bluuebunny/crossref_metadata_2025 huggingface dataset:
Seismic attenuation and pore‐fluid viscosity in clay‐rich reservoir sandstones
Authors: Best Angus I. , McCann Clive
Published: October 2002

The frequency dependence of seismic attenuation in a suite of clay‐rich reservoir sandstones was investigated in the laboratory. Compressional‐ and shear‐wave velocities ([Formula: see text] and [Formula: see text]) and quality factors ([Formula: see text] and [Formula: see text]) were measured as functions of pore‐fluid viscosity at an effective pressure of 50 MPa and at an experimental frequency of about 0.8 MHz using the pulse‐echo technique. The experimental viscosity ranged from 0.3 to 1000 centipoise, which gives equivalent frequencies for a water‐saturated sandstone of 2.6 MHz to 780 Hz, assuming a global‐flow loss mechanism. Two types of behavior were observed: high permeability (greater than 100 millidarcies) sandstones tend to show variable [Formula: see text] and [Formula: see text] which are similar in magnitude to those predicted by the Biot theory over the viscosity range 0.3 to about 20 centipoise (equivalent frequency range 2.6 MHz to about 39 kHz); low permeability (less than 50 millidarcies) sandstones tend to show almost constant [Formula: see text] and [Formula: see text] over the experimental viscosity range that are not predicted by the Biot theory. The Biot theory does not predict the observed [Formula: see text] and [Formula: see text] values in the high permeability sandstones for viscosities greater than about 20 centipoise, where the observed [Formula: see text] values are generally much lower than the Biot predicted values. High permeability sandstones show small velocity dispersions with changing pore‐fluid viscosity that are consistent with the Biot theory. Low permeability sandstones show relatively large increases in velocity with increasing viscosity not explained by the Biot theory, which are consistent with a local flow loss mechanism. The results indicate the presence of two dominant loss mechanisms: global flow (at least down to about 39 kHz in water‐saturated rocks) in high permeability sandstones with only small amounts of intrapore clay, and local flow at ultrasonic frequencies in low permeability, clay‐rich sandstones.
Body‐wave radiation patterns and AVO in transversely isotropic media
Authors: Tsvankin Ilya
Published: October 2002

The angular dependence of reflection coefficients may be significantly distorted in the presence of elastic anisotropy. However, the influence of anisotropy on amplitude variation with offset (AVO) analysis is not limited to reflection coefficients. AVO signatures (e.g., AVO gradient) in anisotropic media are also distorted by the redistribution of energy along the wavefront of the wave traveling down to the reflector and back up to the surface. Significant anisotropy above the target horizon may be rather typical of sand‐shale sequences commonly encountered in AVO analysis. Here, I examine the influence of P‐ and S‐wave radiation patterns on AVO in the most common anisotropic model—transversely isotropic media. A concise analytic solution, obtained in the weak‐anisotropy approximation, provides a convenient way to estimate the impact of the distortions of the radiation patterns on AVO results. It is shown that the shape of the P‐wave radiation pattern in the range of angles most important to AVO analysis (0–40°) is primarily dependent on the difference between Thomsen parameters ε and δ. For media with ε − δ > 0 (the most common case), the P‐wave amplitude may drop substantially over the first 25–40° from vertical. There is no simple correlation between the strength of velocity anisotropy and angular amplitude variations. For instance, for models with a fixed positive ε − δ the amplitude distortions are less pronounced for larger values of ε and δ. The distortions of the SV‐wave radiation pattern are usually much more significant than those for the P‐wave. The anisotropic directivity factor for the incident wave may be of equal or greater importance for AVO than the influence of anisotropy on the reflection coefficient. Therefore, interpretation of AVO anomalies in the presence of anisotropy requires an integrated approach that takes into account not only the reflection coefficient but also the wave propagation above the reflector.
On: “Depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space in direct current methods,” by B. B. Bhattacharya and M. K. Sen (May 1981 GEOPHYSICS, 46, p. 768–780).
Authors: Apparao A. , Srinivas G. S.
Published: October 2002

