Pre‐stack inversion: Sensitivity analysis of the linearized reflection coefficients vs. KnottZoeppritz's equations

Abstract

A question arises when we attempt to do pre-stack seismic inversion; “what should we invert for?“. Naturally Pand Swave velocities and the density are the first things that come to an exploration geophysicist’s mind. Seismic amplitudes as a function of offset contain varying information on the elastic parameters of the geologic layers. Moreover the elastic parameters and velocities are described in terms of each other. For example, the S-wave propagation velocity can be given in terms of shear wave modulus and density. The selection of any of the three unknowns is somewhat arbitrary. We did sensitivity analysis with both the linearized and full Knott-Zoeppritz reflectivity model using different elastic parameter sets to show the effects of parameter choice. We show that acoustic velocities and density are not the appropriate parameters to solve for in non-linear inverse problem, i.e., pre-stack seismic inversion. The results of this study indicates that acoustic impedances (Pand S-wave) are the parameters to estimate. We will give examples by doing global inversion using the Very Fast Simulated Annealing (VFSA) method to support our conclusions. These examples show that inversion run-time can be reduced significantly by choosing right parameters and right reflectivity model.