Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series
Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series (in Advances in seismic imaging and inversion, Stefan Buske (editor), Isabelle Lecomte (editor), Tamas Nemeth (editor), Stephane Operto (editor) and Valenti Sallares (editor))
Geophysics (November 2009) 74 (6, Suppl.): WCD15-WCD27
In the direct nonlinear inversion method and in algorithms for 1D elastic media, P-wave velocity, S-wave velocity, and density are depth dependent. "Direct nonlinear" means that the method uses explicit formulas that (1) input data and directly output changes in material properties without the need for indirect procedures such as model matching, searching, optimization, or other assumed aligned objectives or proxies and that (2) the algorithms recognize and directly invert the intrinsic nonlinear relationship between changes in material properties and the recorded reflection wavefields. To achieve full elastic inversion, all components of data (such as PP, SP, and SS data) are needed. The method assumes that only data and reference medium propertiesare input, and terms in the inverse series for moving mislocated reflectors resulting from the linear inverse term are separated from amplitude correction terms. Although in principle this direct inversion approach requires all components of elastic data, synthetic tests indicate that a consistent value-added result may be achieved given only PP data measurements, as long as the PP data are used to approximately synthesize the PS and SP components. Further value would be derived from measuring all components of the data as the method requires. If all components of data are available, one consistent method can solve for all of the second terms (the first terms beyond linear). The explicit nonlinear inversion formulas provide an unambiguous data requirement message as well as conceptual and practical added value beyond both linear approaches and all indirect methods.