extracted from the seismic volume where 50% noise had been added to the time traces prior Modell, perpendicular to the fault (Figure 3.13). Model 1 Model 1, perpendicular 59 Figure 4.13. A cross section of the coherence image of fault geometry Modell extracted from the seismic volume where 50% noise had been added to the time traces after the time migration procedure. The cross section is through the center of Modell, perpendicular to the fault (Figure 3.13). noise level on the fault signature in the coherence attribute. In order to carry out this examination, the study generated the coherence attribute for all of the noise levels (0 through 50'X) and for both possibilities of noise addition (before and after time migration). To maintain consistency, the test maintained identical input parameters for the coherence algorithm in all 12 cases of coherence extraction. Figure 4.14 shows the coherence signature of the fault for all of the noise levels in the case of adding noise prior to time migration. The time slice was the same for all six images of the fault, 1520 ms. Figure 4.15 illustrates the same for the case of adding noise after time migration. The study concluded from the images shown in these figures that adding random Gaussian noise of up to 50% of the absolute value of the maximum amplitude does not significantly affect the resolution capabilities of the Paradigm's Coherence Cube procedure. Figure 4.14. Time slices at 1520 ms through the six coherence volumes with different noise levels (added prior to time migration). Fault envelope's extent is the same in all six cases, highlighted in green. 60 examina tion, 50%) migration) . inp·ut 4. 15 illustrate-:s the-: same-: noise-: afte-:r time-: migration) . 61 different Figure 4.15. Time slices at 1520 ms through the six coherence volumes with different noise levels (added after time migration). Fault envelope's extent is the same in all six cases, highlighted in green. An adequate assessment of visible features within a seismic volume depends on res­olution, which is defined as the closest distance between two objects at which they are distinguishable as two [34]. As a result, numerous volumes of work address the topic of seismic resolution [11, 12, 21, 30]. This study investigates the resolution of the coherence attribute, a critical property in the process of constructing fault geometry models. The investigation results also provide confidence in the features shown by the coherence attribute. Interpreters use the coherence attribute most frequently for fault picking. The in­terpreter's perspective is considered most important because, regardless of resolution capabilities of the seismic data, what the interpreter sees and outlines is used in the hydrocarbon production workflow. Seismic data commonly distinguish two types of resolution: vertical and horizontal. Typically, vertical resolution represents the thickness of the smallest resolvable deposi-tional unit. Horizontal resolution is typically associated with Fresnel zone dimensions. [35] This study defined the vertical and horizontal resolutions of interest in terms of fault characteristics. The study considered vertical resolution for a fault to be the minimum visible throw. The study considered horizontal resolution measure for a fault to be the minimum distance between two faults at which they are visible as two separate faults. The visibility, again, referred to the interpreter's ability to distinguish it. Testing the coherence attribute on real and model data showed that the resolution of the coherence attribute depends on the specific coherence algorithm and input parameters used. So in this work, the resolution of the coherence attribute also relied on the statistical analysis of the coherence attribute. fault interpretations that would then be evaluated in terms of their spatial relationship to the actual tip line of the modeled fault. The previously described fault geometry Model 1 served this purpose (see Section 3.1.1). Because of the importance of the interpreter's role, an expert interpreter with no prior knowledge of the fault extent or dimensions picked the fault surface. order to address the variability of the coherence attribute, the interpreter completed multiple 62 4.3 Resolution Versus Coherence deposi­tional This study carried out the assessment of the coherence attribute's vertical resolution capabilities with all of the above-mentioned considerations in the following manner. First, the study required a geologic model of a fault with variable throw in order to construct 3.1.1). In r interpretations of the same fault for each of the several coherence volumes provided (see Figure 4.16). From the 10 interpretations provided, the study derived the smallest throw possible to resolve from a coherence volume. The measure of interest here consisted of how close toward the tip line the expert could interpret the fault given the different coherence volumes. The points on the fault interpretations that were farthest away from the center of the model were recorded