Elimination of the overburden response from multicomponent source and receiver seismic data, with source designature and decomposition into PP-, PS-, SP-, and SS-wave responses

Abstract

This paper shows that Betti's reciprocity theorem gives an integral equation procedure to eliminate from the physical multicomponent-source, multicomponent-receiver seismic measurements the effect of the physical source radiation pattern and the response of the physical overburden (that is, the medium above the receiver plane). The physical multicomponent sources are assumed to be orthogonally aligned anywhere above the multicomponentreceiver depth level. Other than the position of the sources, no source characteristics are required. The method, denoted the Betti designature/elastic demultiple, has the following additional characteristics: it preserves primary amplitudes while eliminating all waves scattered from the overburden; it requires no knowledge of the medium below the receiver level; it requires no knowledge of the medium above the receiver level; it requires information only of the local density and elastic wave propagation velocities at the receiver level to decompose the physical seismic measurements into upgoing and downgoing waves.Following the Betti designature/elastic demultiple step is an elastic wavefield decomposition step that decomposes the data into PP-, PS-, SP-, and SS-wave responses that would be recorded from idealized compressional-wave and shear-wave sources and receivers. The combined elastic wavefield decomposition on the source and receiver side gives data equivalent to data from a hypothetical survey with overburden absent, with single-component compressional and shear-wave sources, and single-component compressional and shear-wave receivers.When the medium is horizontally layered, the Betti designature/elastic demultiple scheme followed by the elastic source-receiver decomposition scheme greatly simplifies and is conveniently implemented as deterministic multidimensional deconvolution and elastic source-receiver wavefield decomposition of common-source gathers (or common-receiver gathers when source array variations are negligible).Betti designature/elastic demultiple followed by sourcereceiver wavefield decomposition applies to three different seismic experiments: a 9-component (9C) land seismic experiment, a 12-component (12C) ocean-bottom seismic experiment, and an 18-component (18C) borehole seismic experiment. For the land and ocean-bottom seismic experiments, an additional geophone should be deployed below the zero-offset geophone to predict the source-induced vertical traction vector at the source location.A numerical example for the 12C ocean-bottom seismic experiment over a horizontally layered medium validates the Betti designature/elastic demultiple scheme.

Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances

“…For example, it has been used for multiple elimination from ocean bottom data ͑Wapenaar and Verschuur, 1996;Amundsen, 1999;Holvik and Amundsen, 2005͒. Like the 1D deconvolution method of Snieder et al ͑2006a͒ discussed above, this can be seen as a methodology that changes the boundary conditions of the system; it transforms the response of the subsurface, including the reflecting ocean bottom and water surface, into the response of a subsurface without these reflecting boundaries.…”

Interferometry by Deconvolution of Multicomponent Multioffset GPR Data

“…For general 3-D heterogeneous media, it can only be solved when the decomposed dataP − (x A , x S , ω) andP + (x, x S , ω) are recorded at a sufficient number of receiver positions x A ∈ ∂D 1 and for a sufficient number of source positions x S . It follows that two horizontal source electric dipole orientations are sufficient to solve (14), see, e.g., [31] for an elastic example. In matrix notation [32], (14) can be written aŝ…”

Multi-component acoustic characterization of porous media

“…During all processing, amplitudes should be preserved. The feasibility of such processing has been reported earlier (e.g., Schalkwijk et al, 2003;Ghose & Goudswaard, 2004;Holvik & Amundsen, 2005).…”