bluuebunny/crossref_metadata_2025 huggingface dataset:
1-D seismic inversion of dual wavefield data: Part I, Nonuniqueness and stability
Authors: Hildebrand Steve T. , McMechan George A.
Published: October 2002

The inversion problem for determining seismic impedance is nonunique and nonstable because of limited recording aperture, data bandwidth, and data noise. For large reflection angles, small errors in the reflection coefficients give rise to arbitrarily large errors in the seismic impedance estimates. Spatial resolution of the seismic impedance response is controlled by the dominant wavelength corresponding to the source time wavelet; aperture limitations control the resolution of material impedance and interval velocity. Analysis of a linearization‐approximation approach shows that this method degenerates into a single‐parameter estimator for material impedance when using only small‐offset data and for velocity when using only far‐offset data. A nonlocal inversion method is introduced to estimate the material impedance and interval velocity by exploring interval velocity space and computing an associated variance estimate surface. Using this method, the resolution of the material impedance and compressional and shear interval velocities is shown to be poor in the elastic case because of a “valley” feature in the variance estimate surface; in the acoustic problem, resolution of the material impedance and interval velocity is excellent.
On the Influence of 3-D structures in the Interpretation of transient electromagnetic sounding data
Authors: Goldman Mark , Tabarovsky Leonty , Rabinovich Michael
Published: October 2002

The limitations of a standard 1-D inversion applied to multidimensional (synthetic) data are investigated. Simple correction procedures for interpreting field data distorted by 3-D structures are suggested. Two different transmitter/receiver configurations of the transient electromagnetic (TEM) sounding method are examined: a central loop configuration for the near zone (sometimes called short offset) and a fixed transmitter/moving receiver configuration for the far zone (long offset). The 3-D models are structural depressions and highs in both resistive and conductive basements. The fixed transmitter (grounded dipole) in the long offset TEM configuration is located at a distance significantly greater than both the size and depth of the structure. In all cases, 1-D interpretation of the central loop soundings recovers geoelectric parameters of the section with good reliability, although fictitious layers may appear near vertical boundaries. The 1-D interpretation of long offset soundings does not, in most cases, show the actual structures. The data along various profiles are interpreted in terms of a two‐layer model without the structures. In some cases 1-D interpretation does show the structure, but the errors are far greater than those obtained in the inversion of central loop soundings. In all cases considered, the distortion of central loop soundings caused by 3-D effects is systematic and could, therefore, be corrected by simple procedures. These procedures permit interpretation of real field data that were previously abandoned owing to the strong distortions by lateral inhomogeneities.
Borehole transmission tomography for velocity plus statics
Authors: Squires Livia J. , Stoffa Paul L. , Cambois Guillaume
Published: October 2002

The accuracy of velocity tomograms reconstructed from borehole transmission traveltime data is highly sensitive to traveltime statics. We present a least‐squares tomography algorithm that includes a traveltime static term. The algorithm solves for both the velocity field and the traveltime statics simultaneously. This enables us to separate traveltime signal from traveltime noise, reducing the tomographic velocity artifacts caused by the statics. The incorporation of a priori constraints on the poorly determined spectral components of the velocity field further improves accuracy by reducing velocity artifacts as a result of uneven ray coverage. Application of the algorithm to numerical crosswell data results in velocity and statics’ estimates that are accurate to within 1 percent. Application of the algorithm to Exxon’s Friendswood tomography data results in velocity and statics’ estimates that correlate with independent data.
Finite‐difference and frequency‐wavenumber modeling of seismic monopole sources and receivers in fluid‐filled boreholes
Authors: Kurkjian A. L. , Coates R. T. , White J. E. , Schmidt H.
Published: October 2002

In borehole seismic experiments the presence of the borehole has a significant effect on observations. Unfortunately, including boreholes explicitly in modeling schemes excludes the use of some methods (e.g., frequency‐wavenumber) and adds prohibitively to the cost of others (e.g., finite difference). To overcome this problem, we use the concept of an effective source/receiver array to replace the explicit representation of the borehole by a distributed seismic source/receiver. This method mimics the presence of the borehole at seismic frequencies under a wide variety of conditions without adding a significant computational cost. It includes the effects of dispersive and attenuative tube wave propagation, the generation of secondary sources at interfaces and caliper changes, and the generation of conical waves in low‐velocity layers. Comparison with a finite‐difference scheme with an explicit borehole representation validates the approach. The modeling method applied to a continuity logging geometry demonstrates that the presence of guided waves does not uniquely imply bed connectivity. Results for a single‐well imaging geometry emphasize the dominance of the tube wave in the hydrophone synthetics and demonstrates the necessity of using clamped geophones for single‐well experiments. The concept of an effective source/receiver array is an efficient way of including borehole phenomena in seismic modeling methods at minimal extra computational cost.
A note on 2-D Hartley transform
Authors: Mohan N. L. , Babu L. Anand
Published: October 2002