as inline numbers on both tips of the fault surfaces. These points were converted to feet away from the fault tip and the amount of throw the fault had been set to have at that location in the model. Computations showed this value of throw at 4 ft, which is 1 ft less than the vertical resolution of the model space. Hence, the study concluded from the modeling results that the maximum expected vertical resolution in terms of fault throw visible to an interpreter under conditions similar to those of the Kuparuk River Field's seismic survey matched that of the model grid. The study defined horizontal resolution of the coherence attribute as the smallest distance between two faults at which they become visible as two distinct faults. Model 2 planes of Model 2 was compared to the fault interpretations of the coherence statistical Figure 4.16. Model 1. 10 surfaces corresponding to the 10 expert fault interpretations picked on each of the 10 statistical coherence extractions given. 63 interpretatiolls ::;tudyderived po::;::;iblc "consisted' tt, it Kuparnk was constructed to estimate horizontal resolution. The line of intersection of the two fault experiments carried out by the expert interpreter. This comparison was done for every surface::; time slice in the modeled Kuparuk interval for a total of 18 time slices. Figure 4.17 illustrates expert fault interpretations restricted to a sample time slice. The black square outline marks the location of the true intersection of fault planes at this time slice in the sampling interval of 55 ft. The distance between the different fault interpretations was measured in the crossline and inline directions for every time slice and compared to the crossline-inline coordinates of the true intersection. The study found that the fault interpretations were always within two samples of each other in either crossline or inline directions and also that they were within two samples of the true coordinates of the fault intersection. Most frequently, both of these distances did not exceed a single sample; therefore, the study concluded that the best possible horizontal resolution achievable with the coherence attribute was equal to the horizontal sampling interval of 55 ft. 4.17. statistical given displayed on a single time slice. The time slice here shows one of the coherence volumes in red-blue colormap. 64 interpreta tions 't his ill dIstance t h'e ' iriterpreta tions intersection . t hat interpreta tions t hat t he a t t ribute t he Figure 10 interpretations of the fault intersection of Model 2 corresponding to the 10 expert fault interpretations picked on each of the 10 coherence sta tist ical extractions colormap . Knowing these estimates for the vertical and horizontal resolution capabilities of the coherence attribute added confidence in the features observed in the further modeling results. After creating the first two models and obtaining the estimates of the resolution, the study used them in the design of the other three models to make certain that the features being created would be of the smallest visible scale. 4.4 Model Fault Geometry Versus Coherence This part of the study investigated the coherence attribute response to changing fault geometry in model data. The test was designed to determine if the coherence attribute could detect fault geometry perturbations, such as an intersection with another fault, existence of accompanying smaller faults, or a relay zone. The study designed the fault models (see Subsection 3.1.1) so that the perturbations in fault geometry existed at the minimum resolvable scale with respect to interpreters' perspective (see Section 4.3). These fault geometry perturbations are difficult to identify in seismic cross sections. An interpretation of cross sections through these subtle features (see Figures 4.18 and 4.19) would typically yield only a single through-going fault. Hence, this study evaluated detection capabilities of the coherence attribute with respect to these features through the sampling of the coherence volume surrounding typical interpretations. To imitate a single through-going interpreted fault surface, a plane trending NS and dipping 55 degrees to the east was placed at the center of each seismically imaged model. The main NS faults of all models were then contained within this plane. For example, in Model 2 such a plane included the NS-trending fault in the northern half of the model, an intersection of two faults in the center, and passed through a zone of continuous reflectivity in the southern half . Sampling the coherence volume surrounding this plane as described in Section 3.2.1 involved introducing linear segments across it (see Figure 4.20, bottom left). The horizontal spacing between these linear segments was one sample (55 ft) and vertical spacing was equal to one time sample (4 ms). Statistical measures computed along these linear segments were visualized at the centers of the linear segments as spheres colorrnapped according to their relative values. For example, the bottom right image of Figure 4.20 illustrates the statistical means computed at each of the linear segments sampling the coherence volume. The study used SCIRun[6] computational workbench environment to implement and visualize the sampling methodology. 