BEYOND RAY TOMOGRAPHY - WAVEPATHS AND FRESNEL VOLUMES

Two techniques that account for the band-limited nature of seismic dat a are incorporated into tomographic traveltime inversion schemes. The first technique, the wavepath algorithm, is based upon the wave equati on, the Born approximation, and an adjoint method for computing Freche t derivatives. Computation of a single wavepath requires the forward p ropagation of the seismic wavefield, as well as the reverse propagatio n of a residual wavefield. The second technique, the Fresnel volume ap proach, is based upon the paraxial ray approximation. The Fresnel volu me algorithm requires little more computation than does conventional r ay tracing and an order of magnitude less computer time than our calcu lation of wavepaths. When the Fresnel volume sensitivity functions are normalized by the area of the Fresnel ellipse perpendicular to the ra y, the sensitivity estimates are very similar to the wavepaths. In par ticular, there is heightened sensitivity to velocity structure near th e source and receiver locations. The normalization by the Fresnel elli pse area is necessary to ensure ray theoretical results in the limit o f infinite frequency. Tomographic inversion based upon wavepaths or Fr esnel volumes is more appropriate when considering the arrival time of the peak of the initial pulse rather than the first-arrival time. Fur thermore, using the traveltime of the peak instead of the first-arriva l time reduces the bias of tomograms to high velocity anomalies. The r aypath, wavepath, and Fresnel volume techniques were applied to a set of cross-borehole traveltime observations gathered at the Grimsel Rock Laboratory. All methods imaged a low velocity fracture zone in the gr anitic site, in agreement with independent well information. Estimates of model parameter resolution are similar for the wavepath and Fresne l volume schemes. The source-receiver regions are the most well resolv ed areas. However, the model parameter resolution computed using a con ventional ray-based formalism is more evenly distributed over the cros s-borehole area.