Fast 3D velocity updates using the pre-stack exploding reflector model

Introduction

In areas of complex geology, pre-stack depth migration is required not only for imaging purposes but also for velocity estimation. In such areas, migration by wavefield extrapolation has been widely used to produce the final image because it properly handles complex distortions of the wavefields. Migration velocity analysis by wavefield extrapolation (Sava and Biondi, 2004; Shen and Symes, 2008) promises to produce more reliable results than ray-based methods in those areas. However, due to the high computational cost, wavefield-extrapolation methods are rarely used to estimate the migration velocity model in 3D projects (Fei et al., 2009), and ray-based methods are the industry standards. In addition to the lower cost, ray-based methods are very flexible with respect to strategies for defining the velocity model (Stork, 1992; Kosloff et al., 1997; Billette et al., 1997). But despite their advantages, ray methods do not satisfactorily describe complex wave propagation in the presence of large lateral velocity contrasts. In this case, a more complete description of the wavefield complexities is needed, and therefore we face the challenge of decreasing the cost of migration velocity analysis by wavefield extrapolation while maintaining its robustness.

A typical way of decreasing the cost of wavefield extrapolation is to reduce the amount of input data by linearly combining the wavefields using plane-wave phase encoding (Liu et al., 2006; Whitmore, 1995) and random phase encoding (Sun et al., 2002; Romero et al., 2000). Combination of wavefields is exploited by the prestack-exploding reflector model (PERM) (Biondi, 2006) to significantly reduce the data size while keeping the migrated image crosstalk-free. This is achieved by selecting subsurface-offset common-image gathers (SODCIGs) separated by a decorrelation distance such that the wavefields from different SODCIGs in the same modeling experiment do not correlate during migration. Guerra et al. (2009) show that further reduction can be achieved by randomly phase encoding the modeling experiments, significantly decreasing the cost of migration velocity analysis iterations.

An interesting feature of PERM is that, because the wavefields are upward propagated, data can be collected at any depth level. In migration velocity analysis, PERM wavefields can be propagated only in the region with velocity inaccuracies. As a result the velocity update can be performed in a target-oriented way, which contributes to an additional cost reduction of migration velocity analysis.

In 3D, reduction of the data size can be considerable if the initial image used to model PERM wavefields has only in-line subsurface offsets, as in the common-azimuth approximation. We show that, in this case, 3D-PERM data size can be potentially up to two orders of magnitude smaller than 3D-plane wave data. The usefulness of PERM data to migration-velocity analysis with wavefield extrapolation is illustrated using a North Sea 3D dataset.

Fast 3D velocity updates using the pre-stack exploding reflector model