65 fault, perturbations features 1.'\S half. colormapped methodology. Scisir.ic 10 Figure 4.18. Fault geometry models 1 and 5. Left: An East-West cross section through the seismic image of Model 1 at the point where fault throw is 100 ft. Right: An East-West cross section through the seismic image of Model 5 at the center of the model, through the relay zone. 66 Modell ModelS Colormap for Seisnf c Data -to JO 4 .18 . Left : West Modell ft . East-?'one. Model 2 Model 3 - Model 4 Colormap 10 cross section through the seismic image of Model 4 at the center of the model, through the relay zone where small faulting at the A-units occurs. 67 Modcl2 - Modcl3 - Modcl4 Coiormap for Seismic Data -10 to Figure 4.19. Fault geometry models 2, 3, 4. Left: An East-West cross section through the seismic image of Model 2 across the fault of constant throw of 30 ft. Center: An East-West cross section through the seismic image of Model 3 at the center of the model, through the zone where small faulting at the top Kuparuk occurs. Right: An East-West Figure 4.20. Sampling the coherence volume surrounding the WNW fault of Model 2. Top Left: A view of Model 2 with a transparent seismic cross section at inline 92 and coherence time slice at base Kuparuk level. Top Right: Colormaps used for the data renderings. Second Row Right A view of Model 2 with a seismic cross section at inline 100(center) and coherence time slice at base Kuparuk level. Second Row Left A view of Model 2 with a coherence cross section at inline 100(center) and coherence time slice at base Kuparuk level. Bottom Row Right A zoomed in view of the figure directly above. Coherence around the fault surface is sampled with a linear segment placed across it. Bottom Row Left The same view as the figure to the right amended with a sphere displayed at the center of the linear segment sampling coherence and colormapped according to the statistical mean of coherence along that linear segment. view coherence Coiorrnap for 0 Colormap for -10 Coiormap for 190 68 255 10 255 .. Left : Right : iieiiilllic CW iiii iiection center ) 100 ( center ) fault. segment. Bot tom segment . 69 co­herence procedure described in Section 3.2 to compute the coherence attribute; Figures 4.21, 4.22, 4.23, 4.24, and 4.25 illustrate several time slices through the resulting volumes. example, Figure 4.26 illustrates computed statistical means for four different coherence volumes of Model 4. The statistical parameters were summarized further with the extraction of their minimum, maximum, range, and mean. Using the example of Figure 4.26, the statistical means computed for the set of four different coherence volumes could be summarized by assigning either the minimum, the maximum, the range, or the mean of the four means to each of the linear segments sampling the fault (see Figure 4.27). then assembled with entries ranking the summaries of the statistical parameters with respect to the five models (see Table 4.1). highest rank sum of 4.6 corresponds to the minimum of means. This result makes sense as the minimum of means can also be thought of as measuring the minimum coherence, which is the maximum discontinuity. The study concluded that the minimum of means must be the most robust statistical parameter summary, so minimum of means was the The modeled fault geometry heterogeneities were designed to be visible via the co­herence attribute; however, not every coherence extraction results in a volume where that is the case. Hence, the study adopted the Monte Carlo-based statistical experiments cohereilce 4.21,4.22, The study sampled coherence volumes generated via the coherence statistical ex­periments procedure and extracted statistical measures along each linear segment. For The images clearly show not only variation in the fault geometry detection capabilities among the statistical means (compare images on the top left vs. top right of Figure 4.26), but also that not all of the four summary parameters provide an equally good correspondence to fault geometry (compare images on the top left and top right of Figure 4.27). In order to assess the quality of correspondence to fault geometry changes, the summary images of all five models were compared to the underlying fault geometries and ranked. The ranks were assigned on a scale from 1 to 5, 1 meaning poor correspondence to modeled fault geometry and 5 indicating excellent correspondence to fault geometry. An experienced geophysicist in the field of seismic interpretation, Jennifer Thompson, together with the author of this thesis applied the rankings to the images. A table was Table 4.1 can serve as a guide to selecting statistical parameter summaries with respect to features of interest. The same table also enables the selection of a single statistical summary that best illustrates all five fault geometries of interest. This selection was based on the average of ranks within each of the 16 columns and choosing the highest. The 70 Experiment 1 Experiment 2 Statistical Statistical t I j Coherence [} Model I view at 1540 ms Six statistical coherence experiments carried out for Model 1. The results of these experiments are compared at 1540 ms time slice. Statistical Statistical Statistical Statistical Statlstical Statlstical Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5 Experiment 6 Colormap for CDherence Data o 255 Modell view . at 1540 ms 70 Figure 4.21. 