Bhattacharya and Sen (1981) are the first to study the depths of investigation of various collinear electrode arrays for a homogeneous anisotropic half‐space. In their study they substituted the aniosotropic medium by an appropriate homogeneous medium of resistivity [Formula: see text]. However, they committed a serious error at assuming their basic equation‐13 as the “expression of potential at a point (X, y, Z) due to a point source of current strength I placed over a semi‐infinite homogeneous isotropic medium of resistivity [Formula: see text]”. The error is that X and Z in equation (13) are not independent coordinates. As a consequence, all their expressions for NDICs for different electrode arrays become incorrect. Consequently, their results and conclusions also become invalid. The mistake was detected only recently by the senior author of this paper (A. Apparao) in the course of his writing a book on ‘Developments in geoelectrical methods’. Since the subject of anisotropy is very interesting, there arises an urgent need to derive the correct expressions of the depth investigation characteristics for different electrode arrays. We present in this paper the expressions for normalized depth investigation characteristics (NDIC) for homogeneous and anisotropic half spaces for different electrode systems, including dipolar systems.
A two‐pass approximation to 3-D prestack migration
Authors: Canning Anat , Gardner Gerald H. F.
Published: October 2002

A two‐pass approximation to 3-D Kirchhoff migration simplifies the migration procedure by reducing it to a succession of 2-D operations. This approach has proven very successful in the zero‐offset case. A two‐pass approximation to 3-D migration is described here for the prestack case. Compared to the one‐pass approach, the scheme presented here provides significant reduction in computation time and a relatively simple data manipulation scheme. The two‐pass method was designed using velocity independent prestack time migration (DMO‐PSI) applied in the crossline direction, followed by conventional prestack depth migration in the inline direction. Velocity analysis, an important part of prestack migration, is also included in the two‐pass scheme. It is carried out as a 2-D procedure after 3-D effects are removed from the data volume. The procedure presented here is a practical full volume 3-D prestack migration. One of its main benefits is a realistic and efficient iterative velocity analysis procedure in three dimensions. The algorithm was designed in the frequency domain and the computational scheme was optimized by processing individual frequency slices independently. Irregular trace distribution, a feature that characterizes most 3-D seismic surveys, is implicitly accounted for within the two‐pass algorithm. A numerical example tests the performance of the two‐pass 3-D prestack migration program in the presence of a vertical velocity gradient. A 3-D land survey from a fold and thrust belt region was used to demonstrate the algorithm in a complex geological setting. The results were compared with images from other 2-D and 3-D migration schemes and show improved resolution and higher signal content.
Seismic anisotropy and natural fractures from VSP and borehole sonic tools—A field study
Authors: Beckham Wallace E.
Published: October 2002

A multicomponent vertical seismic profile (VSP), cross‐dipole shear‐wave log, formation micro imaging (FMI) log, and oriented core were obtained in the Brady Ranch 1–5 well, Carter County, Oklahoma in November 1992. The intent was to study the properties of fractured intervals and the response of the seismic data with respect to fracture orientation. The primary zones of interest were the Sycamore and Hunton carbonates. A full nine‐component VSP was obtained from 152 to 3010 m. Data from a cross‐dipole shear‐wave log were obtained primarily in the deep carbonates at 2600–2900 m. The VSP and cross‐dipole data gave estimates of the orientation of azimuthal anisotropy in the section, and indicate three changes in the orientation of azimuthal anisotropy with depth. An east‐northeast orientation was obtained in the deepest zone, which includes the carbonate interval. The cross‐dipole data indicate anisotropy having east‐northeast, east‐south‐east, and approximately north‐south orientations in this zone. The cross‐dipole tool may be responding to small scale microcracks, which may have more random orientations than the larger scale macrofractures. FMI log data and oriented core, also obtained in the deep carbonate section, indicate macrofractures oriented in east‐northeast and east‐southeast directions.
Combining reflection tomography with layer replacement for velocity analysis of near‐surface reefs
Authors: Carroll Steven , Beresford Greg
Published: October 2002

Reefs in the Browse Basin on the Australian North West Shelf typically have strong lateral velocity inhomogeneity on the reef flanks and produce an irregular sea‐floor topography. The combination of these two factors reduces the effectiveness of conventional velocity analysis as moveout on common midpoint (CMP) gathers is no longer hyperbolic. Consequently, the velocity structure on the reef flanks cannot be resolved properly. An accurate velocity structure is needed for these reefs if seismic data acquired in the vicinity are to be migrated correctly. Tomographic velocity analysis, using a simultaneous iterative reconstruction technique (SIRT), was found to improve the velocity analysis of the reef when compared to conventional analysis. However, the reef’s profile and rapid internal velocity gradients prevent accurate raypath determination. This technique can be further improved by preconditioning the data with wave‐equation datuming. The water is replaced with an average reef velocity by downward and upward continuation. This effectively removes most of the raypath distortions resulting from ray bending at the sea floor, thus reducing the nonlinearity of the forward modeling and improving the convergence of an iteratively linearized inversion. The velocities obtained from this method give an accurate picture of the reef’s internal velocity structure, as well as the lower portion of the seismic section below the reef.
Diffraction tomography for inhomogeneities in layered background medium
Authors: Harris Jerry M. , Wang Guan Y.
Published: October 2002

