Seismic inversion using complex spherical-wave reflection coefficient at different offsets and frequencies

Compared with the plane-wave reflection coefficient, the spherical-wave reflection coefficient (SRC) can more accurately describe the reflected wavefield excited by a point source, espe-cially in the case of low seismic frequency and short travel distance. However, unlike the widely used plane-wave ampli-tude-variation-with-offset/frequency (AVO/AVF) inversion, the practical application of spherical-wave AVO/AVF inversion in multilayer elastic media is still in the exploratory stage. One of the difficulties is how to fully use the amplitude and phase infor-mation of the complex-valued SRC and the spherical-wave re-sponse property of each frequency component to obtain the spherical-wave synthetic seismogram in multilayer elastic media. In view of this, we have developed a complex convolution model considering the amplitude and phase information of an SRC to obtain the complex synthetic seismogram of a certain frequency component. A simple harmonic superposition method is further developed. By superposing the complex synthetic seismograms of different frequency components, the synthetic seismogram of the full-frequency band can be obtained. In addition, a novel three-parameter SRC in terms of P-and S-wave moduli and den-sity is derived. Based on the SRC and complex seismic traces with different offsets (or incidence angles) and frequency com-ponents, an inversion approach of complex spherical-wave am-plitude and phase variation with offset and frequency is proposed. A noisy synthetic data example verifies the robustness of our com-plex spherical-wave inversion approach. Field data examples in-dicate that the P-and S-wave moduli estimated by the complex spherical-wave inversion approach can reasonably match the fil -tered well-logging data. Considering spherical waves rather than plane waves can improve the accuracy of seismic inversion results.

Automated summary

Compared with the plane-wave reflection coefficient, the spherical-wave reflection coefficient provides a more accurate description of the reflected wavefield, especially at low seismic frequencies and short travel distances. However, the practical application of spherical-wave inversion in multilayer elastic media is still in its early stages. This study develops a complex convolution model and a simple harmonic superposition method to obtain synthetic seismograms in multilayer elastic media using the amplitude and phase information of the spherical-wave reflection coefficient.