71 Statistical 1 Statistical Experiment Statistical Statistical Statistical Statistical [ 1 4k Six statistical coherence experiments (tarried out for Model 2. The results of these experiments are compared at 1540 ms time slice. Experiment 1 Experimenr 2 Experiment 3 Experiment -4 Experiment 5 . Experiment 6 Colormap for Coherence Data I o 255 Model 2 view at 1540ms N Figure 4.22. st atistical carripd t hese ar e 72 Experiment 1 Statistical Experiment 2 Statistical Experiment 3 Statistical Experiment 4 t Colormap 0 Model 3 Figure 4.23. Six statistical coherence experiments carried out for Model 3. The results of these experiments are compared at 1532 ms time slice. Statistical Colomlap for Coherence Data o 255 Statistical Statistical Experiment 5 Experiment 6 view at 1532 ms 4.23 . t hese 73 Statistical Experiment Statistical Experiment Statistical Experiment 3 Statistical Experiment 4 Statistical Experiment 5 Statistical Experiment 6 Model 4 view ^ at 1572 ms A r - - - N ! • 1 -* 1 » 1J _ 1 \ Figure 4.24. Six statistical coherence experiments carried out for Model 4. The results of these experiments are compared at 1572 ms time slice. Statistic at Statistic at Ex erirnent 1 Ex rirnent 2 Colormap for Coherence Data o 255 1572ms Mortel t hese 74 Experiment i I - Colorniap Model 5 A view 15*8ms Figure 4.25. Six statistical coherence experiments carried out for Model 5. The results of these experiments are compared at 1548 ms time slice. Statistical Statistical Statistical Statistical Statistical Statistical Experiment 1 Experiment 2 Experilllent 3 Experiment 4 Experiment 5 Experiment 6 Colormap for Coherence Data I o 255 Model5 , N view __ ..--P: ;. ~ ."', ',~ at 1548 ms \ . _ i~ __ A 4.25 . t hese a t 75 the cross through the center of the model, coherence is extracted on the time slice at 1536 ms. The four different extractions of coherence have been used to compute the mean along the sampling linear segments. Colormap for -10 10 Colormap for 190 255 Figure 4.26. Model 4, view from t he North-East. The East-West seismic crO:';8 line runs t he 76 Figure 4.27. Summary computations for the means of Figure 4.26. Top Left: Minimum of statistical means. Top right: Maximum of statistical means. Bottom Left: Range of statistical means. Bottom right: Mean of statistical means. range of means 4 coherence volumes Colormap for o Colormap for Seismic Data -10 190 255 10 255 76 Left : i;tatisti<:al st atistical meani;. Left : Bot tom stati stical able 1 ^he of corres pondence changes Mean min max mean Model 1 5 1 4 1 1 1 3 5 1 1 2 Model 2 4 4 1 4 1 3 1 1 4 1 1 1 Model 3 5 2 2 2 2 4 4 5 3 3 5 1 4 1 4 1 5 2 5 5 5 3 5 3 5 2 3 2 2 3 2 Average 4.6 3.8 3.6 3.6 3 2.8 4 2 2.6 2.4 3.6 2.8 2.4 . ^ 1 - I Table 4.1. The table ranks the quality of correspondence to fault geometry changes. Model Standard Deviation Skewness Kurtosis min max range mean lnax range lnean min max range mean min max range mean Modell 4 4 4 2 4 5 3 4 3 1, 5 5 4 3 3 Model 4 5 5 5 3 5 1 4 Model 5 4 4 4 4 3 II I 3.8 2.2 I 3 I ' summary applied to the Kuparuk River Field in the subsequent section. To examine the behavior of the statistical coherence extractions, the study used the methodology of Section 3.2.2. Convergence estimate values, such as those plotted in Figure 3.34, were depicted on the fault surfaces in the same way the statistical parameters were in Figure 4.26. Figures 4.28, 4.29, 4.30, 4.28, and 4.32 illustrate the convergence behavior for all five of the fault geometry models. The more blue the values are, the smaller the effect of adding more statistical coherence extractions on the particular statistical parameter. An overwhelming majority of the fault surfaces displayed in these figures are blue and white, which leads to an assessment of the behavior of the coherence statistical experiments as overall convergent. limitations resolve small linear segments placed at every seismic sample, the fault intersection was clearly visible (see Figure 4.33). On the other hand, when the linear segments sampling the coherence envelope were placed at the vertices of the triangles representing an interpreted fault surface, the fault intersection feature could no longer be distinguished (see Figure 4.34). The linear segments in this case are simply too far apart to detect the coherence space affected by the fault intersection. Of course, an obvious solution to this problem could be to add more linear segments to the fault surface. Pursuing this path, however, is not feasible at this time as the computational resources that would be required for processing significantly more linear segments would greatly exceed those typically available for geophysicists at this time. It is intended to pursue recognition and better imaging of fault intersections and other small scale features as part of the future research for this project via optimizing the algorithms involved and sampling areas of interest more densely. 