Scattering attenuation in randomly layered structures with finite lateral extent: A hybrid Q model

Abstract

Since the pioneering work of O'Doherty and Anstey (1971), much research has been devoted to understand the effect of stratigraphic filtering of seismic waves, i.e., the problem of multiple scattering in 1D random structures (e.g., Burridge et al., 1993; Shapiro and Hubral, 1999). For many subsurface structures, such as sedimentary basins, the assumption of layering is reasonable as a first approximation. However, real geostructures do not show perfect layering but exhibit a finite lateral extent in their elastic properties. This becomes particularly important when studying overburden effects in reflection seismology, where amplitude information is used in subsequent data analysis. For example, Malme et al. (2003) showed that the amplitude variation with offset (AVO) response for a vertical seismic profile (VSP) experiment over a North Sea field is significantly distorted by nonlayered overburden inhomogeneities. They demonstrated by seismic forward modeling that pointlike diffractors and large-scale, gas-filled sand bodies can be responsible for strong amplitude fluctuations. In this short note, we study the transmission behavior of seismic primaries when the finite lateral extent of the inhomogeneities is accounted for. Physically speaking, we intend to quantify the combined effects of scattering attenuation due to thin layering and random diffractions and refractions. It is important to understand that our approach describes scattering attenuation of seismic primaries and not attenuation of the mean field (ensemble averaged wavefield) as presented in earlier works (e.g., Lerche, 1986). We use the model of an anisotropic 3D random medium. Anisotropy in this context means that the randomly distributed inhomogeneities have three different characteristic length scales and are characterized by a spatially anisotropic correlation function. We also assume that the medium is lossless, so that no intrinsic wave attenuation occurs. A sketch of such a structure is shown in Figure 1, resembling a realization of a 2D …