Diffraction tomography was originally formulated for a constant velocity background medium. A variable background medium, e.g., layered, with embedded finer scale heterogeneities is a more practical model for subsurface reservoirs than the uniform background. The variable background of large scale variations may be determined from well logs or transmission tomography. To image the finer scale heterogeneities, we have developed a Fourier diffraction back‐propagation method for point sources in a layered background. The method is based on the normal mode solution to the acoustic wave equation in cylindrical coordinates. The Fourier spectrum of the scattered fields is first decomposed into contributions from different layers. Then, a selection rule is applied to sort out the heterogeneity spectrum of the individual layers. The selection rule relates the scattered field in diffraction space to the spectrum of the heterogeneities, i.e., a Fourier diffraction theorem for layered media. The theorem differs from its counterpart for a uniform background medium by a matrix filter that reduces to unity as the stratification degenerates to a uniform background. A reconstruction algorithm based on this theorem is implemented and tested for an arbitrary layered background. The theory deals directly with point sources; therefore, the resulting algorithm does not require application of the “2.5-D correction” to field data as required in previously published diffraction tomography algorithms. Results obtained for both synthetic and field data demonstrate that an inversion with spatial resolution on the order of a wavelength can be achieved for crosswell data. The computations involved are much more efficient than those of traveltime tomography or crosswell migration. Unlike migration or CDP mapping, the diffraction tomography algorithm provides quantitative estimates for fine scale velocity.
Quasi‐linear approximation in 3-D electromagnetic modeling
Authors: Zhdanov Michael S. , Fang Sheng
Published: October 2002

The Born approximation in electromagnetic (EM) numerical modeling has limited application for solving 3-D electromagnetic induction problems, because in structures with high conductivity contrasts and at high frequencies, this approximation is inaccurate. In this paper, we develop a new and relatively simple approximation for the EM field called a quasi‐linear approximation, which is based on the evaluation of the anomalous field [Formula: see text] by a linear transformation of the normal (primary) field: [Formula: see text], where [Formula: see text] is called the electrical reflectivity tensor. The reflectivity tensor inside inhomogeneities can be approximated by a slowly varying function that can be determined numerically by a simple optimization technique. The new approximation gives an accurate estimate of the EM response for conductivity contrasts of more than one hundred to one, and for a wide range of frequencies. It also opens the possibility for fast 3-D electromagnetic inversion.
A unified approach to 3-D seismic reflection imaging, Part I: Basic concepts
Authors: Hubral Peter , Schleicher Jörg , Tygel Martin
Published: October 2002

Given a 3-D seismic record for an arbitrary measurement configuration and assuming a laterally and vertically inhomogeneous, isotropic macro‐velocity model, a unified approach to amplitude‐preserving seismic reflection imaging is provided. This approach is composed of (1) a weighted Kirchhoff‐type diffraction‐stack integral to transform (migrate) seismic reflection data from the measurement time domain into the model depth domain, and of (2) a weighted Kirchhoff‐type isochrone‐stack integral to transform (demigrate) the migrated seismic image from the depth domain back into the time domain. Both the diffraction‐stack and isochrone‐stack integrals can be applied in sequence (i.e., they can be chained) for different measurement configurations or different velocity models to permit two principally different amplitude‐preserving image transformations. These are (1) the amplitude‐preserving transformation (directly in the time domain) of one 3-D seismic record section into another one pertaining to a different measurement configuration and (2) the transformation (directly in the depth domain) of a 3-D depth‐migrated image into another one for a different (improved) macro‐velocity model. The first transformation is referred to here as a “configuration transform” and the second as a “remigration.” Additional image transformations arise when other parameters, e.g., the ray code of the elementary wave to be imaged, are different in migration and demigration. The diffraction‐ and isochrone‐stack integrals incorporate a fundamental duality that involves the relationship between reflectors and the corresponding reflection‐time surfaces. By analytically chaining these integrals, each of the resulting image transformations can be achieved with only one single weighted stack. In this way, generalized‐Radon‐transform‐type stacking operators can be designed in a straightforward way for many useful image transformations. In this Part I, the common geometrical concepts of the proposed unified approach to seismic imaging are presented in simple pictorial, nonmathematical form. The more thorough, quantitative description is left to Part II.
A unified approach to 3-D seismic reflection imaging, Part II: Theory
Authors: Tygel Martin , Schleicher Jörg , Hubral Peter
Published: October 2002

