Tomographic Inversion of Crosshole Seismic Data

Included in Research as Applied Geophysics No. 39, Geophysics Laboratory, University of Toronto.A crosshole seismic experiment deploys sources and receivers at many depth positions in parallel boreholes. The resulting ray paths form a crisscrossing pattern through the intervening rock. Many tomographic interpretations of the traveltimes have approximated the ray paths with straight lines, ignoring ray path curvature. While the approximation is valid in weakly inhomogeneous media, many regions of interest have large velocity variations which cause significant ray curvature. The interpretation problem is that the ray paths are required in order to accurately determine the velocity structure but these ray paths depend on the unknown velocity structure. This thesis presents a method of interpreting crosshole data which accurately accounts for the curved ray paths in an inhomogeneous medium. The nonlinear inverse problem of estimating the velocity structure from traveltime data is solved iteratively. The traveltimes and partial derivatives for the current model are calculated during raytracing. The difference between the data and current model traveltimes are then used to determine perturbations to the velocity model. The partial derivatives relating the velocity perturbations to the traveltime differences are recalculated at each iteration, as they depend upon the changing ray paths. Difficulties in interpreting crosshole seismic data arise because of limited angular coverage. The impossibility of imaging features parallel to the boreholes is investigated, as are the resolution limitations inherent in other source-receiver borehole geometries. A method of estimating the spatial resolution possible with large datasets is also presented. Results using synthetic data demonstrate the accuracy of the inversion method, which is then successfully applied to two sets of real crosshole data. Regions of low seismic velocity in the final models correlate well with known zones of fracturing along the boreholes. The good correspondence of synthetic seismograms and observed seismograms also confirms the validity of the velocity models obtained with this method. The same methods are extended to the inversion of amplitude data for the determination of attenuation structure, accurately taking into account the previously determined velocity structure. They are applied to a field dataset and the resulting attenuation structure is shown to agree with other geophysical and geological data.Ph.D