Migration velocity analysis for anisotropic models

Introduction

Since first reported in exploration seismology in the 1930s (McCollum and Snell, 1932), anisotropy has become increasingly important in seismic imaging and exploration. Until now, the transverse isotropic (TI) model has been the most commonly used model in seismic imaging. Postma (1955), Helbig (1956) and Backus (1962) have shown that a sequence of isotropic layers on a scale much smaller than the wavelength leads to an anisotropic medium. If the layers are horizontal, the medium is defined as a vertical TI (VTI) medium. A VTI medium is commonly formed because of thin bedding during deposition. If the layers become dipping due to deformation, a tilted TI (TTI) medium is formed. Many authors (Shan, 2009; Fei and Liner, 2008; Zhang and Zhang, 2009; Fletcher et al., 2009) have developed migration and processing schemes for VTI and TTI media; however, the challenge of estimating the anisotropy model remains a bottleneck for the exploration workflow.

The existing anisotropic model-building schemes are mostly based on measuring the non-hyperbolic moveout along the traveltime curve to flatten the common image gathers (CIG) (Woodward et al., 2008; Zhou et al., 2003; Cai et al., 2009; Zhou et al., 2004; Yuan et al., 2006). However, traveltime ray-based methods are prone to errors and unrealistic results when multi-pathing exists in areas of complex overburden. Hence, we propose to apply wave-equation tomography for anisotropic model building.

Wave-equation tomography has been widely studied in isotropic velocity building and can be implemented either in the data space, commonly known as Full-Waveform Inversion (FWI) (Woodward, 1992; Tarantola, 1984) or in the image space, commonly known as Wave-Equation Migration Velocity Analysis (WEMVA) (Shen, 2004; Sava and Biondi, 2004b; Shen and Symes, 2008; Sava and Biondi, 2004a; Guerra et al., 2009). Several advantages drive us to use the image-space wave-equation tomography instead of data-space wave-equation tomography: first, WEMVA does not require as accurate an initial model to avoid the cycle-skipping problem as FWI requires. In fact, many studies (Guerra and Biondi, 2010; Tang and Biondi, 2010; Guerra et al., 2009) show that the resolution gap between ray-based tomography and FWI could be linked by the image-space WEMVA method; second, the objective function is directly related to the final image; third, the migrated image is often much cleaner than the recorded wavefields. Therefore, we choose to extend image-space WEMVA from isotropic velocity building to anisotropic model building.

In this paper, we first generalize the methodology of image-space WEMVA from an isotropic medium to an anisotropic medium and explain our parameterization. We show that the gradient of the tomographic objective functional for an isotropic medium can be modified to describe an anisotropic medium by simply adding a term for the additional parameter. Finally, we test our inversion scheme on a shallow part of the Hess anisotropic synthetic dataset.

Migration velocity analysis for anisotropic models