Exact angle‐mute pattern for a transversely isotropic medium with vertical symmetry axis and its implication in offset‐to‐angle transform

Abstract

Computing an accurate angle mute pattern is vital to the offset‐to‐angle transform of prestack seismic data. Here, we use a ray‐based approach to calculate this angle‐mute pattern. From any given zero‐offset time sample, we ray‐trace through the medium to the corresponding source and receiver locations and compute the ray‐path length, travel time, offset for a given central angle. We then increase and decrease the angle value in each side of the central angle and calculate the corresponding ray‐path length, travel time, offset until the difference in ray‐path length of central angle and present angle is equal to one‐fourth of the wavelength in each‐side. The traces within this offset range retain the energy reflected from the given central angle, and the corresponding offset range defines the angle‐mute pattern. A constrained cubic‐spline interpolation is then designed within this angle‐mute pattern to obtain the times corresponding to those offsets and are partially stacked to obtain the corresponding zero‐offset angle domain response. The method allows us to compute both primary (P‐P) and converted wave (P‐SV) angle gathers. Additionally, by computing an exact ray‐path length, we can apply an exact geometric spreading compensation to the computed gathers. This present approach calculates angle gathers that are accurate out to large angles in a horizontally stratified transversely isotropic medium with a vertical symmetry axis (VTI medium). By calculating the exact angle‐mute pattern and total ray‐path length in a VTI medium both for P‐P and P‐SV reflections, we are able to preserve the accurate energy associated with the respective rays. The angle‐mute pattern in an anisotropic medium is significantly different from that calculated for the same medium if it is considered isotropic. Accurate angle gathers out to large angles from observed seismic data can be used in a multicomponent prestack waveform inversion to match with synthetic angle gathers. In addition, the velocity and anisotropic parameters of the medium can be obtained by changing the elastic parameters and ray‐tracing in a AVO sensitive semblance type analysis. These results, if not exact but close, can eventually be used as initial model to any linear or non‐linear seismic inversion scheme.