Changxi Zhou

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...

Elastic wave equation traveltime and waveform inversion of crosswell data

A method is presented for reconstructing P‐ and S‐velocity distributions from elastic traveltimes and waveforms. The input data consist of crosswell hydrophone records generated by a piezoelectric borehole source. Borehole effects are partially accounted for by using a low‐frequency Greens function to simulate the pressure generated in the fluid‐filled receiver well. The tube waves in the borehole are ignored, on the assumption that they can be removed from the field data by median filtering. In addition, the source‐radiation pattern is partially taken into account by inverting for the equivalent stress components acting on the earth at the source location. The elastic wave equation traveltime and waveform inversion (WTW) method is applied to both synthetic crosswell data and the McElroy field crosswell data. As predicted by theory, results show that elastic WTW tomograms provide a sharper interface image than delineated in the traveltime tomograms. The spatial resolution of the McElroy traveltime tomogr...

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.

A quasi‐Monte Carlo approach to efficient 3-D migration: Field data test

The quasi-Monte Carlo migration algorithm is applied to a 3-D seismic data set from West Texas. The field data were finely sampled at approximately 220-ft (67-m) intervals in the in-line direction but were sampled coarsely at approximately 1320-ft (402-m) intervals in the cross-line direction. The traces at the quasi-Monte Carlo points were obtained by an interpolation of the regularly sampled traces. The subsampled traces at the quasi-Monte Carlo points were migrated, and the resulting images were compared to those obtained by migrating both regular and uniform grids of traces. Results show that, consistent with theory, the quasi-Monte Carlo migration images contain fewer migration aliasing artifacts than the regular or uniform grid images. For these data, quasi-Monte Carlo migration apparently requires fewer than half the number of the traces needed by regular-grid or uniform-grid migration to give images of comparable quality. These results agree with related migration tests on synthetic data computed for point scatterer models. Our results suggest that better migration images might result from data recorded on a coarse quasi-random grid compared to regular or uniform coarse grids.

Elastic waveform inversion of pressure field data

An elastic waveform inversion method for inverting crosswell pressure field data is presented. In this method a low frequency approximation is used to analytically simulate the pressure generated in the fluid filled well. The tube wave in the borehole is not simulated based on the assumption that it can be removed from the field data by median filtering. The inversion method inverts for both Pand S-velocity tomograms at the same time. Therefore it requires fewer data processing procedures and honors the original amplitude information. The field data example shows that this method can provide superior images of the Pand S-velocity structures compared to the traveltime tomogram. The correlation between the Pand S-velocity tomograms is quite reasonable. Comparisons between the tomogram velocity profiles and the sonic logs show a good match. The resolution of the S-velocity tomogram is about the twice that of the P-velocity tomogram. 2 I N T R O D U C T I O N In many crosswell experiments, the hydrophone is used to record the pressure field in a fluid-filled borehole. Zhou et al. (1993) proposed an acoustic waveform inversion method for inverting hydrophone records which don’t contain strong S-wave arrivals. But when strong S-wave arrivals are extant, this inversion method is not valid. The remedy to this problem is to use an elastic waveform inversion method, which is generally applicable to two or three component particle velocity or displacement records (Tarantola et al., 1985; Mora, 1987; Zhou et al., 1994) However it is not straightforward to apply this method to pressure field data and ignoring the borehole effects might prove harmful. So Zhou and Hassanzadeh (1994) presented a divide and conquer strategy to de-complexify the data and invert the Pand S-velocity tomograms separately. Unfortunately there are some drawbacks with that strategy: 1. Skillful data processing procedures are required to separate both the PPand SS-reflections from the original data. The separation is done by FK filtering which usually contaminates the records with coherent noise. It also eliminates many useful parts of the records, such as the truncation of PP-reflections, and the PS-converted waves in the SS-reflections are unable to be eliminated. Consequently, the PSconversions will be treated as coherent noise in the inversion. 2. Scalar waveform inversion is used to separately invert both the Pand Stomograms. The elastic amplitudes must be corrected to match the amplitude distribution of acoustic wave propagation. This rough correction can distort the amplitude information in the original data and may result in an incorrect impedance reconstruction. In this report we apply a full elastic waveform inversion method to the pressure field data. By using a low frequency assumption, we analytically calculate the pressure field in the well from the hypothetical stress distribution on the wall of the well. The inversion method inverts both the Pand S-velocites at the same time to avoid massive data processing. 3 M E T H O D O L O G Y In this section we present the implementation of the general elastic waveform inversion (Zhou et al., 1994) for crosswell pressure field data. 3 . 1 F O R W A R D M O D E L I N G We only disscuss the situation that volume expansion sources and hydrophone receivers are used in the fluid filled source and receiver wells. The source generates the pressure that acts on the wall to generate seismic waves between the wells. Once the seismic waves reach the receiver well, the stresses on the wall generate the pressure in the receiver well which is recorded by the hydrophones. The modeling of seismic wave propagation within the source well can be neglected by inverting the equivalent source on the wall of the source well. The pressure field in the receiver well can be calculated from the stress components on the wall of the well by a low frequency assumption (White and Lessinger,

