Elastic modulus extraction based on generalized pre-stack PP–PS joint linear inversion

Joint PP–PS inversion offers better accuracy and resolution than conventional P-wave inversion. P- and S-wave elastic moduli determined through data inversions are key parameters for reservoir evaluation and fluid characterization. In this paper, starting with the exact Zoeppritz equation that relates P- and S-wave moduli, a coefficient that describes the reflections of P- and converted waves is established. This method effectively avoids error introduced by approximations or indirect calculations, thus improving the accuracy of the inversion results. Considering that the inversion problem is ill-posed and that the forward operator is nonlinear, prior constraints on the model parameters and modified low-frequency constraints are also introduced to the objective function to make the problem more tractable. This modified objective function is solved over many iterations to continuously optimize the background values of the velocity ratio, which increases the stability of the inversion process. Tests of various models show that the method effectively improves the accuracy and stability of extracting P and S-wave moduli from underdetermined data. This method can be applied to provide inferences for reservoir exploration and fluid extraction.