In recent years the application of the Hartley transform, originally introduced by Hartley (1942), has gained importance in seismic signal processing and interpretation (Saatcilar et al., 1990, 1992). The Hartley transform is similar to the Fourier transform but is computationally much faster than even the fast Fourier transform (Bracewell, 1983; Bracewell et al., 1986; Sorensen et al., 1985; Pei and Wu, 1985; Duhamel and Vetterli, 1987; Zhou, 1992). Surprisingly, we have not seen a clear definition of the 2-D Hartley transform in the published literature.
On a nonlinear autoregressive method applied to geophysical signals
Authors: Bracalari Mauro , Salusti Ettore
Published: October 2002

A nonlinear second‐order autoregressive analysis of time varying signals leads to simple inhomogeneous linear algebraic equations. This method was applied to the analysis of three types of geophysical signals: the fluctuation of sea level at Venice (Italy), “harmonic tremors” at Stromboli (Eolian Islands), and the earth’s crustal motion at L’Aquila (Italy). For more regular motions (earth’s crustal motion), linear and nonlinear methods give essentially equivalent results. Compared to the customary linear autoregressive method, our method more accurately predicts nonlinearities whenever there is a sudden increase of the signal amplitude, such as sea level fluctuations and seismic tremors.
On: “Computing the Fourier transform in geophysics with the transform decomposition DFT,” by Michael J. Reed, Hung V. Nguyen, and Ronald E. Chambers (November 1993 GEOPHYSICS, 58, p. 1701–1709).
Authors: Lichman Eugene
Published: October 2002

The authors recently presented the illustration of the frequency spectrum computation technique which allows a reduction of the overall amount of computations (compared to a conventional FFT method) when the input time‐domain sequence contains significant number of zero values.
Finite differences on minimal grids
Authors: Magnier Sophie‐Adélade , Mora Peter , Tarantola Albert
Published: October 2002

Conventional approximations to space derivatives by finite differences use orthogonal grids. To compute second‐order space derivatives in a given direction, two points are used. Thus, 2N points are required in a space of dimension N; however, a centered finite‐difference approximation to a second‐order derivative may be obtained using only three points in 2-D (the vertices of a triangle), four points in 3-D (the vertices of a tetrahedron), and in general, N + 1 points in a space of dimension N. A grid using N + 1 points to compute derivatives is called minimal. The use of minimal grids does not introduce any complication in programming and suppresses some artifacts of the nonminimal grids. For instance, the well‐known decoupling between different subgrids for isotropic elastic media does not happen when using minimal grids because all the components of a given tensor (e.g., displacement or stress) are known at the same points. Some numerical tests in 2-D show that the propagation of waves is as accurate as when performed with conventional grids. Although this method may have less intrinsic anisotropies than the conventional method, no attempt has yet been made to obtain a quantitative estimation.
A DIRECT READING PHASE SHIFT METER
Authors: Eisler Joseph D.
Published: October 2002

A direct reading phase shift meter is described which is entirely electronic. The meter is capable of continuously indicating phase shift to within 1° in the frequency range between 10 and 1000 cps., has calibration independent of supply voltages, and is portable.
SEISMIC VELOCITIES IN THE SOUTHEASTERN SAN JOAQUIN VALLEY OF CALIFORNIA
Authors: Stulken E. J.
Published: October 2002

For the first time, seismic velocity measurements from well surveys have been made intensively enough to justify an analysis of the velocity field in an entire area instead of just along lines between wells. Maps are drawn showing velocity changes in the southeastern San Joaquin Valley of California. A portion of the valley floor in the neighborhood of Bakersfield, about twenty‐five miles wide and thirty‐five miles long, was chosen for study because of the number of wells in the area whose velocities were known. Differences in average velocity of 1700 feet per second for a constant depth are observed, and horizontal velocity gradients averaging over 100 feet per second per mile are computed. Correction schemes for the adjustment of seismic data are suggested, and correction maps shown. An attempt is made to establish a connection between stratigraphy and seismic velocity. Comparative study of the logs of wells and the velocities observed in them yields certain qualitative conclusions, but attempts to express the relation in a quantitative way fail.
PROSPECTING EFFECTIVENESS
Authors: Rosaire Esme Eugene
Published: October 2002

