Acoustic Wave Equation Traveltime And Waveform Inversion of Crosshole Seismic Data

A hybrid wave-equation traveltime and waveform inversion method is presented that reconstructs the interwell velocity distribution from crosshole seismic data. This inversion method, designated as WTW, retains the advantages of both full wave inversion and traveltime inversion; i.e., it is characterized by reasonably fast convergence which is somewhat independent of the initial model, and it can resolve detailed features of the velocity model. In principle, no traveltime picking is required and the computational cost of the WTW method is about the same as that for full wave inversion. We apply the WTW method to synthetic data and field crosshole data collected by Exxon at their Friendswood, Texas, test site. Results show that the WTW tomograms are much richer in structural information relative to the traveltime tomograms. Subtle structural features in the WTW Friendswood tomogram are resolved to a spatial resolution of about 1.5 m, yet are smeared or completely absent in the traveltime tomogram. This suggests that it might be better to obtain high quality (distinct reflections) crosshole data at intermediate frequencies, compared to intermediate quality data (good quality first arrivals, but the reflections are buried in noise) at high frequencies. Comparison of the reconstructed velocity profile with a log in the source well shows very good agreement within the O-200 m interval. The 200-300 m interval shows acceptable agreement in the velocity fluctuations, but the tomogram’s velocity profile differs from the sonic log velocities by a DC shift. This highlights both the promise and the difficulty with the WTW method; it can reconstruct both the intermediate and high wavenumber parts of the model, but it can have difficulty recovering the very low wavenumber parts of the model. two extremes, traveltime inversion (Dines and Lytle, 1979; INTRODUCTION Paulsson et al., 1985; Ivansson, 1985; Bishop et al., 1985; Lines, 1988; and many others) and full wave inversion Among the various seismic inversion methods there are (Tarantola, 1986, 1987; Mora, P. 1987; Crase et al., 1992; and others). In traveltime tomography, the time of flight information is inverted for the smooth features of the velocity model, while waveform inversion inverts the amplitude and phase information for the fine details of the earth model. Both methods have complementary strengths and weaknesses. than that from full wave inversion. On the other hand, the as does the source wavelet. In addition, the resolution of the traveltime misfit function (sum of squared errors between observed and calculated traveltimes) can be quasi-linear reconstructed model from traveltime inversion is much less (Luo and Schuster, 1991b) with respect to the normed difference between the starting and actual velocity models. This means that successful inversion can be achieved even if the starting model is far from the actual model. The characteristics of full wave inversion are complementary to those of traveltime inversion. While sensitive to the choice of starting model or noisy amplitudes, full wave inversion can sometimes reconstruct a highly resolved earth model. This is because there are no high-frequency assumpA weakness of traveltime inversion is that it employs a high frequency approximation and so it can fail when the earth’s velocity variations have nearly the same wavelength Manuscript received by the Editor May 17, 1993; revised manuscript received June 3, 1994. *Formerly Department of Geology and Geophysics, University of Utah, Salt Lake City, UT 84112; currently TomoSeis, 1650 W. Sam Houston Pkwy. N., Houston, TX 77043. *Formerly Dept. of Geology and Geophysics, University of Utah, Salt Lake City, UT 84112; presently Chevron Oil Field Research Co., P.O. Box 446, La Habra, CA 90633-0446. §Sun Microsystems Computer Corp. , 2550 Garcia Avenue, MS PAL1-316, Mountain View, CA 94043-1100. © 1995 Society of Explorat ion Geophysicists . All r ights reserved.