THE USE OF FORWARD- AND BACK-SCATTERED P-, S- AND CONVERTED WAVES IN CROSS-BOREHOLE IMAGING1

The principles of imaging, for example that of prestack migration, can be applied to cross-borehole seismic geometry just as they can to surface seismic configurations. However, when using actual cross-borehole data, a number of difficulties arise that are rarely or never encountered in imaging surface seismic data: discontinuities may reflect or diffract incident seismic waves in any direction. If a discontinuity lies between the lines of sources and receivers, forward-scattered, or interwell, events may be recorded. If a discontinuity lies outside the interwell region, back-scattered, or extra-well, events may be recorded. Many angles of incidence are possible, and all possible reflected modes (P–P, P–S, S–P and S–S) are present, frequently in nearly equal proportions. The planes of the reflectors dip from 0 to ±90°. In order to deal with these complexities we first separate propagation modes at the receiver borehole using both polarization and velocity. Next we compensate for phase distortion due to dispersion. Finally, and most importantly, we migrate or image the data in cross-borehole common-source gathers. To do this, a finite-difference solution to the 2D scalar wave equation, using reverse time, for an arbitrary distribution of velocities, is used to project the separated, reflected-diffracted wavefield back into the medium. There are four reflection modes (P–P, P–S, S–P and S–S), so we can apply four different imaging conditions. The zones outside the boreholes as well as inside the boreholes can be imaged with these conditions. These operations are repeated for each common-source gather: each common-source gather generates four partial images in each image space. This multiplicity of partial images can be stacked in various combinations to yield a final image of the subsurface. Our experiments using solid (not fluid) physical models indicate that when these procedures are correctly applied, high quality cross-borehole images can be obtained. These images appear with great clarity even though some of the weak diffractions causing diffraction images may be almost totally obscured by other high-amplitude events on the raw data.