The overall prospecting effectiveness or power of any given method is made up of four component parts. Three of these tend to increase with successful use and the passage of time. These are (a), the operating effectiveness, which, referring to getting the data, is based on the cost of field operations in time and money; (b), the technical effectiveness, which, referring to the quality of the data, is measured by the magnitude of the observational errors; and, (c), the resolving effectiveness, which, referring to the interpretation of the data, is measured by the ability to translate the data into terms of economic significance. The fourth component tends to decrease with successful use and the passage of time, and is, (d), the finding effectiveness, which is determined by the ratio of the magnitudes of findable anomalies to the magnitudes of the current observational errors. At any given time, the overall prospecting effectiveness of a given method is determined by that particular component which displays the minimum effectiveness. In the major petroleum producing provinces of the U.S.A., negligible or decreasing structure finding effectiveness is displayed by all of the successfully used structural prospecting methods with one exception, the drill, the overall structural prospecting power of which is limited by a low operating effectiveness. However, these methods with existing low structural finding powers, surface geology, gravity methods, and seismic methods, display a more than appreciable finding effectiveness for anomalies which cannot be readily interpreted in terms of structure. This situation indicates that the existing low overall efficacy of these various methods is determined not so much by a low absolute finding effectiveness as by a resolving power which is low because of structural inhibitions upon interpretation. The sedimentary hydrocarbon prospecting method was introduced upon a theoretical basis which involved the depth of the source and the postulate of local lateral homogeneity, but did not attain any measure of overall prospecting potency until its interpretation technique was relieved of such purely theoretical inhibitions. Subsequent development has shown that similar limitations upon refraction interpretation were responsible for the collapse of that method in 1930 after the method had displayed marked prospecting effectiveness for shallow high relief structure. Attention is called to the possibility that the removal of similar inhibitions also may result in a similar increase in resolving power for other methods which today display a low structure finding effectiveness, and thus lead to their renaissance because of their thereby increased overall prospecting effectiveness.
Seismic anisotropy of fractured rock
Authors: Schoenberg Michael , Sayers Colin M.
Published: October 2002

A simple method for including the effects of geologically realistic fractures on the seismic propagation through fractured rocks can be obtained by writing the effective compliance tensor of the fractured rock as the sum of the compliance tensor of the unfractured background rock and the compliance tensors for each set of parallel fractures or aligned fractures. The compliance tensor of each fracture set is derivable from a second rank fracture compliance tensor. For a rotationally symmetric set of fractures, the fracture compliance tensor depends on only two fracture compliances, one controlling fracture compliance normal, the other, tangential, to the plane of the fractures. The stiffness tensor, which is more useful in the consideration of elastic wave propagation through rocks, can then be obtained by inversion. The components of the excess fracture compliance tensor represent the maximum amount of information that can be obtained from seismic data. If the background rock is isotropic and the normal and shear compliance of each fracture are equal, although different from those of other fractures, the effective elastic behavior of the fractured rock is orthorhombic for any orientation distribution of fractures. A comparison of the theory with recent ultrasonic experiments on a simulated fractured medium shows near equality of the normal and shear compliance for the case of air‐filled fractures.
Amplitude responses of thin beds: Sinusoidal approximation versus Ricker approximation
Authors: Chung Hai‐Man , Lawton Don C.
Published: October 2002

The amplitude response of a thin bed with arbitrary upper and lower normal incidence reflection coefficients is studied. Two analytical expressions for the normal incidence amplitude response as a function of the thickness are derived and are both valid for weak reflectivities and for thicknesses below [Formula: see text], where [Formula: see text] is the dominant wavelength. The first expression is based on the substitution of a cosine wave for the source wavelet, and the second is based directly on the analytical expression for a Ricker wavelet. The results calculated from these two expressions are compared to numerical modeling results for a Ricker wavelet for several models. We found that the differences between the two expressions are small, and both are good approximations. Above the [Formula: see text] thickness, the percentage differences increase rapidly for both expressions, implying that the thin‐bed assumptions in both derivations break down rapidly beyond the [Formula: see text] thickness. Below the [Formula: see text] thickness, except in the case where the two reflection coefficients are equal in magnitude but opposite in sign, the amplitude dependence on the thickness is nonlinear.
Imaging of fracture zones in the Finnsjön area, central Sweden, using the seismic reflection method
Authors: Juhlin Christopher
Published: October 2002

In 1987 the Swedish Nuclear Fuel and Waste Management Co. (SKB) funded the shooting of a 1.7-km long, high‐resolution seismic profile over the Finnsjön study site using a 60‐channel acquisition system with a shotpoint and geophone spacing of 10 m. The site is located about 140 km north of Stockholm and the host rocks are mainly granodioritic. The main objective of the profile was to image a known fracture zone with high hydraulic conductivity dipping gently to the west at depths of 100 to 400 m. The initial processing of the data failed to image this fracture zone. However, a steeply dipping reflector was imaged indicating the field data were of adequate quality and that the problem lay in the processing. These data have now been reprocessed and a clear image of the gently dipping zone has been obtained. In addition, several other reflectors were imaged in the reprocessed section, both gently and steeply dipping ones. Correlations with borehole data indicate that the origin of these reflections are also fracture zones. The improvement over the previous processing is caused mainly by (1) refraction statics, (2) choice of frequency band, (3) F-K filtering, and (4) velocity analyses. In addition to reprocessing the data, some further analyses were done including simulation of acquisition using only the near‐offset channels (channels 1–30) and the far‐offset channels (channels 31–60), and determining the damping factor Q in the upper few hundred meters based upon the amplitude decay of the first arrivals. The data acquisition simulation shows the far‐offset contribution to be significant even for shallow reflectors in this area, contrary to what may be expected. A Q value of 10, determined from observed amplitude decay rates, agrees well with theoretical ones assuming plane wave propagation in an attenuating medium.
Constitutive model and wave equations for linear, viscoelastic, anisotropic media
Authors: Carcione Jose M.
Published: October 2002

