Stereographic imaging condition for wave-equation migration

Introduction

Conventional depth migration consists of two steps: wavefield reconstruction of seismic wavefields at all locations in the imaging volume from data recorded on the acquisition surface, and imaging used to extract reflectivity information from wavefields reconstructed from the sources and receivers. Accurate imaging requires accurate implementation of both steps. Recent seismic imaging research places larger emphasis on wavefield extrapolation than on imaging, partly due to the larger computational cost of extrapolation relative to imaging.

This paper concentrates on the imaging condition assuming that wavefield extrapolation is performed in a sufficiently accurate velocity model. The imaging condition is often implemented as a cross-correlation of source and receiver wavefields extrapolated from the acquisition surface (Claerbout, 1985). The reason for this choice is that conventional cross-correlation imaging is fast and robust, producing good images in complex environments. The alternative deconvolution imaging condition is not discussed in this paper.

Conventional imaging condition operates in a simple way: source and receiver wavefields are probed to determine the locations where they match, i.e. where the traveltime of events forward-propagated from the source and backward-propagated from the receivers are equal. This is usually achieved by extracting the zero-lag of the temporal cross-correlation between the two wavefields computed at every location in the image. However, this imaging condition ignores the structure of the analyzed seismic wavefields, i.e. the imaging condition does not use the local space-time coherence of the reflected wavefields. This characteristic is contrary to conventional analysis of space-time kinematic coherence of seismic data, which is one of the most important attributes employed in their analysis.

The consequence of this deficiency is that different seismic events present in the extrapolated wavefields interfere with one-another leading to artifacts in seismic images. This interference, also known as cross-talk, occurs between unrelated events which should not contribute to the formed image. It is often possible to identify events that occur at the same time, although they describe different propagation paths in the subsurface. As a consequence, such unrelated events appear as real reflections due to the imaging condition and not due to a geological cause.

This paper presents an extension of the conventional imaging condition. This extension is designed to exploit the local space-time coherence of extrapolated wavefields. Different seismic events are matched both function of propagation time and a local coherence attributes, e.g. local slope measured function of position and time. Therefore, events with different propagation paths are differentiated from one-another, although their propagating time to a given point in the subsurface may be identical (Stolk and Symes, 2004). This property can be used to suppress artifacts due to cross-talk and generate cleaner seismic images.

Stereographic imaging condition for wave-equation migration