A construct of internal multiples from surface data only: the concept of virtual seismic events

Abstract

S U M M A R YWe here describe one way of constructing internal multiples from surface seismic data only. The key feature of our construct of internal multiples is the introduction of the concept of virtual seismic events. Virtual events here are events, which are not directly recorded in standard seismic data acquisition, but their existence allows us to construct internal multiples with scattering points at the sea surface; the standard construct of internal multiples does not include any scattering points at the sea surface.The mathematical and computational operations invoked in our construction of virtual events and internal multiples are similar to those encountered in the construction of free-surface multiples based on the Kirchhoff or Born scattering theory. For instance, our construct operates on one temporal frequency at a time, just like free-surface demultiple algorithms; other internal multiple constructs tend to require all frequencies for the computation of an internal multiple at a given frequency. It does not require any knowledge of the subsurface nor an explicit knowledge of specific interfaces that are responsible for the generation of internal multiples in seismic data. However, our construct requires that the data be divided into two, three or four windows to avoid generating primaries. This segmentation of the data also allows us to select a range of periods of internal multiples that one wishes to construct because, in the context of the attenuation of internal multiples, it is important to avoid generating short-period internal multiples that may constructively average to form primaries at the seismic scale.

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.…”

“…The traveltimes at normal incidence are indicated in the figure. We refer to these events as virtual events, using the terminology of Ikelle (2006), who also observed these artefacts of inverse wavefield extrapolation and reasoned how they may be used to predict internal multiples. However, our approach is different from that of Ikelle (2006), in the sense that we base our observations on the coupled Marchenko equations, where we do not have to identify these virtual events in practice, since they are separated automatically from the Green's functions by the actions of at each iteration.…”

Far-field superresolution by imaging of resonance scattering

“…Other iterative algorithms have been developed (Soni & Verschuur 2014) that theoretically predict and invert all internal multiples in the data under ideal circumstances. This work improves upon earlier developments for predicting internal multiples from surface seismic data (Jakubowicz 1998a,b;ten Kroode 2002;Ikelle 2006). The next section presents examples where multiple migration is used to achieve superresolution imaging with both synthetic and field data sets.…”

Adaptive overburden elimination with the multidimensional Marchenko equation

“…This is an interpretation that is commonly used in seismic interferometry (Schuster, 2009), which is also well-known in the field of IME (Ikelle, 2006) and Marchenko redatuming (van der Neut et al, 2015a). In Figure 6a and 6b, we show how the internal multiples "at the receiver side" are predicted by ͡ M f1 through the crosscorrelations of three primary reflections.…”

“…This is achieved by a multidimensional convolution of these representations with the direct wavefield G Because the projection point is always located at the acquisition surface throughout this paper, we omit to indicate depth z a in the arguments of all projected wavefields, for notational convenience. We may refer to the quantities v − and v þ m as virtual events, which is a terminology that was originally introduced by Ikelle (2006), who studies similar wavefields and demonstrates their use for IME. In a similar way as we did for the focusing function, we introduce the following projection of the upgoing Green's function: The wavefield U − can be interpreted as a subset of the reflection data.…”