Amplitude variation with angle inversion using the exact Zoeppritz equations — Theory and methodology

To overcome the weaknesses of conventional prestack amplitude variation with angle inversion based on various linear or quasi-linear approximations, we have conducted a nonlinear inversion method using the exact Zoeppritz matrix (EZAI). However, the inversion using the exact Zoeppritz matrix was highly nonlinear and often unstable, if not properly treated. To tackle these issues, we have used an iteratively regularizing Levenberg-Marquardt scheme (IRLM), which regularizes the inversion problem within an algorithm that minimizes the misfit between the observed and the modeled data at the same time by incorporating the Tikhonov regularization method. As a result, the new EZAI method solved using the IRLM scheme is feasible for seismic data sets with large incidence angles, even up to or beyond the critical angle as well as strong parameter contrasts. Single and multilayered synthetic examples were used to test these features. These tests also showed that EZAI is robust on noisy gathers for parameter extraction and has weak dependence on the initial model. For the influence of inaccurate amplitudes, dominant frequencies, and phase angles, we found that EZAI is less sensitive to the variation in amplitude and phase shifts than to the dominant frequencies. Specifically, the inversion results of EZAI for P- and S-wave velocities and density were reliable if the inaccurate range for the amplitude was within 20% or the angle of the phase shift was no more than 20°. The superiority of EZAI makes it a very promising method for the estimation of subsurface elastic parameters.