Combining wave‐equation imaging with traveltime tomography to form high‐resolution images from crosshole data

Abstract

Traveltime tomography is an appropriate method for estimating seismic velocity structure from arrival times. However, tomography fails to resolve discontinuities in the velocities. Wave‐equation techniques provide images using the full wave field that complement the results of traveltime tomography. We use the velocity estimates from tomography as a reference model for a numerical propagation of the time reversed data. These “backpropagated” wave fields are used to provide images of the discontinuities in the velocity field. The combined use of traveltime tomography and wave‐equation imaging is particularly suitable for forming high‐resolution geologic images from multiple‐source/multiple‐receiver data acquired in borehole‐to‐borehole seismic surveying. In the context of crosshole imaging, an effective implementation of wave‐equation imaging is obtained by transforming the data and the algorithms into the frequency domain. This transformation allows the use of efficient frequency‐domain numerical propagation methods. Experiments with computer‐generated data demonstrate the quality of the images that can be obtained from only a single frequency component of the data. Images of both compressional [Formula: see text] and shear wave [Formula: see text] velocity anomalies can be obtained by applying acoustic wave‐equation imaging in two passes. An imaging technique derived from the full elastic wave‐equation method yields superior images of both anomalies in a single pass. To demonstrate the combined use of traveltime tomography and wave‐equation imaging, a scale model experiment was carried out to simulate a crosshole seismic survey in the presence of strong velocity contrasts. Following the application of traveltime tomography, wave‐equation methods were used to form images from single frequency components of the data. The images were further enhanced by summing the results from several frequency components. The elastic wave‐equation method provided slightly better images of the [Formula: see text] discontinuities than the acoustic wave‐equation method. Errors in picking shear‐wave arrivals and uncertainties in the source radiation pattern prevented us from obtaining satisfactory images of the [Formula: see text] discontinuities.