Diffraction imaging and time-migration velocity analysis using oriented velocity continuation

Introduction

Seismic diffraction occurs when a seismic wave encounters a heterogeneity without a clearly defined tangent plane, such as an edge or tip, and the reflection part of the ray theory breaks down (Klem-Mus-atov, 1994). These divergent diffraction rays have similar behavior to a subsurface secondary source located at the heterogeneity (Keller, 1962). Analyzing diffraction moveout behavior in different domains can provide subsurface velocity information analogous to analyzing reflection moveout behavior from a surface source.

The fact that diffractions migrated with correct velocity collapse to points motivated Harlan et al. (1984) to propose the idea of separating diffractions from specular reflections and using diffraction focusing as a tool for velocity analysis. Separation of diffraction events from seismic data is a necessary step for velocity analysis because diffraction signals are typically significantly weaker than those of reflections (Klem-Mus-atov, 1994). Fomel et al. (2007) developed a constructive procedure for diffraction separation based on plane-wave destruction and diffraction focusing analysis based on velocity continuation and local kurtosis. The procedure was extended to 3-D azimuthally-anisotropic velocity analysis by Burnett and Fomel (2011). However, local kurtosis may not be an optimal measure for diffraction focusing because it requires smoothing or windowing in space, which reduces spatial velocity resolution through the smoothing window parameters.

A particularly convenient domain for separating diffractions and reflections and for analyzing migration velocities is dip-angle gathers (Brandsberg-Dahl et al., 2003; Biondi and Symes, 2004; Landa et al., 2008; Reshef and Landa, 2009; Klokov and Fomel, 2012). In the dip-angle domain, specular reflections appear as hyperbolic events centered at the reflector dip and bending upwards, even when over or under-migrated, and diffractions appear flat when imaged at the location of the diffractor with the correct velocity (Reshef, 2007). Measuring flatness of diffraction events in dip-angle gathers, as opposed to flatness of reflection and diffraction events in reflection-angle gathers, provides an alternative constraint on seismic velocity (Reshef and Landa, 2009). Traditionally, dip-angle gathers are constructed with Kirchhoff migration (Xu et al., 2001; Bashkardin et al., 2012; Klokov and Fomel, 2013; Cheng et al., 2011; Brandsberg-Dahl et al., 2003; Koren and Ravve, 2011; Fomel and Prucha, 1999).

In this paper, we adopt an analogous method to the dip-angle approach used by Reshef and Landa (2009) to devise a constructive and highly parallel procedure for estimating velocities in time-domain processing using data decomposition in slope (Ghosh and Fomel, 2012) and velocity continuation in the midpoint-time-slope domain. By analogy with the ``oriented wave equation'' (Fomel, 2003a), we call this approach oriented velocity continuation (OVC) and develop a fast spectral method for its implementation on common-offset data. This differs from the methods devised by Reshef and Landa (2009), which utilize a separate Kirchhoff-based angle prestack time or depth migration and calculation of travel time tables for each tested migration velocity. OVC uses a continuation approach where a single migration is used to determine an initial image in the midpoint-time-slope domain to which a velocity dependent phase shift is applied over the range of plausible migration velocities, enabling OVC to test a greater number of velocities at a lower computational cost.

Using a field-data experiment, we demonstrate the effectiveness of oriented velocity continuation in zero-offset diffraction imaging and velocity analysis, and using a synthetic model we observe that higher velocity resolution can be achieved when multiple offsets are included in the process.

Diffraction imaging and time-migration velocity analysis using oriented velocity continuation