4.5 Real Fault Geometry Versus Coherence study differed for different fault geometries in real data, specifically in the Kuparuk River Field. In order to accomplish this, the signature was tested to determine whether visibly different fault geometries were still visibly different in the renderings of their statistical coherence extraction results. The study previously distinguished several fault geometry styles in the Kuparuk River 78 parameters convergence particular a;,; One of the limitation;,; of the developed technique is resolution. At this time it is not always possible to re;,;olve ;,;mall scale features, such as fault intersections. For example, consider Model 2. When coherence along the N-S fault of Model 2 was sampled with ;,;egments inter;,;ection (;,;ee segment;,; ;,;arnpling repre;,;enting di;,;tingui;,;hed (;,;ee ;,;pace i;,; This section of the ;,;tudy investigated whether the signature of the coherence attribute Figure 4.28. 1. estimates the locations the sampled. convergence of mean convergence of skewness Colormap for \ h P l'P n{',. Data o 255 Coiormap for Seismic Data -10 Colormap for Convergence convergent -4 4 10 convergence of standard deviation Kuparuk b ase, top Kuparuk 79 Model L Convergence e~timates plotted along t he main fault at locatiolls where t he coherence had been sampled. 80 convergence of mean Colormap Coherence Data 0 Colormap Seismic Data -10 convergi convergence of standard deviation convergence / of kurtosis NS fault surface estimates convergence of skewness Colonnap for o 255 Colomlap for Colormap for Convergence convergent -4 4 10 Figure 4.29. Model 2. Convergence estima tes plotted along the main fault at locations where the coherence had been sampled. 81 convergent -4 4 sampled. convergence of skewness Colormap for o 255 Colormap for -10 Colormap for Convergence convergeat 10 convergence of kurtosis Figure 4.30. Model 3. Convergence estimates plotted along the main fault at locations where the coherence had been sampled . 82 - converge -4 locations where the coherence had been sampled. convergence of skewness Colormap for o Colormap for Seismic Data ·10 Colormap for Convergence 255 10 convergent ·4 Kuparuk surface Figure 4.31. Model 4. Convergence estimates plotted along the main fault at locat ions sampled . o 255 Colormap for -10 Colormap for Convergence convergent -4 4 10 83 Figure 4.32. Model 5. Convergence estimates plotted along the main fault at locations where the coherence had heen sampled. 4.33. Model segments placed at every seismic sample. The fault intersection feature is clearly visible in green and blue in contrast to the orange colored fault surface. 84 ColOfmap 101 S 'smic Data -10 10 0 255 192 255 Figure 4.33 . yIodel 2. Statistical mean measured along the N-S fault using linear pla<.:eJ seisrni <.: intersedion d early cont rast 85 Figure 4.34. Model 2, two fault interpretations. The N-S fault is displayed as a black wireframe, the second fault is displayed as a triangulated surface colored by the statistical mean values of the coherence attribute, measured using the linear segments placed at vertices of t h e triangles representing the fault surface. The statistical mean measure does not show a distinguishable feature at the location of the faults' intersection. COiormap tor Seismic Data 10 192 255 inline 80 lop Kuparuk peak triangulat ed the intersection . 86 Field (see Section 2.3). The two most easily distinguishable fault styles typically corre­sponded to the two different fault orientations observed in this field. The WNW-trending faults frequently have a sharp break at the base of the Kuparuk section and transition toward more of a fold-like character at the top. The N-trending faults often have the opposite geometry with a sharp offset and large throw at the top of the Kuparuk section instead. Seismic d a t a reveal these differences in fault geometry quite clearly. For example, Figure 4.35 illustrates a seismic cross section of a N-trending fault interpreted in cyan. This fault has a sharp break in reflectivity at the t o p Kuparuk horizon and smaller breaks at the base. Figure 4.36 illustrates a seismic cross section through a WNW-trending fault interpreted in blue. At the location of this fault, the reflectivity at the top Kuparuk horizon is fairly continuous, albeit changing dip. A clearly visible sharp reflectivity break is positioned at the base Kuparuk horizon. A careful examination of existing fault interpretations in the pad 1A volume of the Kuparuk River Field insured they were representative of the two styles and 20 of them (10 WNW-trending and 10 N-trending) were selected for the purposes of this experiment. Fault 14 (NS) top 4.35. Fault 14, trending North-South displayed on a seismic cross section. A sample coherence volume is co-rendered with the seismic volume onto the seismic cross section as well as used for the colormapping on the top and base Kuparuk. 