| Description |
The research reported herein is divided into four chapters which introduce new ideas in modeling electric and electromagnetic geophysical data The first chapter has to do with inversion to a plane-layered earth model of 120 Schlumberger resistivity soundings made as part of a tydrogeological study in the Apodi Valley in the state of Rio Grande do Norte, in Brazil. The soundings were conducted primarily to map the thicknesses of a known alluvial aquifer and of a potential sandstone aquifer. These Thicknesses have been determined to within an error of 20% as estimated from the ridge regression inversion statistical analysis and from the available drill hole information. The inversion costs are very low, mainly because the forward solutions were obtained through the fast digital filter algorithm. The increase in speed and accuracy in the evaluation of the forward problem has also allowed calculation of the Schlumberger apparent resistivity from potential differences, instead of the electric field. Consequently there is no difficulty in the interpretation of data where large receiver electrode (MN) spacing has been used or where discontinuities have been introduced by changing the MN spacing on a layered-earth model containing large resistivity contrasts. Chapter two discusses a single modular finite element algorithm capable of treating four different problems of two-dimensional symmetry in electromagnetic geophysical theory. Two-dimensional steady state groundwater and heat flow problems associated with three-dimensional sources or sinks can be treated by the same modular finite element approach. By using a simple but illustrative example I document that the finite element method, finite difference and network analysis methods are computationally equivalent modeling techniques. Chapter three explores the flexibility of the finite element software developed in Chapter two, in modeling topographic effects of hill, valley and slope on the dipole-dipole induced-polarization and resistivity pseudosections of conductive and polarizable bodies. We have found that a hill produces a resistivity high, a valley produces a resistivity low and a slope produces an asymmetric resistivity pseudosection, with a resistivity low under the base of the slope and a resistivity high on the top of the slope. Practically no topograhic effects are seen in the induced polarization results. Chapter four presents for the first time a guideline for multispectral electromagnetic interpretation of two-dimensional geologic structures using a plane wave finite element modeling. The distribution of electric current within the earth furnishes an explanation of why broad-band ellipticity data develop fluctuations and sign reversals, much important information about the model parameters may be determined. |