Rocks are far from being isotropic and elastic. Such simplifications in modeling the seismic response of real geological structures may lead to misinterpretations, or even worse, to overlooking useful information. It is useless to develop highly accurate modeling algorithms or to naively use amplitude information in inversion processes if the stress‐strain relations are based on simplified rheologies. Thus, an accurate description of wave propagation requires a rheology that accounts for the anisotropic and anelastic behavior of rocks. This work presents a new constitutive relation and the corresponding time‐domain wave equation to model wave propagation in inhomogeneous anisotropic and dissipative media. The rheological equation includes the generalized Hooke’s law and Boltzmann’s superposition principle to account for anelasticity. The attenuation properties in different directions, associated with the principal axes of the medium, are controlled by four relaxation functions of viscoelastic type. A dissipation model that is consistent with rock properties is the general standard linear solid. This is based on a spectrum of relaxation mechanisms and is suitable for wavefield calculations in the time domain. One relaxation function describes the anelastic properties of the quasi‐dilatational mode and the other three model the anelastic properties of the shear modes. The convolutional relations are avoided by introducing memory variables, six for each dissipation mechanism in the 3-D case, two for the generalized SH‐wave equation, and three for the qP − qSV wave equation. Two‐dimensional wave equations apply to monoclinic and higher symmetries. A plane analysis derives expressions for the phase velocity, slowness, attenuation factor, quality factor and energy velocity (wavefront) for homogeneous viscoelastic waves. The analysis shows that the directional properties of the attenuation strongly depend on the values of the elasticities. In addition, the displacement formulation of the 3-D wave equation is solved in the time domain by a spectral technique based on the Fourier method. The examples show simulations in a transversely‐isotropic clayshale and phenolic (orthorhombic symmetry).
High‐resolution crosswell imaging of a west Texas carbonate reservoir: Part 2—Wavefield modeling and analysis
Authors: Van Schaack Mark , Harris Jerry M. , Rector James W. , Lazaratos Spyros
Published: October 2002

We have collected low‐noise crosswell data in a high‐velocity carbonate environment with a spatial sampling interval of 2.5 ft (0.76 m). This sampling reveals a variety of coherent events not previously identified in coarsely sampled gathers. Nearly every event in our field record can be explained using simple approximations for the geology, source, and receivers without accounting for the presence of the boreholes. We have used synthetic records as a guide in a moveout‐based analysis of the field data. Our analysis shows that much of the full wavefield energy, i.e., scattered waves, in our data are converted modes arising from the direct P‐ and S‐waves. This observation suggests that for crosswell reflection imaging, the focus of acquisition and wavefield separation techniques should be on the suppression of once‐converted modes.
Crosswell seismic study in a seismically poor data area
Authors: Lee Doo Sung , Lazaratos Spyros K. , Walden Arthur F.
Published: October 2002

Crosswell traveltime tomography and reflection imaging assisted a reservoir characterization effort in an area of poor‐quality surface seismic data. Both the tomogram and the reflection image proved useful in the description of the fractured reservoir interval. The velocity tomogram shows that: (1) the vertical resolution was sufficient to identify and characterize a 50-ft (15 m) thick lithological unit of brittle rocks, which was the most important interval for the characterization of this fractured reservoir; (2) different lithological units present sufficient velocity contrast to be identifiable on the tomogram; and (3) the tomogram velocity is higher than the sonic velocity implying that the rocks in the interwell area may be anisotropic. Correlation of the lithologies with the tomogram implies that the major controlling factor of the anisotropy is the shale content in the formation. The crosswell reflection image, generated by a VSP‐CDP mapping technique, defines the fractured reservoir interval in terms of high‐frequency reflections. The lateral resolution of this reflection image is difficult to define because the survey coverage is nonuniform as a result of the receiver spacing being much larger than the source spacing. The dips of the reflections do not quite agree with the dips that are inferred from well log ties. We believe this disagreement is a result of the anisotropy of the medium and the use of an isotropic imaging algorithm. Improved data acquisition (finer spatial sampling) that would allow better wavefield separation techniques to be used would probably have produced higher quality crosswell reflection images.
Crosswell electromagnetic tomography: System design considerations and field results
Authors: Wilt M. J. , Alumbaugh D. L. , Morrison H. F. , Becker A. , Lee K. H. , Deszcz‐Pan M.
Published: October 2002