2.3) . fi eld. WNW-'i t top, N:treiiding instead, data cyan . top trending fault Kuparuk reflectivity trending lOp Kuparuk base Kuparuk Figure Kuparuk. Fault 23 (WNW) 4.36. Fault trending WNW displayed on a seismic cross section. A sample coherence volume is co-rendered with the seismic volume onto the seismic cross section as well as used for the colormapping on the top and base Kuparuk. As in the previous section, the study carried out the coherence statistical experiments on the seismic volume of the area of interest in the Kuparuk River Field. The linear segments sampling the generated coherence volumes were placed along the 20 interpreted surfaces corresponding to the selected faults. The locations of the linear segments were determined by the triangulation of the surfaces as they were placed at the vertices of the triangles, normally to the surface (see Figure 4.37). The results of the statistical experiments were presented in the form of minimum of means, similarly to those for Model 4 in Figure 4.27 (top left), except that here the minimum of means was colormapped onto the triangulated interpreted surface instead of being displayed as colormapped spheres at central locations of the linear samples. Figure 4.38 displays the rendering of the minimum of means for Fault 14 and Figure 4.39 shows the rendering of the minimum of means for Fault 23. Figure 4.38 shows clearly that the minimum of means is consistently lower at the top of the Kuparuk section compared to the base. This distribution matched the fault geometry observed in the seismic data for this fault - a large, sharp discontinuity at the top and numerous small discontinuities at the base. Consider a fault of the second style. Fault number 23 is a WNW-trending fault; Figure 4.39 provides a rendering of its base Kuparuk Fauit23 -(WNW). 87 Figure 23, Kuparuk. t he t he genera ted t riangles, 4.37) . st atistical left) , her e colorrnapped minimum consist ently Kuparnk t his fa ult trending Figure 4.37. An example of sampling the coherence envelope around an interpreted fault surface within the pad 1A area of the Kuparuk River Field seismic survey. Colormap for Seismic Data Colormap for Coherence Data o 255 88 interpret ed lA 89 Colormap for r... l inimum of Means o 255 Figure 4.38. Fault 14, trending North-South displayed with transparent top and base Kuparuk horizons. The colormapping of the fault corresponds to the minimum of means of the coherence statistical experiments. Figure 4.39. Kuparuk Colormap for Minimum of Means a 255 90 Coiormap for -10 10 Fault 23, trending WNW displayed with transparent top and base Kuparuk horizons. The colormapping of the fault corresponds to the minimum of means of the coherence statistical experiments. 91 minimum of statistical means. For this fault, the distribution of t h e minimum of means is the opposite of that shown in Figure 4.38; the discontinuity at the top of the reservoir appears to be consistently more coherent compared to t h e base. The same correspondence was determined for the 18 other faults selected from the area of study. Figure 4.40 shows a cumulative rendering of their minimum of means. These observations confirmed that the coherence a t t r i b u t e does respond differently to different fault geometries in real data tests. Using the methodology presented in this work, it is now possible to highlight regions of potentially different fault geometries along interpreted fault surfaces. Even though the study confirmed that the two fault styles are clearly distinguishable through the analysis of statistical coherence experiments, it also revealed significant Figure 4.40. Fault 23, trending WNW displayed with transparent top and base Kuparuk horizons. The colormapping of the fault corresponds to the minimum of means of the coherence statistical experiments. the minimuni the correspondence cumula tive attribute rlifferent significant Colormap for Minimum of Means Colormap for o 255 -10 10 Kuparuk the minimum faults present at a particular subsurface location, can be discerned from core data and/or well data. Even though such data are available for the Kuparuk River Field, there are a number of difficulties associated with using those for validation purposes. One such issue is that both well and core data are in depth and seismic and coherence data are in time. A careful velocity analysis must be carried out in order to achieve a reliable correspondence. The process of velocity analysis, selecting appropriate wells, core data, and doing the comparisons is a project on its own and is intended to be carried out as part of the future research in close collaboration with the team developing with Kuparuk Field. A validation of fault geometry predictions via drilling new wells is also intended. 