General Elastic Inversion, Orange Basin Case Study
Authors: Berge T.B. 
Published: October 2008

Abstract
General Elastic Inversion is a specific inversion process that is designed to combine both ?Vp (pseudo compressional interval velocity) and ?Vs (pseudo shear interval velocity) volumes in a straightforward and meaningful way to emphasize pore fluid type. The calibrated results are simple and values nonarbitrary. Good data seismic quality and high fold are preferred, and a good quality dipole sonic curve from an area well can be used for calibration but is not required.
In essence the process has 2 steps and proper execution of both is required to get good results. The first step is generation of the ?Vs and ?Vp volumes and the second step is the combination and re-projection of the ?Vp and ?Vs volumes.
A critical step is generation of the ?Vs volume which must be done in the pre-stack domain. The objective is to estimate converted-wave shear amplitude at different offset angles. On problem is that some methods result in only a linear transform of the P-wave amplitudes which will not produce a separation of gas and water cases in the P and S crossplot domain. We present a rigorous 'full Zoeppritz' solution involving ray-tracing that provides meaningful, nonlinear calculation of what the converted shear-wave amplitudes by offset would have been had they been recorded. In essence, the S wave AVO is modeled.
Secondly the P and S reflectivity volumes are inverted, scaled to pseudo-velocity, and then calibrated to well control. The resulting ?Vp and ?Vs volumes are combined and reprojected to produce a 'fluid' volume and a 'porosity' volume. The process is simple enough in concept that we propose it as a general solution to Elastic Inversion. Like the Fluid Factor (Smith and Gidlow, 1987) and Rp-Rs (Castagna and Smith, 1994) methods it combines both volumes by summation of Vp and Vs.
Examples are from the giant Ibhubesi gas fields offshore the Republic of South Africa in the Orange River Basin,Fig. 1, Location of Ibhubesi Gas Field, offshore the West Coast of the Republic of South Africa. (Available in full paper) however this method has been used in other area, both land and marine, with excellent predictive results.

Introduction to the Inverse Problem
What is Inversion? The name implies it is an inverse method, that is-one that has multiple possible solutions. This is the opposite of the forward method, where the conditions and experiment are known and the results are measured and repeatable. The results are always the same and the experiment may be repeated. With the inverse method (and more specifically the 'Inversion' used here,), the results and experiment are known and we are asked to solve for the original conditions. While it is true that there are multiple solutions, that is different geologic conditions may give rise to the same measurement, usually the practical possibilities may be narrowed. Most geological problems are in fact inverse procedures and understanding this relationship is both simple and profound, as non-uniqueness imposed by the inverse method is the fundamental reason for risk and uncertainty in Geology and Geophysics.