Appendix B: Elastic Wavefield Radiation Patterns and Vertical Source Arrays
Published:January 01, 2016
This appendix illustrates various source radiation patterns related to VP/VS ratios of elastic media. The force term from the wave equation is defined in terms of point forces and a moment tensor. Radiation patterns of wavefield amplitude are illustrated in polar diagrams for point forces on the free surface. These are based on the theory of Miller and Pursey (1954) for computing the displacement field in a half-space. They derive asymptotic expressions for the far-field strength at infinity in the solid. Synthetic seismograms from a single explosive charge are compared with the wavefield from vertical arrays of distributed charges. These are illustrated in the space domain computed from acoustic finite-difference models. The last example shows the P-wave radiation patterns from shear couples.
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3C Seismic and VSP: Converted waves and vector wavefield applications
3C seismic applications provide enhanced rock property characterization of the reservoir that can complement P-wave methods. Continued interest in converted P- to S-waves (PS-waves) and vertical seismic profiles (VSPs) has resulted in the steady development of advanced vector wavefield techniques. PS-wave images along with VSP data can be used to help P-wave interpretation of structure in gas obscured zones, of elastic and fluid properties for lithology discrimination from S-wave impedance and density inversion in unconventional reservoirs, and of fracture characterization and stress monitoring from S-wave birefringence (splitting) analysis. The book, which accompanies the 2016 SEG Distinguished Instructor Short Course, presents an overview of 3C seismic theory and practical application: from fundamentals of PS-waves and VSPs, through to acquisition and processing including interpretation techniques. The emphasis is on unique aspects of vector wavefields, anisotropy, and the important relationships that unify S-waves and P-waves. Various applications and case studies demonstrate image benefits from PS-waves, elastic properties and fluid discrimination from joint inversion of amplitude variations with offset/angle (AVO/A), and VSP methods for anisotropic velocity model building and improved reservoir imaging. The book will be of interest to geophysicists, geologists, and engineers, especially those involved with or considering the use of AVO/A inversion, fracture/stress characterization analyses, or interpretation in gas-obscured reservoirs.