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By Mrinal K. Sen

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We note here that much seismic data analysis is done assuming an isotropic Earth model and, unless otherwise stated, we will restrict all of our discussions within this text to isotropic media. , Thomsen 1986) but the discussion of such a vast and growing discipline is beyond the scope of this text. 2 Equation of Motion In the definitions of stress and strain tensors, we consider a cubic element in the medium to he bounded by faces that are parallel to the three coordinate planes in a Cartesian axis system (Fig.

As shown in Fig. 7, the reflection and transmission of P- and S-waves satisfy Snell's law such that The above equations clearly demonstrate that the angle made by the incident P-wave ray is the same as the angle made by the reflected P-wave ray in the upper layer. In addition to changes in the direction of the ray path, the amplitudes of the reflected and transmitted P- and S-waves are also expected to exhibit changes. because of partitioning of energy at the interface. The reflection and transmission coefficients of PP and PS waves, denoted by Rpp, Rps, Tpp, and Tps, measure the amplitudes of reflected and transmitted P- and S-waves because of an incident plane wave of unit amplitude.

Amplitude variation with offset. Inverse Theory 51 ITERATIVE FORWARD MODELING Fig. 2—In a model-based inversion scheme, model parameters are estimated by iterative forward modeling. Fig. 3—Because of inaccuracies in the data and inadequate forward modeling, an inversion requires estimation of model parameters as well as uncertainties. 52 Seismic Inversion Reservoir Engineering • History matching. • Pressure transient analysis. Medical Imaging • Transmission computed tomography (CT). • Emission computer tomography (SPECT—single photon emission computerized tomography; PET—positron emission tomography).

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