James W. Rector

Shear waves in acoustic anisotropic media

Acoustic transversely isotropic (TI) media are defined by artificially setting the shear‐wave velocity in the direction of symmetry axis, VS0, to zero. Contrary to conventional wisdom that equating VS0 = 0 eliminates shear waves, we demonstrate their presence and examine their properties. Specifically, we show that SV‐waves generally have finite nonzero phase and group velocities in acoustic TI media. In fact, these waves have been observed in full waveform modeling, but apparently they were not understood and labeled as numerical artifacts.Acoustic TI media are characterized by extreme, in some sense infinite strength of anisotropy. It makes the following unusual wave phenomena possible: (1) there are propagation directions, where the SV‐ray is orthogonal to the corresponding wavefront normal, (2) the SV‐wave whose ray propagates along the symmetry axis is polarized parallel to the P‐wave propagating in the same direction, (3) P‐wave singularities, that is, directions where P‐ and SV‐wave phase velocitie...

High-resolution crosswell imaging of a West Texas carbonate reservoir; Part 1, Project summary and interpretation

A carbon dioxide flood pilot is being conducted in a section of Chevron’s McElroy field in Crane County, west Texas. Prior to CO2 injection, two high‐frequency crosswell seismic profiles were recorded to investigate the use of seismic profiling for high‐resolution reservoir delineation and CO2 monitoring. These preinjection profiles provide the baseline for time‐lapse monitoring. Profile #1 was recorded between an injector well and an offset observation well at a nominal well‐to‐well distance of 184 ft (56 m). Profile #2 was recorded between a producing well and the observation well at a nominal distance of 600 ft (183 m). The combination of traveltime tomography and stacked CDP reflection amplitudes demonstrates how high‐frequency crosswell seismic data can be used to image both large and small scale heterogeneity between wells: Transmission traveltime tomography is used to image the large scale velocity variations; CDP reflection imaging is then used to image smaller scale impedance heterogeneities. The...

Permeability dependence of seismic amplitudes

Can permeability be determined from seismic data? This question has been around since Maurice Biot, working for Shell in the 1950s, introduced the idea that seismic waves induce fluid flow in saturated rocks due to fluid-pressure equilibration between the peaks and troughs of a compressional wave (or due to grain accelerations in the case of a shear wave). Biot (1956) established a frequency-dependent analytical relation between permeability and seismic attenuation. However, laboratory, sonic log, crosswell, VSP, and surface seismic have all demonstrated that Biots predictions often greatly underestimate the measured levels of attenuation—dramatically so for the lower-frequency measurements. Yet, if an unresolved link truly exists between seismic amplitudes and permeability, the potential benefit to the oil industry is enormous. For this reason, the Department of Energy (DOE) brought together 15 participants from industry, national laboratories, and universities to concentrate for two days on whether permeability information is conceivably contained in and retrievable from seismic data. The present article represents much of the workshop discussion (which took place 5–6 December 2001 in Berkeley, California), but is not strictly limited to it. Not all connections between hydrological and seismic properties are considered. Three-dimensional seismic images and time-lapse seismic monitoring are routinely used by reservoir engineers in constructing and constraining their reservoir model. Such imaging applications of seismic surveys to hydrological modeling are not discussed. Furthermore, in fractured reservoirs it is reasonable to postulate that any locally determined seismic anisotropy defines a symmetry class for the geologic material that must also be satisfied by the permeability tensor. Neither are such material-symmetry constraints discussed. The focus here is only on whether the permeability of the rocks through which seismic waves propagate directly influences the decay of the wave amplitudes with distance. Key to addressing this question is an up-to-date discussion of the likely attenuation …

A workshop examination of shallow seismic reflection surveying

In September 1996 the Office of Basic Energy Sciences of the U.S. Department of Energy (DOE) sponsored a research workshop in Berkeley, California, where approximately 20 participants analyzed the potential and limitations of near‐surface seismic‐reflection methods.

Radiation pattern and seismic waves generated by a working roller-cone drill bit

The seismic body wave radiation pattern of a working roller‐cone drill bit can be characterized by theoretical modeling and field data examples. Our model of drill‐bit signal generation is a pseudo‐random series of bit‐tooth impacts that create both axial forces and tangential torques about the borehole axis. Each drill tooth impact creates an extensional wave that travels up the drill string and body waves that radiate into the earth. The model predicts that P‐waves radiate primarily along the axis of the borehole, and shear waves radiate primarily perpendicular to the borehole axis. In a vertical hole, the largest P‐waves will be recorded directly above and below the drill bit; whereas, the largest shear waves will be recorded in a horizontal plane containing the drill bit. In a deviated borehole, the radiation patterns should be rotated by the inclination angle of the drill bit. This proposed seismic body wave radiation pattern is investigated with field data examples. The presence of the drill string ...

Characterization of resolution and uniqueness in crosswell direct-arrival traveltime tomography using the Fourier projection slice theorem

The process of acquiring a crosswell seismic direct‐arrival traveltime data set can be approximated by a series of truncated plane‐wave projections through an interwell slowness field. Using this approximation, the resolution and uniqueness of crosswell direct‐arrival traveltime tomograms can be characterized by invoking the Fourier projection slice theorem, which states that a plane‐wave projection through an object constitutes a slice of the object’s spatial spectrum. The limited vertical aperture of a crosswell survey introduces a small amount of nonuniqueness into the reconstructed tomogram by truncating the plane‐wave projection. By contrast, the limitations on angular aperture have a significant effect on resolution. The reconstructed tomogram is smeared primarily along the limiting projection angles, with the amount of smearing dependent upon the well spacing and the angular aperture. The amount of smearing was found to be inversely proportional to tan Δϕ, where Δϕ is the angular aperture illuminat...

