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Show 9 {2.5) {2.6) {2.7) and Hooke's Law of elasticity provides the following expressions for the corresponding stresses : {2.8) (2.9) (2.10) ( au av) Txy = Tyx = fl ay + ax ' (2.11) ( au ow) Txz = Tzx = fl az + ax , (2.12) (ov ow) Tyz = Tzy = fl az + ay {2.13) These nine equations are referred to a.5 The Elastic Wave Equation. A full derivation of the above equations is presented in Telford et al. [17, pp. 222-229]. This reference also contains detailed descriptions and definitions for many of the seismological terms used later in this manuscript such a.5 P-wave velocity, S-wave velocity, Poisson's ratio, seismogram, and seismic section. 2.3 Staggered Grid Formulation For a staggered grid formulation of the above equations, one needs to determine the appropriate locations where each of the displacement and stress components should be de-fined in order to satisfy the fourth-order formulation for each of the stress and displacement |