92 variability in fault geometry even along single fault surfaces. This observation suggests that the two fault styles offer inadequate descriptions of the variability in fault geometry in the Kuparuk River Field and that much greater faulting complexity is present. There are other ways to validate fhe correspondence of the minimum' of means to fault geometry. For example, aspects of fault geometry, such as the number of faults Kuparuk Even though the influence of fault geometry on this attribute was the primary of coherence. The research confirmed the importance of migration in obtaining focused images of faulting, and that the accuracy of available velocity information is key in doing so. The study found that random Gaussian noise of up to 50% of the absolute value of the maximum amplitude has little impact on the coherence attribute's appearance. The study established resolution capabilities of the coherence attribute to match the model grid. Hence in the case of the dataset being studied, the size of visible small-scale features was on the order of the sample spacing of the seismic data. The most significant finding of this work was that the coherence attribute consistently responded differently to different fault geometries in model and real data. The ability of a coherence volume to distinguish between different fault geometries depended on the input parameters used to generate it as well as on the frequency of sampling of the coherence envelope around the fault of interest. Statistical analysis of the coherence attribute proved to be a practical and rigorous method in recognizing variability in fault geometry. It would take numerous hours to arrive at the same answer using the conventional approach of examining seismic and coherence data. geometries are easily recognized on the given surfaces. When a fault is interpreted and visualized as a surface in three dimensions using traditional seismic interpretation software, it lacks any information about possible heterogeneities along it with respect to seismic data much less with respect to any geological characteristics. One currently known methodology that addresses this problem involves mapping seismic attributes onto interpreted fault surfaces. This approach produces three shortcomings. First, any CHAPTER 5 CONCLUSIONS AND FUTURE WORK The study investigated the seismic coherence attribute response from multiple per­spectives. objective of the research, the study also explored the effect of other processes on the ap­pearance features distinguish generate As its main contribution this research created a workflow that derives a geophysical attribute for existing fault interpretations such that regions of potentially different fault interpreted currently sensitive representation of the features. Third, even though geophysical attributes are implied to have correspondence to geological properties, researchers have not established such ties formally, so a rendering of any seismic attribute does not carry information formally correlated with geological properties. The workflow developed in this study introduced a sampling methodology that does not restrict sampling of an attribute to the surface of the fault. By also employing statistical experiments that include several versions of the attribute of interest in the analysis, the workflow makes the result robust with respect to interpreters' bias and saves interpretation and testing time. The result is an attribute proven to correlate to fault geometry. With the developed workflow, scientists can quickly and robustly render a visualization that recognizes regions of potentially different fault geometry along interpreted fault surfaces. visibility. Of course, a significant addition to this research would consist of conducting a similar study on a different subsurface dataset and comparing the findings. 94 . . colormapping of a geophysical attribute onto an interpreted fault surface will be biased by the exact placement of the surface and any imprecisely interpreted areas will suffer from lack of illustrating proper attribute response. Second, geophysical attributes, such as the coherence attribute, are often sensItive to the algorithm or input parameters used to compute them; hence, a poor choice of algorithm or input parameters may result in a poor Numerous paths exist for future research in the direction of this study. Perhaps the most significant is establishing a quantitative correlation of the coherence attribute to fault geometry and the possibility of using that information to produce detailed subsurface fault geometry interpretations. Another interesting undertaking could be carrying out the same type of statistical experiment analysis for other geophysical attributes such as curvature. At the forward modeling stages of this research, one could experiment with different model resolutions and investigate the visibility of features below seismic Paradigm EP0S3: Data Sharing and Application Interoperability Framework. 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