Comparison of methods for modeling phase variation with angle

In another paper (Zhu and McMechan, 2011, hereinafter paper I), we show that least squares phase variation with angle (PVA) is capable of being reliably inverted for elastic parameters. A requirement for convergence to the correct solutions is consistency of the forward modeling methods for the synthetic observed data, and the predicted data. This indicates we have to look for a modeling method which can handle realistic geologic structures and produce synthetic (predicted) PVA as close as possible to the field (observed) PVA. This paper is a first step toward this goal. Three methods of measuring phase of a local wavelet are proposed and tested. Three kinds of methods for PVA modeling are discussed, including reflected spherical wave (RSW), reflectivity, and high-order finite difference (FD). Full-wave methods (reflectivity and FD) are preferred over the RSW. For laterally inhomogeneous structures, the differential solution (FD) is preferred over the integral solutions (RSW and reflecivity).