Introduction

As seismic imaging is applied to more challenging situations where the overburden is ever more complex (e.g., imaging under complex and rugose salt bodies) and the illumination of important reflectors is spotty, we need to use all the events in the data to generate interpretable images. Two classes of events that are often neglected, but that are also often present in complex data are overturned reflections Li et al. (1983) and prismatic reflections Broto and Lailly (2001). These two classes of events share the challenge that they cannot be imaged correctly (at least in laterally varying media) by downward-continuation migration methods. This obstacle prompted me to look at reverse time migration Baysal et al. (1983), and in particular at reverse time migration of shot profiles Etgen (1986b).

However, the current status of reverse-time migration technology has some limitations that need to be addressed before it can be used effectively to image either overturned or prismatic reflections. The main challenge is the extraction of useful and robust velocity updating information from the migrated image. In complex media, velocity is usually updated from the information provided by migrated Common Image Gathers (CIG). Filho (1992) presented the only other method that I am aware of to compute angle-domain CIGs (ADCIGs) by reverse time migration. He applied the method to Amplitude Versus Angle (AVA) analysis. His method is computationally involved and does not seem to be particularly robust because it requires the identification of local plane waves.

In this paper, I extend to reverse-time shot-profile migration the method that Rickett and Sava (2001) proposed to compute CIGs by downward-continuation shot-profile migration. The idea is to compute offset-domain CIGs by a modified imaging condition that introduces the concept of a subsurface offset. Simple testing using synthetic data confirmed that the CIG computed applying the proposed method can be used for velocity updating. They should also be useful for AVA analysis, though I have not yet analyzed their amplitude properties. However, for both overturned reflections and prismatic reflections, the source wavefield and the receiver wavefield may be propagating along opposite vertical directions at the reflection point. For these two classes of events, the imaging principle should be generalized to include a vertical subsurface offset as well an horizontal one. I have not tested this generalization of the CIG methodology yet.

The proper imaging of both overturned waves and prismatic reflections presents another challenge related to the discrimination between the image contributions of reflections generated from either side of an interface. These two reflections need to be discriminated both for imaging of reflectivity and for robust velocity updating, because these two reflections have usually opposite polarity, and their kinematics are affected by different areas of the velocity model. I present a simple generalization of the imaging condition that enables the determination of the propagation direction of the reflections, and thus the separation of the image contributions related to different events.

Reverse time migration has some other known disadvantages that need to be addressed. One of them is the computational cost. A companion short note in this report Biondi (2002) is an attempt to address this issue, at least for 3-D marine data. The artifacts caused by discontinuities in the migration velocity model are a more fundamental problem. There are a number of proposed solutions in the literature Baysal et al. (1984); Etgen (1986a); Filho (1992). None of them is completely satisfactory, and thus more research on the subject is needed.