In cross-hole tomography straight lines connecting the source and receiver are often used to approximate the true ray paths, thus linearizing the inverse problem. A recent paper by Bregman et al. (1989 a) has shown that this approximation may be very poor in the regions of greatest interest where large velocity gradients cause significant ray curvature. The interpretation method presented by Bregman et al. (1989 a) iteratively ray traces and updates the velocity model with model perturbations obtained by a damped least squares inversion of the travel time residuals. This paper presents a modification of the travel time tomography method so that it may be applied to the inversion of first motion amplitudes for inverse quality factor Q-1. After determining the velocity structure using travel time tomography the amplitudes are inverted using a similar scheme. No additional ray tracing is required for the amplitude inversions.

The effect of the velocity structure previously determined through travel time tomography is taken into account so that amplitude variations due to the focusing and defocusing effects of the velocity structure are not interpreted as being due to attenuation structure. Both the travel time and amplitude tomography methods are applied here to field data from a cross-hole experiment in crystalline rock (Wong et al., 1983). The frequency range of the seismograms is 1--6.6 kHz, allowing resolution of velocity structure on a scale of several meters. The resulting velocity image shows good agreement with other geological and geophysical data. Reversing the model by placing the model boreholes on opposite sides relative to the original reconstruction yields almost identical results, indicating that the interpolation scheme used in the forward modeling has not biased the final model. Synthetic Maslov seismograms calculated for the derived velocity model agree well with the waveform data, further confirming the validity of the model. In addition, the amplitude tomography results place absorptive regions in the same location as the most pronounced low-velocity features which correlate with fractures in the boreholes. Highly transmissive regions also correlate well with high-velocity regions ¿ American Geophysical Union 1989