Zeoppritz-based joint AVO inversion of PP and PS waves in Ray parameter domain

Abstract

Reflected and transmitted angle are important parameters for joint PP and PS AVO inversion in angle domain whether based on approximation formula or exact Zeopppritz equation. But the precision of angle derived from ray trace is depended on velocity model. This paper makes efforts to explore nonlinear simultaneous PP and PS inversion in ray parameter domain. The method uses the exact Zoeppritz equations rewritten as the function of four independent ratios parameters and ray parameter to invert the ratio of density, P-wave velocity and S-wave velocity and P-wave velocity using the PP and PS plane wave reflection coefficients. For alone PP and PS inversion, the values of least-square objective function don't converge around a large neighborhood of chosen true model parameters. Fortunately for joint PP and PS inversion the values of the least-square objective function show closed contours with single minima. According to Snell's law, the reflection coefficient formula actually involves four different angle, incident and transmitted angle of P wave, reflected and transmitted angle of S wave. To have better AVO inversion, all four angle must be correct, which is impossible in fact. However the ray path is characterized by the ray parameter p, which is a constant along the same ray. The ray parameter p is derivatives of travel time with