L2 norm-constrained adaptive edge preservation filter inversion of exact Zoeppritz equation

Abstract

Since traditional pre-stack inversion via amplitude variation with offset (AVO) uses an approximate formula, it is insufficiently accurate at large angles. To overcome this shortcoming, we used the exact Zoeppritz equation for nonlinear AVO inversion. A second-order difference matrix is ​​added to suppress the disturbance of the inversion in the case of noise.We used an adaptive edge preservation (Ad-EPS) filter to process the iterative model. An Ad-EPS filter can find the optimal window size for each filtered sample so that the formation boundary is sharper and more accurate in the inversion. For nonlinear optimization problems, we used the Levenberg–Marquardt method. The LM method adds a damping factor to the iterative equation to reduce the ill-posedness of the inversion and can add a second-order-difference L2-norm-regularization term directly to the algorithm to make the inversion data closer to the model data. The LM method combines the exact Zoeppritz equation, L2 regularization constraints, and Ad-EPS filter into a nonlinear AVO inversion method called EZL2AEPS. The EZL2AEPS method is more accurate than the generally accurate Zoeppritz pre-stack inversion (EZPI) with respect to details such as formation boundaries and overall disturbances. The EZL2AEPS method can also suppress noise to a certain extent, reduce the effect of noise disturbance on the inversion, and produce blocky inversion results. Actual data show that the EZL2AEPS method achieves better inversion results and is a very advantageous AVO inversion method.