Reverse-time migration using wavefield decomposition

Introduction

RTM is a migration method based on wavefield extrapolation in time. As a two-way wave-equation migration, it can image very steeply dipping reflectors and even overturned events. This method is based on two consecutive steps: numerical propagation of wavefields from the recording surface into image space, followed by the image formation process using these wavefields. RTM was first used for poststack depth migration of 2D seismic data in the late 1970s (Whitmore, 1983; Baysal et al., 1983).

Poststack RTM involves the extrapolation of receiver wavefields from recorded seismic data by computing the full two-way solution for the acoustic wave equation with time running backwards. In contrast, prestack RTM involves the extrapolation of source and receiver wavefields.

Prestack RTM for a shot profile consists of three steps: 1) forward extrapolating the source wavefield $S(t,\vec{x})$ from time $t=0$ to $t=t_{\text{max}}$ , 2) backward extrapolating the receiver wavefield $R(t,\vec{x})$ from time $t=t_{\text{max}}$ to $t=0$ , and 3) applying a suitable imaging condition to construct the reflectivity image (Biondi, 2005). The conventional imaging condition for RTM is the zero-lag cross-correlation of source and receiver wavefields (Claerbout, 1985). Since RTM is a type of shot-gather migration, each shot profile is migrated independently. Thus, the final RTM image is the sum of the images from all individual profiles.

The extrapolated wavefields are full two-way solutions of the wave equation. These two-way solutions do not limit the propagation directions of wavefields. Therefore, RTM can correctly image very steeply dipping reflectors and even overturned events. In extremely complex areas, it can also handle strong lateral velocity variations and multi-path arrivals (Etgen et al., 2009). Thus, RTM can produce more accurate images than other popular migration methods such as Kirchhoff, beam, and one-way wave-equation migration. Nevertheless, the two major drawbacks of RTM are strong low-frequency artifacts and high computational cost. Such artifacts are generated due to the nature of the conventional RTM imaging condition. Many remedies, such as velocity smoothing and post-migration filtering, have been proposed to suppress these artifacts, but they all have severe limitations.

This paper focuses on a promising technique for attenuating artifacts in correlation-based RTM images called wavefield decomposition. This technique is to decompose source and receiver wavefields into the appropriate components based on their propagation direction, so that the decomposed wavefields can produce the image without artifacts (Liu et al., 2007,2011). In this paper, I first provide an overview of RTM, its artifacts, and some common solutions for attenuating them. Next, I examine RTM using wavefield decomposition. Finally, I discuss the benefits and drawbacks of this technique and its practical implications.

Reverse-time migration using wavefield decomposition