An inverse‐scattering series method for attenuating multiples in seismic reflection data

Abstract

We present a multidimensional multiple‐attenuation method that does not require any subsurface information for either surface or internal multiples. To derive these algorithms, we start with a scattering theory description of seismic data. We then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering. These include (1) the idea that the inversion process can be viewed as a series of steps, each with a specific task; (2) the realization that the inverse‐scattering series provides an opportunity for separating out subseries with specific and useful tasks; (3) the recognition that these task‐specific subseries can have different (and more favorable) data requirements, convergence, and stability conditions than does the original complete inverse series; and, most importantly, (4) the development of the first method for physically interpreting the contribution that individual terms (and pieces of terms) in the inverse series make toward these tasks in the inversion process, which realizes the selection of task‐specific subseries. To date, two task‐specific subseries have been identified: a series for eliminating free‐surface multiples and a series for attenuating internal multiples. These series result in distinct algorithms for free‐surface and internal multiples, and neither requires a model of the subsurface reflectors that generate the multiples. The method attenuates multiples while preserving primaries at all offsets; hence, these methods are equally well suited for subsequent poststack structural mapping or prestack amplitude analysis. The method has demonstrated its usefulness and added value for free‐surface multiples when (1) the overburden has significant lateral variation, (2) reflectors are curved or dipping, (3) events are interfering, (4) multiples are difficult to identify, and (5) the geology is complex. The internal‐multiple algorithm has been tested with good results on band‐limited synthetic data; field data tests are planned. This procedure provides an approach for attenuating a significant class of heretofore inaccessible and troublesome multiples. There has been a recent rejuvenation of interest in multiple attenuation technology resulting from current exploration challenges, e.g., in deep water with a variable water bottom or in subsalt plays. These cases are representative of circumstances where 1-D assumptions are often violated and reliable detailed subsurface information is not available typically. The inverse scattering multiple attenuation methods are specifically designed to address these challenging problems. To date it is the only multidimensional multiple attenuation method that does not require 1-D assumptions, moveout differences, or ocean‐bottom or other subsurface velocity or structural information for either free‐surface or internal multiples. These algorithms require knowledge of the source signature and near‐source traces. We describe several current approaches, e.g., energy minimization and trace extrapolation, for satisfying these prerequisites in a stable and reliable manner.

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

“…These events are constructed by crosscorrelating two primary reflections and the direct wavefield. This mechanism is closely related to that of various other schemes that predict internal multiples at the surface by crosscorrelation of three primary reflections (Weglein et al 1997;Jakubowicz 1998;Ten Kroode 2002;Ikelle 2006). This analogy has Fig.…”

Adaptive curvelet-domain primary-multiple separation

“…Surface-related multiple elimination ͑SRME͒ ͑Verschuur et al, 1992;Fokkema and van den Berg, 1993;Berkhout and Verschuur, 1997;Weglein et al, 1997͒ involves two stages, multiple prediction and primary-multiple separation. During the second stage, measures are taken to compensate for imperfections in the multiple predictions.…”

True-azimuth 3D Internal Multiple Attenuation without identifying the multiple generators

“…The same principle can be applied to model 3D IMs without identifying specific multiple-generating horizons. To fulfill the lower-higher-lower relationship (Weglein et al, 1997) that is crucial in the modeling of IMs, input data within the apertures is segmented into different windows, as shown in Figure 1b, in such a way that the window responsible for the downward reflections of the IMs (w j ) is always at a "higher" level (shorter traveltime) than the two windows that account for the upward reflections. With this implementation, all the IMs that have their top generators located within w j can then be modeled.…”

“…Approaches such as inverse scattering series (Weglein et al, 1997), layer-based method (Verschuur and Berkhout, 2005), window-based method (Hung and Wang, 2012;Retailleau et al, 2012) have been suggested for predicting IMs without subsurface information. However, besides the work of Retailleau et al, most of these approaches are limited to 2D applications only.…”