Electrical conductivity is an important petroleum reservoir parameter because of its sensitivity to porosity, pore fluid type, and saturation. Although induction logs are widely used to obtain the conductivity near boreholes, the poor resolution offered by surface‐based electrical and electromagnetic (EM) field systems has thus far limited obtaining this information in the region between boreholes. Low‐frequency crosswell EM offers the promise of providing subsurface conductivity information at a much higher resolution than was previously possible. Researchers at Lawrence Livermore National Lab (LLNL) and Lawrence Berkeley Laboratories (LBL), together with an industrial consortium, recently began a program to conduct low‐frequency crosswell EM surveys and develop suitable inversion techniques for interpreting the data. In developing the field instrumentation we used off‐the‐shelf components whenever possible, but custom‐designed induction coil transmitters and receivers were built for the field experiments. The assembled field system has adequate power for moderate to high‐resolution imaging, using boreholes spaced up to 500 m apart. The initial field experiment was undertaken in flat lying terrain at the British Petroleum test site in Devine, Texas. Using wells spaced 100 m apart, we collected a complete crosswell EM data set encompassing a 30 m thick, 10 ohm‐m limestone layer at a depth of 600 m. The resulting profiles were repeatable to within 1% and showed an excellent sensitivity to the layered structure, closely matching the borehole induction resisitivity log. At the UC Richmond field station, crosswell EM measurements were made to track an injected slug of salt water. Conductivity images of data collected before and after injection showed a clear anomaly as a result of the salt water plume and indicated that the plume had migrated in a northerly direction from the injection borehole.
On: “3-D true‐amplitude finite‐offset migration,” by J. Schleicher, M. Tygel, and P. Hubral (August 1993 GEOPHYSICS, 58, 1112–1126).
Authors: Vermeer Gijs J. O.
Published: October 2002

In a very interesting paper Schleicher et al. discuss true‐amplitude prestack depth migration of single‐fold subsets of various 3-D geometries. In the following, I would like to make some remarks, and I would like to present other candidates for inclusion in the list of seismic measurement configurations.
An examination of the relationship between time‐domain integral chargeability and the Cole‐Cole impedance model
Authors: Duckworth Kenneth , Calvert H. Thomas
Published: October 2002

The Cole‐Cole impedance model developed in Pelton et al. (1978) for describing the induced polarization (IP) phenomenon has proven to be useful for characterizing the electrical properties of rocks. The model characterizes the impedance Z(ω) of a rock using only four parameters as follows [Formula: see text] where [Formula: see text] is the DC resistivity, m is the dimensionless chargeability, τ is the time constant, c is the frequency dependence, and [Formula: see text] [Formula: see text]
The effect of steam quality on the electrical behavior of steam‐flooded sands: A laboratory study
Authors: Butler David B. , Knight Rosemary J.
Published: October 2002

Laboratory measurements of the effects of steam injection on the electrical conductivity of sands can aid in the interpretation of electrical surveys used to monitor subsurface steam‐injection projects. The effect of variations in injected steam quality was measured in the experiments presented here. The injection of low‐quality steam, boiled from a 0.01 mol/L NaCl solution, into clean sand saturated with 0.01 mol/L NaCl, resulted in a net decrease in conductivity and a constant equilibrium conductivity in the steam zone. The injection of high‐quality steam, using the same saturating and injection salinities, caused the conductivity to first drop to a minimum and then to increase to an equilibrium value similar to that seen in the low‐quality injection. The local conductivity minimum deepened with time and traveled with the steam front. The appearance of the conductivity minimum at the steam front can be attributed to the formation of a dilution bank, which temporarily decreases the local salinity. The extent of the dilution increases with time, resulting in the decrease of the conductivity over time. The conductivity then increases as injected salt moves through the sand. The steam quality controls the appearance of this minimum because it determines the relative speeds of the steam front and the steam liquid: a minimum will not occur if the steam front moves more slowly than the steam liquid.
Geophysical prospecting for petroleum in marine carbonate areas of the lower Yangtze region of southern China
Authors: Deng Dumming , Ou Qingxian
Published: October 2002

