Iterative Ray Tracing between Boreholes for Underground Image Reconstruction

A computerized method is described for calculating an image of the refractive index distribution in a plane bounded by two underground boreholes. The scanning geometry is assumed to be limited to probing from borehole to borehole, with rays at numerous depths and angles to effectively cover the cross section between holes. A geometrical optics model is assumed for the transmission data. We stress situations where significant bending of electromagnetic or seismic rays occurs. Image reconstruction involves an iterated sequence of numerical ray tracing and linear system inversion. A similar approach, discussed in the literature, sometimes fails to converge. We report here our refinements of this method, including use of a smoothness constraint.