Decomposition and Inversion of Elastic Reflection Data; First-Order Angular Dependence and Applications

✍ Scribed by Alvin K. Benson

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 882 KB
• Volume: 121
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1995.1182

✦ Synopsis

The elastic wave displacement equation is transformed into pressure-stress coordinates, where the Born approximation of the Lippman-Schwinger equation in the Fourier-transform domain is employed to decompose the observed fields into their scattered components: (P-P, P-S, S-P), and (S-S). Triple Fourier transforms of the scattered elastic wave data are linear combinations of the double Fourier transforms of the relative changes in the medium properties. Angular-dependent reflection coefficients for each of the scattering modes are constructed, and an inversion algorithm is outlined. Inversion of the observed elastic wave fields is accomplished in a manner similar to the acoustic problem. Density, bulk modulus, and shear modulus variations in an elastic earth can be recovered by utilizing the angular-dependent information present in the observed wave fields. Examples illustrate these points. Transforming the elastic wave data back to displacement coordinates and assuming a compressional source, an analysis of recorded amplitudes yields some practical answers about converted-wave data. Significant amounts of (P \rightarrow S) data should typically be generated by compressional sources, with significant contributions at smaller angles. However, signal-to-noise calculations suggest that more sweeps and more geophone channels at longer offsets will typically be necessary to get (P)-S sections of comparable quality to (P-P) sections. 1995 Academic Press, Inc.