Linear equations relate small changes in rock properties across an interface to seismic reflectivity (Aki and Richards, 1980). These equations for P-wave and P-SV wave reflectivity can be inverted exactly or in a least-squares sense to provide estimates of relative changes in density, P-wave velocity and SV-wave velocity. By using two observations (P and P-SV reflectivity), this inversion promises better rock property estimates. Based on synthetic seismic data, an error analysis is performed on this joint P and P-SV inversion method. Two steps are taken in this inversion. First, a least squares adjustment is applied to the joint P and P-SV inversion to estimate relative changes in P - wave and SV -wave velocity across an interface. Second, to update the actual P - wave and S - wave velocities from the relative changes, the generalized linear inversion is used. Effects of systematic error and random error in both velocity and reflectivity on the inversion velocity structures are analyzed. Compared with the conventional method (using only P-P reflectivity), the joint P-P and P-SV inversion gives more reliable results for S - wave velocity, especially in the presence of noise in the reflectivities.
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