Practical seismic inversion
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Seismic data contain information regarding the phase and amplitude of reflected events. Variations in amplitude, traveltime, and waveform as a function of offset are controlled by changes in the subsurface elastic properties. Analysis of prestack seismic data provides the opportunity to distinguish between changes in compressional-wave velocity, shear-wave velocity, and density, in the context of an isotropic, locally one-dimensional earth. A practical approach to prestack seismic inversion is developed and applied to a portion of a real data set. As a data preprocessing step, a predictive deconvolution algorithm is devised which incorporates the angle, time, and spatial dependence of the reverberation period into the deconvolution operator. An impedance model is obtained by use of a matched filter which represents the data as a superposition of simple-interface and thin-layer reflections. The inversion results are used to substantiate a modification to the statistically estimated seismic wavelet for a nonwhite reflectivity spectrum. One-dimensional velocity estimation is cast as a linear inverse problem. An initial velocity model, which is parameterized as a superposition of cubic B-splines, is adjusted to account for the residual moveout of selected events. The velocity analysis is fully automated. Residual moveout estimates are obtained implicitly without picking, and the resulting velocity function is guaranteed to be smooth. Primaries-only ray tracing, in which the linearized approximation to the Zoeppritz equations describes the reflection coefficients, serves as the forward modeling algorithm. The linear prestack inversion is based on the three-term linearized approximation to the Zoeppritz equations. This expression is reformulated so that one term incorporates the apriori relationships between the elastic properties and the other two represent perturbations from the apriori assumptions. Effects of thin layering, the seismic wavelet, and normal moveout stretch are incorporated into the Frechet derivatives. A single-iterate maximum-likelihood solution estimates the model parameter perturbations relative to the smooth starting model. Real data results illustrate the importance of a judicious selection of the data and model covariance matrices. Known hydrocarbon accumulations are detected as perturbations relative to the apriori assumptions.