Wide-azimuth angle gathers for wave-equation migration

Introduction

In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth's interior. The quality of the final image greatly depends on the quality of the velocity model and on the quality of the technique used for wavefield reconstruction in the subsurface (Gray et al., 2001).

However, structural imaging is not the only objective of wave-equation imaging. It is often desirable to construct images depicting reflectivity as a function of reflection angles. Such images not only highlight the subsurface illumination patterns, but could potentially be used for image postprocessing for amplitude variation with angle analysis. Furthermore, angle domain images can be used for tomographic velocity updates.

Angle gathers can be produced either using ray methods (Brandsberg-Dahl et al., 2003; Xu et al., 1998) or by using wavefield methods (Xie and Wu, 2002; Mosher et al., 1997; Rickett and Sava, 2002; Wu and Chen, 2006; Sava and Fomel, 2003; Biondi and Symes, 2004; Prucha et al., 1999; de Bruin et al., 1990). Gathers constructed with these methods have similar characteristics since they simply describe the reflectivity as a function of incidence angles at the reflector. However, as indicated by Stolk and Symes (2004), even in perfectly known but strongly refracting media angle gathers are damaged by undersampling of data on the surface, regardless of the method used for their construction. In this paper, we address the problem of wavefield-based angle decomposition.

Angle decomposition can be applied either before or after the application of an imaging condition. The two classes of methods differ by the objects used to study the angle-dependent illumination of subsurface geology. The methods operating before the imaging condition decompose the extrapolated wavefields from the source and receivers (Prucha et al., 1999; Mosher et al., 1997; de Bruin et al., 1990; Wu and Chen, 2006). This type of decomposition is costly since it operates on individual wavefields characterized by complex multipathing. In contrast, the methods operating after the imaging condition decompose the images themselves which are represented as a function of space and additional parameters, typically refered to as extensions (Rickett and Sava, 2002; Sava and Vasconcelos, 2011; Sava and Fomel, 2006,2003). In the end, the various classes of methods lead to similar representations of the angle-dependent reflectivity represented by the so-called scattering matrix. The main differences lie in the complexity of the decomposition and in the cost required to achieve this result. In this paper, we focus on angle decomposition of extended images.

Conventionally, angle-domain imaging uses common-image-gathers (CIGs) describing the reflectivity as a function of reflection angles and a space axis, typically the depth axis. An alternative way of constructing angle-dependent reflectivity is based on common-image-point-gathers (CIP) selected at various positions in the subsurface. As pointed out by Sava and Vasconcelos (2011), CIPs are advantageous because they sample the image at the most relevant locations (along the main reflectors), they avoid computations at locations that are not useful for further analysis (inside salt bodies), they can have higher density at locations where the structure is more complex and lower density in areas of poor illumination, and they avoid the depth bias typical for gathers constructed as a function of the depth axis. In this paper, we focus on angle decomposition using extended CIPs.

A recent development in wave-equation imaging is the use of wide-azimuth data (Michell et al., 2006; Regone, 2006; Clarke et al., 2006). Imaging with such data poses additional challenges for angle-domain imaging, mainly arising from the larger data size and the interpretation difficulty of data of higher dimensionality. Several techniques have been proposed for wide-azimuth angle decomposition, including ray-based methods (Koren et al., 2008) and wavefield methods using wavefield decomposition before imaging (Biondi and Tisserant, 2004; Zhu and Wu, 2010) or after imaging (Sava and Fomel, 2005). Here, we complete the set of techniques available for angle gather construction by describing an algorithm applicable to extended common-image-point-gathers.

Wide-azimuth angle gathers for wave-equation migration