Crosshole seismic tomography

Abstract

Many tomographic interpretations of crosshole seismic traveltimes have approximated the raypaths with straight lines connecting the source and receiver. This approximation is valid where the velocity does not vary greatly, but in many regions of interest velocity variations of 10–20 percent or more are observed, causing significant ray curvature. Other work has taken this nonlinear effect into account, but there do not appear to be many cases of demonstrated success in its application to the crosshole seismic problem. We present here an iterative inversion scheme based on two‐dimensional ray tracing and its successful application to field data. The interpretation method iteratively ray traces and then updates the velocity model. Within each iteration, the differences between the data and the current model traveltimes obtained by ray tracing are related to the unknown velocity perturbations through a system of linear equations. A damped least‐squares method solves for the velocity perturbations which update the model. The iterations continue until the synthetic traveltimes fit the data to within the data error or until no improvement in the fit of the traveltimes is observed. The method is demonstrated on a small synthetic data set, where convergence to the correct solution is achieved in a few iterations. The method is then applied to field data from a crosshole experiment in crystalline rock. The frequency range of the seismograms is 1 to 6.6 kHz, allowing resolution of velocity structure on a scale of several meters. The resulting velocity image shows good agreement with other geologic and geophysical data. Synthetic Maslov seismograms calculated for the derived velocity model agree well with the waveform data, providing an independent test of the validity of the inversion method.