The lower Yangtze region extends over the Jiangsu Province in eastern China. Most of the region is a huge alluvial plain formed by the delta of the mighty Yangtze River. Beneath the alluvial plain, thick marine carbonates of late Sinian to Middle Triassic age make up a substantial portion of the subsurface sediments of southern China. After deposition of the thick carbonates, this region was subjected to a stage of deformation and extensive erosion. During the Mesozoic and Cenozoic time intervals, clastic deposits formed a continental basin. In the past, most of the petroleum exploration in the region targeted the structures in the continental basins, and some minor oil fields were found. Marine carbonate formations in this region are expected to be more promising for petroleum exploration. Seismic surveys aimed at identifying carbonate structures in this region show that the subsurface structures caused by intense deformation are complex. Structural complexity and extensive erosion have made it difficult to obtain reliable seismic data to resolve the geology of the area. Some new techniques, including wide‐line profiling and 3-D seismic acquisition, along with integrated regional profiles, have overcome some of the difficulties in recent years and significant advances have been made.
Investigating the resolution of IP arrays using inverse theory
Authors: Beard Les P. , Tripp Alan C.
Published: October 2002

Using a fast 2-D inverse solution, we examined the resolution of different resistivity/IP arrays using noisy synthetic data subject to minimum structure inversion. We compared estimated models from inversions of data from the dipole‐dipole, pole‐dipole, and pole‐pole arrays over (1) a dipping, polarizable conductor, (2) two proximate conductive, polarizable bodies, (3) a polarizable conductor beneath conductive overburden, and (4) a thin, resistive, polarizable dike. The estimated resistivity and polarizability models obtained from inversion of the dipole‐dipole data were usually similar to the pole‐dipole estimated models. In the cases examined, the estimated models from the pole‐pole data were more poorly resolved than the models from the other arrays. If pole‐pole resistivity data contain even a fraction of a percent of Gaussian noise, the transformation of such data through superposition to equivalent data of other array types may be considerably distorted, and significant information can be lost using the pole‐pole array. Though the gradient array is reputed to be more sensitive to dip than other arrays, it evidently contains little information on dip that does not also appear in dipole‐dipole data, for joint inversion of dipole‐dipole and gradient array data yields models virtually identical to those obtained from inversion of dipole‐dipole data alone.
A statistical methodology for deriving reservoir properties from seismic data
Authors: Fournier Frédérique , Derain Jean‐François
Published: October 2002

The use of seismic data to better constrain the reservoir model between wells has become an important goal for seismic interpretation. We propose a methodology for deriving soft geologic information from seismic data and discuss its application through a case study in offshore Congo. The methodology combines seismic facies analysis and statistical calibration techniques applied to seismic attributes characterizing the traces at the reservoir level. We built statistical relationships between seismic attributes and reservoir properties from a calibration population consisting of wells and their adjacent traces. The correlation studies are based on the canonical correlation analysis technique, while the statistical model comes from a multivariate regression between the canonical seismic variables and the reservoir properties, whenever they are predictable. In the case study, we predicted estimates and associated uncertainties on the lithofacies thicknesses cumulated over the reservoir interval from the seismic information. We carried out a seismic facies identification and compared the geological prediction results in the cases of a calibration on the whole data set and a calibration done independently on the traces (and wells) related to each seismic facies. The later approach produces a significant improvement in the geological estimation from the seismic information, mainly because the large scale geological variations (and associated seismic ones) over the field can be accounted for.
Gaussian beam depth migration for anisotropic media
Authors: Alkhalifah Tariq
Published: October 2002

Gaussian beam migration (GBM), as it is implemented today, efficiently handles isotropic inhomogeneous media. The approach is based on the solution of the wave equation in ray‐centered coordinates. Here, I extend the method to work for 2-D migration in generally anisotropic inhomogeneous media. Extension of the Gaussian‐beam method from isotropic to anisotropic media involves modification of the kinematics and dynamics in the required ray tracing. While the accuracy of the paraxial expansion for anisotropic media is comparable to that for isotropic media, ray tracing in anisotropic media is much slower than that in isotropic media. However, because ray tracing is just a small portion of the computation in GBM, the increased computational effort in general anisotropic GBM is typically only about 40%. Application of this method to synthetic examples shows successful migration in inhomogeneous, transversely isotropic media for reflector dips up to and beyond 90°. Further applications to synthetic data of layered anisotropic media show the importance of applying the proper smoothing to the velocity field used in the migration. Also, tests with synthetic data show that the quality of anisotropic migration of steep events in a medium with velocity increasing with depth is much more sensitive to the Thomsen anisotropy parameter ε than to the parameter δ. Thus, a good estimate of ε is needed to apply anisotropic migration with confidence.
Prestack depth migration with compensation for absorption and dispersion
Authors: Mittet Rune , Sollie Roger , Hokstad Ketil
Published: October 2002

In prestack depth migration using explicit extrapolators, the attenuation and dispersion of the seismic wave has been neglected so far. We present a method for accommodating absorption and dispersion effects in depth migration schemes. Extrapolation operators that compensate for absorption and dispersion are designed using an optimization algorithm. The design criterion is that the wavenumber response of the operator should equal the true extrapolator. Both phase velocity and absorption macro models are used in the wavefield extrapolation. In a model with medium to high absorption, the images obtained are superior to those obtained using extrapolators without compensation for absorption.
Estimation of anisotropy and anisotropic 3-D prestack depth migration, offshore Zaire
Authors: Ball Greg
Published: October 2002

