Wenying Cai

Finite-difference solution of the eikonal equation along expanding wavefronts

We show that a scheme to solve the 2-D eikonal equation by a finite‐difference method can violate causality for moderate to large velocity contrasts (V2/V1>2). As an alternative, we present a finite‐difference scheme in which the solution region progresses outward from an “expanding wavefront” rather than an “expanding square,” and therefore honors causality. Our method appears to be stable and reasonably accurate for a variety of velocity models with moderate to large velocity contrasts. The penalty is a large increase in computational cost and programming effort.

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 sugg...

High-resolution cross-well imaging by seismic traveltime+waveform inversion

Enhanced oil recovery (EOR) operations promise to increase the yield of existing reservoirs of oil and gas. The USGS estimates there are more than 300 billion bbl oil “locked in” the continental US alone. One of the most promising tools that helps “unlock” these reserves is cross‐well seismic tomography. This technique, in essence, consists of seismic sources in one well, data collection by receivers in an adjacent well, and data analysis via tomography to determine interwell lithology which, in turn, can be used to design/modify a steam or fire flood EOR operation.

Electromagnetic velocity inversion using 2-D Maxwell`s equations

We adapt the wave‐equation traveltime inversion (WT) method to the reconstruction of the dielectric distribution from crosswell radar traveltime data. The data misfit gradient is computed using finite‐difference solutions to the 2-D Maxwell’s equations. An advantage of the wave‐equation method over ray‐tracing radar tomography is that it accounts for scattering and diffusion effects and works well in both resistive and moderately conductive rocks. Comparisons with ray‐tracing tomography show that the wave equation method is more robust and accurate when the rock conductivity is larger than .002 S/m. The methods are about equally effective when the conductivity is less than or equal to .001 S/m. The major disadvantage of the wave equation scheme is that it generally requires at least several orders of magnitude more computational time than ray tracing. We also derive the general equation for the waveform radar inversion method, which is closely related to the equations for the WT method and prestack radar ...

First Arrival Inversion of Crosswell Radar Data by Finite‐Difference Solutions to Maxwell's Equations

The wave equation traveltime inversion (WT) method is adapted to the reconstruction of the dielectric distribution from first arrival traveltime radar data. A gradient optimization algorithm is used and the gradient function is computed from finitedifference solutions to the 2-D Maxwell’s equations. The key advantage of the radar WT method over conventional ray tracing radar tomography is that it accounts for scattering and diffusion effects in the data and works well in both highly resistive and moderately conductive rocks. This technique is successfully applied to both synthetic and real radar data. Comparisons with a ray tracing (RT) tomography scheme show that the radar WT method is more reliable and accurate than the RT method when rock conductivity is larger than .002 S/m. The WT and RT methods are about equally effective when conductivity is less than or equal to .OOl S/m. The disadvantage of the WT scheme is that it generally demands an order of magnitude more computational time than the RT method.

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.

Hybrid wave equation traveltime+waveform inversion of crosswell seismic data

We present the first successful waveform inversion of real crosswell seismic data. The methodology is to first invert for the smooth velocity structure by inverting the first arrival traveltimes, and then invert for the fine-detailed velocity structure by waveform inversion of the seismograms. This method will be called WTW or wave equation traveltime and waveform inversion. WTW mitigates the problem of getting stuck in local minima when the starting velocity model is far from the true model. The spatial resolution of the WTW tomogram for Exxons Friendswood data is about 6 times that of the traveltime tomogram. WTW opens up a new door in monitoring Enhanced Oil Recovery operations in oil and gas fields.