Abstract
SUMMARY Short-period internal multiples, resulting from closely spaced interfaces, may interfere with their generating (bandlimited) primaries, and hence they pose a long-standing challenge in their prediction and removal. A recently proposed method based on the Marchenko equation enables removal of the entire overburden-related scattering by means of calculating an inverse transmission response. However, the method relies on time windowing and can thus be inexact in the presence of short-period internal scattering. In this work, we present a detailed analysis of the impact of band-limitation on the Marchenko method. We show the influence of an incorrect first guess, and that adding multidimensional energy conservation and a minimum phase principle may be used to correctly account for both long- and short-period internal multiple scattering. The proposed method can currently only be solved for media with a laterally invariant overburden, since a multidimensional minimum phase condition is not well understood for truly 2-D and 3-D media. We demonstrate the virtue of the proposed scheme with a complex acoustic numerical model that is based on sonic log measurements in the Middle East. The results suggest not only that the conventional scheme can be robust in this setting, but that the ‘augmented’ Marchenko method is superior, as the latter produces a structural image identical to one where the finely layered overburden is missing. This is the first demonstration of a data-driven method to account for short-period internal multiples beyond 1-D.
Highlights
Most seismic imaging algorithms of reflection data still rely on a single-scattering assumption, making multiply scattered energy often an undesired signal component
We show the influence of an incorrect first guess, and that adding multidimensional energy conservation and a minimum phase principle may be used to correctly account for both long- and short-period internal multiple scattering
In the same section we describe why the problem is best approached inside the overburden elimination setting, rather than by Marchenko redatuming the sources and receivers below the scattering overburden; in combination with the minimum phase argument the former setting is the more natural choice
Summary
Most seismic imaging algorithms of reflection data still rely on a single-scattering assumption, making multiply scattered energy often an undesired signal component. A detailed analysis of the conventional and augmented Marchenko scheme in a band-limited setting allows us to solve this problem and point out ways for general 2-D and 3-D media Since such an analysis is crucial for this work and has not yet been presented in detail elsewhere, we dedicate Section 2 to this analysis. The conventional Marchenko method provides blurred functions [panel (a)] that do not properly account for SPIM Injecting it into the medium [panels (c), (e) and (g)] yields a blurred focus [panel (e)], and many overburden-related internal multiples that are not properly handled remain and reach the focusing position after the actual focusing [panel (g)]. We show how the coupled Marchenko equations are derived and solved (Section 2.3), we highlight the implications of band-limitation (Section 2.4), and present the effects of SPIM on the augmented Marchenko equations (Section 2.5)
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