JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 94, NO. B6, PAGES 7577-7587, JUNE 10, 1989 Travel Time and Amplitude Analysis in SeismicTomography NINA D. BREGMAN Department oJ Physics, University oJ Toronto, Toronto, Ontario, Canada CHRISTOPHER H. CHAPMAN 1 Bullard Laboratories, Cambridge University, Cambridge, England RICHARD C. BAILEY Departments of Geology and Physics, University of Toronto, Toronto, Ontario, Canada In cross-holetomography straight lines connecting the source and receiver are often used to approximate the true ray paths, thus linearizing the inverseproblem. A recent paper by Bregman et al. (1989a) has shown that this approximation may be very poor in the regions of greatest in- terest where large velocity gradients cause significant ray curvature. The interpretation method presented by Bregman et al. (1989a) iteratively ray tracesand updatesthe velocitymodel 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 tothe inversion offirst motion amplitudes for inverse quality factor Q-1. After deter- mining 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 alefocusing 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 veloc- ity model agree well with the waveform data, further confuaxfing the validity of the model. In addition, the amplitude tomography results place absorptive r•gions 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. INTRODUCTION Cross-hole seismic exploration deploys both sourcesand receivers in boreholes below the near-surface layer in order to avoid the attenuation and scattering caused by this zone. This allows the use of the high-frequency signals necessttry to delineate fine earth structure. Seismic tomographyis the process by which information characterizingthe first arrivMs is inverted for the velocity or attenuation structure in the "slice" defined by the boreholes. In travel time tomography the first arrival times between a series of downhole sources Amplitude tomography uses the amplitudes of the first arrivals to make an image of the quality factor Q or the ab- sorption Q-1. Although amplitude tomography is common in medical applications (see, for example,Herman [1980] or Brooks and di Chiro[1976]), its application to cross-hole seismic data is rare. Wong et al. [1983,1985]haveinverted the amplitudes of cross-hole data for transparency structure using simple back projection. This paper is an extensionof the work presented by Breg- man et al. [1989a]which describes a method of invert- and receivers can be used toconstruct a tomographic image ing travel times fortwo-dimensional seismic velocity struc- of the compressional wave velocity between the holes. Ex- ture which iteratively raytraces and updates thevelocity amples of travel time tomography in cross-hole seismology model with model perturbations obtained by adamped least include Bols et al. [1972], Wong et al. [1983, 1984, 1985,squares inversion ofthe travel time residuMs. Bregman et 1987],Peterson et al. [1985], Dines and Lyric[1979], lvaas- son [1985], and Bregman et al. [1989a, 1989c]. 1Now at Department of Physics, University of Toronto, Toronto, Ontario, Canada. Copyright 1989 by the American Geophysical Union. Paper number 88JB04048. 0148-0227/89/88JB-04048505.00 al. [1989a] applied this technique first to a synthetic data set as a demonstration and then to a field data set, obtaining a velocity model which agreedwith other geophysical data. In addition, synthetic seismograms calculated for the derived velocity model matched the waveform data. Bregman et al. [1989b] examines the theoretical resolution possible with different source/receiver geometries. Here the travel time inversion technique described by Bregmanet al. [1989a]is adapted to the problem of inverting the amplitudes of the first arriving signal for attenuation structure. Both intrinsic attenuation and attenuation due to scattering of the seis- 7577