Quasi-random migration applied to 3D West Texas CDP data

The quasi-random migration (QM) method is tested on 3D seismic data from West Texas. Results show that the QM images, at 1/4 subsampling of the entire data set, are about the same quality as regularly migrated (RM) images obtained from a regular 1/4 subsampling of the original data. However, it appears that there are fewer artifacts in the QM images than in the regular images. At 1/8 subsampling the QM images have moderately better quality than the corresponding RM images. Previous studies suggested that the QM images should be of much higher quality than the regularly sampled images. Our field test results did not show this to be true because the source and receiver lines were spaced more than 1300 feet apart, and so did not allow for a good quasi-random sampling of the data.

Crosshole Elastic WTW Inversion of the McElroy Data

The authors apply the elastic wave equation traveltime and waveform inversion (elastic WTW) method to the McElroy crosshole data. These data are characterized by a well offset of 184 ft and a wide-band source wavelet (250--2,000 Hz). Numerical tests indicate that the following processing steps are necessary, but not sufficient, for successful waveform inversion: FK filtering of the upgoing and downgoing waves, FK-fan filter extraction of the PP and SS reflections, and balancing the amplitudes of the upgoing and downgoing reflections. To reduce the complexity of the data they use a divide and conquer strategy, i.e., extract the PP reflections and SS reflections, then invert each wave mode separately. Numerical results show that vertical spatial resolution of the WTW P-wave and S-wave tomograms are approximately 7--10 feet and 4 feet, respectively. This compares favorably to the 40--50 feet vertical resolution of the P-velocity tomogram obtained from the first arrival traveltime data. there is good to very good agreement between the sonic logs and the velocity from the WTW tomogram. These results demonstrate the high resolution Poisson ratio, S-velocity, and P-velocity tomograms can be extracted from crosshole data, and therefore can be used for lithological interpretation.

Elastic wave equation travel time and waveform inversion of crosshole seismic data

We apply the elastic wave equation traveltime and waveform inversion (elastic WTW) method to the McElroy crosshole data. These data are characterized by a well offset of 184 ft and a wide-band source wavelet (250 - 2000 Hz). Numerical tests indicate that the following processing steps are necessary, but not sufficient, for successful waveform inversion: FK filtering of the upgoing and downgoing waves, FK-fan filter extraction of the PP and SS reflections, and balancing the amplitudes of the upgoing and downgoing reflections. To reduce the complexity of the data we follow the divide and conquer strategy, i.e., extract the PP reflections and SS reflections, then invert each wave mode separately. Numerical results show that the vertical spatial resolution of the WTW P-wave and S-wave tomograms are approximately 7 - 10 feet and 4 feet, respectively. This compares favorably to the 40 - 50 feet vertical resolution of the P-velocity tomogram obtained from the first arrival traveltime data. There is good to very good agreement between the sonic logs and the velocity from the WTW tomogram. These preliminary results demonstrate that high resolution Poisson ratio, S- velocity, and P-velocity tomograms can be extracted from crosshole data, and therefore can be used for lithological interpretation.

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.