Chevron (operator), Teikoku Oil, and Unocal hold the offshore Zaire concession, West Africa. Recently, Unocal performed an anisotropic 3-D prestack depth migration in an attempt to optimally image tilted fault blocks in the presalt section. Depth migration was required because large‐displacement faults juxtaposed a high‐velocity massive carbonate and a low‐velocity marl. Large compressional‐wave anisotropy caused by thin layering was inferred for most of the depth section. Evidence on the nature and magnitude of the anisotropy came from comparing stacking velocities with well velocities, analyzing a multioffset vertical seismic profile (VSP), thin‐layer modeling in the massive carbonate using well log data, and rock physics laboratory velocity measurements on core from the marl. The subsurface was characterized as being locally transversely isotropic and the Thomsen parameters were used to describe the anisotropy. This required that five parameters be specified at each subsurface location to represent the compressional‐wave 3-D velocity field. The observed anisotropy deviated far from the elliptical condition, and modeling indicated that isotropic migration would exhibit misfocusing and mispositioning of events, and its quality would be dip‐dependent. The anisotropic migration was performed using Kirchhoff summation for which the traveltimes were determined using a finite‐difference scheme. Interpreted horizons in the migrated depth section accurately tied well depths.
On: “The application of TEM to Cyprus‐type massive sulfide exploration in Cyprus,” by Nick J. Cooper and Roland Swift (February 1994 GEOPHYSICS, 59, p. 202–214).
Authors: Webster Steve
Published: October 2002

Though I concur with most of the authors’ comments and procedure, I must disagree with the sweeping conclusion “it is unlikely that a Cyprus‐type deposit could be detected using TEM alone.” I realize this quote is somewhat out of context, but others may also read the statement that way. It was not mentioned by the authors that these deposits may occur in different electrical environments than their study area and, thus, be readily observed using TEM techniques.
Efficient computation of apparent resistivity curves for depth profiling of a layered earth
Authors: Das Umesh C. , de Hoop Adrianus T.
Published: October 2002

The problem of computing the electrical potential as a result of a direct current electric source in a layered earth is reformulated to avoid instability in the numerical computation that may occur with the standard propagator matrix formalism described in a number of textbooks. The present spectral formalism involves constituents that contain only exponential functions with nonpositive arguments. The vertical spectral input admittances at the interface levels up to the source level are calculated recursively, starting at the uppermost and lowermost interfaces of the layered earth. These admittances at the source level are then used to compute the electrical voltage at the source level. With the known voltage and the admittances at the source level, the spectral amplitudes at the source level are known. Computation of the amplitudes at the other interfaces is, progressively, carried out by expressing the amplitudes at any interface above the source level in terms of the amplitude on the interface just below it and expressing the amplitudes at any interface below the source level in terms of the amplitude on the interface just above it. This results in an efficient scheme for computing electrical potential in any arbitrary depth levels (required for imaging subsurface conductivity). We simulate single‐borehole and hole‐to‐hole experiments. Neglecting the influence of the boreholes, we consider a plane layered earth model in which point electrodes along a vertical line (source line) inject and extract a stationary electric current, and point electrodes either along the source line or along another vertical line (receiver line) measure a potential difference. From the potential measurements, apparent resistivities are computed along the vertical lines.
Shallow seismic investigation of a site with poor reflection quality
Authors: Jeng Yih
Published: October 2002

A shallow seismic reflection experiment was performed on a construction site to determine the feasibility of using reflection seismology to investigate the shallow structure in a weathered sand‐gravel interlayered zone that was known to be a poor transmission of high‐frequency seismic energy. Field‐recording parameters were designed to fit the limited space of the urban construction survey area. A 7 kg sledgehammer was used to generate P‐waves and SH‐waves. Single 100 Hz geophones were deployed at 1.0 m/0.5 m group intervals, and 200/100-Hz low‐cut filters were applied prior to A to D conversion to attenuate ground roll. For SH‐wave reflections, single 14 Hz geophones and a 70-Hz low‐cut filter on the seismograph were used. The dominant frequency bands ranged from 33 to 275 Hz and were centered around 110 Hz for P‐waves. Lower dominant frequency bands 20 to 160 Hz with a dominant frequency of around 85 Hz were observed on SH‐wave records. Four seismic lines, three P‐wave recordings and one SH‐wave recording, using different sets of recording parameters and an appropriate seismic‐wave generation method produced reflections from varying depth ranges and at different resolutions. The results show that the techniques employed in this experiment may resolve the structure of a site with poor reflection quality. An f-k dip filtering and deconvolution were necessary in processing the reflection data to eliminate various types of unwanted energy. The seismic interpretations in this study were verified by drilling and by a nearby excavation.
Frequency‐dependent Q‐estimation of Love‐type channel waves and the application of Q‐correction to seismograms
Authors: Li Xiao‐Ping , Schott Wolfgang , Rüter Horst
Published: October 2002