High-resolution crosswell imaging of a west Texas carbonate reservoir: Part 4 - Reflection imaging

Reliable crosswell reflection imaging is a challenging task, even after the data have been wavefield-separated in the time domain. Residual, strong coherent noise is still present in the data. Stacking is complicated by the wide range of reflection incidence angles available for imaging. With wavelengths of a few feet, small misalignments as a result of velocity or geometric errors produce destructive interference and degrade the quality of the stacked image. We present an imaging sequence that addressed these complications and allowed us to produce high-quality stacked images for both P- and S-waves from a large-volume crosswell data set. A very good tie was achieved at both wells. Heterogeneities imaged from well to well included very thin beds [less than 5 ft (1.5 m) thick] within the reservoir, pinchouts, and a major angular unconformity-the Grayburg/San Andres-that could not be observed reliably with any other technique (log correlation, surface seismic imaging, or tomography). In fact, the produced crosswell reflection images exhibit dramatically higher resolution and continuity than the P-wave traveltime tomogram.

Crosswell traveltime tomography in three dimensions

Conventional crosswell direct-arrival traveltime tomography solves for velocity in a 2-D slice of the subsurface joining two wells. Many 3-D aspects of real crosswell surveys, including well deviations and out-of-well-plane structure, are ignored in 2-D models. We present a 3-D approach to crosswell tomography that is capable of handling severe well deviations and multiple-profile datasets. Three-dimensional pixelized models would be even more seriously underdetermined than the pixelized models that have been used in 2-D tomography. We, therefore, employ a thinly layered, vertically discontinuous 3-D velocity model that greatly reduces the number of model parameters. The layers are separated by 2-D interfaces represented as 2-D Chebyshev polynomials that are determined using a priori structural information and remain fixed in the traveltime inversion. The velocity in each layer is also represented as a 2-D Chebyshev polynomial. Unlike pixelized models that provide limited vertical resolution and may be overparameterized horizontally, this 3-D model provides vertical resolution comparable to the scale of wireline logs, and reduces the degrees of freedom in the horizontal parameterization to the expected in-line and out-of-well-plane horizontal resolution available in crosswell traveltime data. Ray tracing for the nonlinear traveltime inversion is performed in three dimensions. The 3-D tomography problem is regularized using penalty constraints with a continuation strategy that allows us to extrapolate the velocity field to a 3-D region containing the 2-D crosswell profile. Although this velocity field cannot be expected to be accurate throughout the 3-D region, it is at least as accurate as 2-D tomograms near the well plane of each 2-D crosswell profile. Futhermore, multiple-profile crosswell data can be inverted simultaneously to resolve better the 3-D distribution of velocity near the profiles. Our velocity parameterization is quite different from pixelized models, so resolution properties will be different. Using wave-modeled synthetic data, we find that near horizontal raypaths have the largest mismatch between ray-traced traveltimes and traveltimes estimated from the data. In conventional tomography, horizontal raypaths are essential for high vertical resolution. With our model, however, the highest resolution and most accurate inversions are achieved by excluding raypaths that travel nearly parallel to the geologic layering. We perform this exclusion in both a static and model-based manner. We apply our 3-D method to a multiple-profile crosswell survey at the Cymric oil field in California, an area of very steep structural dips and significant well trajectory deviations. Results of this multiple-profile 3-D tomography correlate very well with the independently-processed single profile results, with the advantage of an improved tie at the common well.

Imaging shallow objects and heterogeneities with scattered guided waves

Current surface seismic reflection techniques based on the common‐midpoint (CMP) reflection stacking method cannot be readily used to image small objects in the first few meters of a weathered layer. We discuss a seismic imaging method to detect such objects; it uses the first‐arrival (guided) wave, scattered by shallow heterogeneities and converted into scattered Rayleigh waves. These guided waves and Rayleigh waves are dominant in the shallow weathered layer and therefore might be suitable for shallow object imaging. We applied this method to a field data set and found that we could certainly image meter‐size objects up to about 3 m off to the side of a survey line consisting of vertical geophones. There are indications that cross‐line horizontal geophone data could be used to identify shallow objects up to 10 m offline in the same region.

Analysis and removal of multiply scattered tube waves

Because of irregularities in or near the borehole, vertical seismic profiling (VSP) or crosswell data can be contaminated with scattered tube waves. These can have a large amplitude and can interfere with weaker upcoming reflections, destroying their continuity. This type of organized noise cannot always be removed with filtering methods currently in use. We propose a method based on modeling the scattered tube‐wave field and then subtracting it from the total data set. We assume that the scattering occurs close to the borehole axis and therefore use a 1-D impedance function to characterize borehole irregularities. Estimation of this impedance function is one of the first steps. Our method also accounts for multiply scattered tube waves. We apply the method to an actual VSP data set and conclude that the continuity of reflected, upcoming events improves significantly in a washout zone.