We present the absorption dispersion relation of Love‐type channel waves for a simple, symmetric, homogenous, three‐layered, linear elastic model assuming that the quality factors of coal [Formula: see text] and country rock [Formula: see text] are constant. We introduce complex propagation functions into the known dispersion relation describing most of the properties of the Love‐ type channel waves. The complex dispersion relation is expanded into power series of [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] factor of the Love‐type channel wave). The real part of the ensuing dispersion relation gives the usual dispersion relation. The imaginary part yields the frequency relation between the quality factor of Love‐type channel waves and the constant quality factors of coal and rock. In this case, [Formula: see text] depends on the frequency because the phase velocity is a function of frequency. Therefore, the attenuation coefficient is a nonlinear function of frequency. The analysis of the analytical result shows that at high frequencies the Love‐type channel wave energy is completely propagating inside the coal seam, and hence its propagation is determined by the physical properties of the coal alone. As the frequency approaches zero, the Love‐type channel wave energy is completely propagating in the rock, since the thickness of the coal is small compared to the wavelength of the channel wave, and hence the channel wave does not “see” the coal seam. The spectral ratio method is used to estimate the frequency‐dependent quality factor [Formula: see text] of Love‐type channel waves. This technique is demonstrated by applying it first to synthetic data and then to data of a well‐designed transmission survey. Finally, we use the estimated [Formula: see text] to derive an inverse Q‐operator and apply it for Q‐correction to both data sets.
Beyond ray tomography: Wavepaths and Fresnel volumes
Authors: Vasco Don W. , Peterson John E. , Majer Ernest L.
Published: October 2002

Two techniques that account for the band‐limited nature of seismic data are incorporated into tomographic traveltime inversion schemes. The first technique, the wavepath algorithm, is based upon the wave equation, the Born approximation, and an adjoint method for computing Frechet derivatives. Computation of a single wavepath requires the forward propagation of the seismic wavefield, as well as the reverse propagation of a residual wavefield. The second technique, the Fresnel volume approach, is based upon the paraxial ray approximation. The Fresnel volume algorithm requires little more computation than does conventional ray tracing and an order of magnitude less computer time than our calculation of wavepaths. When the Fresnel volume sensitivity functions are normalized by the area of the Fresnel ellipse perpendicular to the ray, the sensitivity estimates are very similar to the wavepaths. In particular, there is heightened sensitivity to velocity structure near the source and receiver locations. The normalization by the Fresnel ellipse area is necessary to ensure ray theoretical results in the limit of infinite frequency. Tomographic inversion based upon wavepaths or Fresnel volumes is more appropriate when considering the arrival time of the peak of the initial pulse rather than the first‐arrival time. Furthermore, using the traveltime of the peak instead of the first‐arrival time reduces the bias of tomograms to high velocity anomalies. The raypath, wavepath, and Fresnel volume techniques were applied to a set of cross‐borehole traveltime observations gathered at the Grimsel Rock Laboratory. All methods imaged a low velocity fracture zone in the granitic site, in agreement with independent well information. Estimates of model parameter resolution are similar for the wavepath and Fresnel volume schemes. The source‐receiver regions are the most well resolved areas. However, the model parameter resolution computed using a conventional ray‐based formalism is more evenly distributed over the cross‐borehole area.
1-D layered media: Part 1, 3-D elastic modeling
Authors: Jurado Fabrice , Cuer Michel , Richard Vincent
Published: October 2002

The growing importance of prestack amplitude analysis requires the development of accurate and fast full‐wave elastic 3-D modeling algorithms for guiding and checking the interpretation of seismic data as well as for seismic inversion. The approach we propose in this paper is restricted to horizontally layered elastic media. First, a set of 1-D equations is obtained by direct Hankel transform of the equations of motion with respect to the horizontal variable. These equations of motion are standard except that we use an appropriate change of variables. For each horizontal wavenumber k, the 1-D equations are solved numerically using a second‐order‐centered, finite‐difference scheme on a grid system staggered in space and time. Stresses and velocities are obtained by an inverse Hankel transform with the Candel algorithm. This method is at least two times more efficient than conventional second‐order, finite‐difference schemes in the (r, z, t) domain. In addition, the method can be used to compute surface and well seismograms from earth models whether they are represented by a stack of elastic layers (with possible parameter gradients in the layers) or finely discretized. We review the equation of motion and then discuss the numerical aspects of the method using the advantage of rotational symmetry about a vertical axis. We conclude with two numerical examples to illustrate the capabilities and the efficiency of the method.