Diffraction‐stack and isochrone‐stack integrals are quantitatively described and employed. They constitute an asymptotic transform pair. Both integrals are the key tools of a unified approach to seismic reflection imaging that can be used to solve a multitude of amplitude‐preserving, target‐oriented seismic imaging (or image‐transformation) problems. These include, for instance, the generalizations of the kinematic map‐transformation examples discussed in Part I. All image‐transformation problems can be addressed by applying both stacking integrals in sequence, whereby the macro‐velocity model, the measurement configuration, or the ray‐code of the considered elementary reflections may change from step to step. This leads to weighted (Kirchhoff‐ or generalized‐Radon‐type) summations along certain stacking surfaces (or inplanats) for which true‐amplitude (TA) weights are provided. To demonstrate the value of the proposed imaging theory (which is based on analytically chaining the two stacking integrals and using certain inherent dualities), we examine in detail the amplitude‐preserving configuration transform and remigration for the case of a 3-D laterally inhomogeneous velocity medium.
High‐ and low‐frequency elastic moduli for a saturated porous/cracked rock‐Differential self‐consistent and poroelastic theories
Authors: Le Ravalec Mickaële , Guéguen Yves
Published: October 2002

Although P‐ and S‐wave dispersion is known to be important in porous/cracked rocks, theoretical predictions of such dispersions have never been given. We report such calculations and show that the predicted dispersions are high in the case of low aspect ratio cracks [Formula: see text] or high crack density [Formula: see text]. Our calculations are derived from first‐principle computations of the high‐ and low‐frequency elastic moduli of a rock permeated by an isotropic distribution of pores or cracks, dry or saturated, with idealized geometry (spheres or ellipsoids). Henyey and Pomphrey developed a differential self‐consistent model that is shown to be a good approximation. This model is used here, but as it considers cracks with zero thickness, it can not account for fluid content effects. To remove this difficulty, we combine the differential self‐consistent approach with a purely elastic calculation of moduli in two cases: that of spherical pores and that of oblate spheroidal cracks with a nonzero volume. This leads to what we call the “extended differential, self‐consistent model” (EM). When combining these EM results with the Gassmann equation, it is possible to derive and compare the theoretical predictions for high‐ and low‐frequency effective moduli in the case of a saturated rock. Since most laboratory data are ultrasonic measurements and in situ data are obtained at much lower frequencies, this comparison is useful for interpreting seismic data in terms of rock and fluid properties. The predicted dispersions are high, in agreement with previous experimental results. A second comparison is made with the semi‐empirical model of Marion and Nur, which considers the effects of a mixed porosity (round pores and cracks together).
Regularizing 3-D data sets with DMO
Authors: Canning Anat , Gardner Gerald H. F.
Published: October 2002

The combination of DMO and [Formula: see text] is used here to change the original acquisition geometry of a 3-D seismic data set into a more convenient form. For example, irregular 3-D surveys can be projected onto a regular midpoint‐offset grid with zero source‐receiver azimuth and equal increments in offset. The algorithm presented here is based on a new, nonaliased 3-D DMO algorithm in (f, x) domain. It does not require any knowledge of the velocity function for constant or rms velocity variations. The computer program was designed to process and to output very large multifold 3-D data sets. A synthetic example of a point diffractor in 3-D space and a 3-D experiment in a physical modeling tank are used to demonstrate the procedure. In both cases, the results obtained after the data set is regularized are compared with a data set that was acquired initially with the desired configuration. These comparisons show very good agreement. Analysis of the procedure indicates that it may not reconstruct AVO correctly. This is an inherent problem that occurs because the reorganization procedure changes the angle of incidence.
Transformation to zero offset in transversely isotropic media
Authors: Alkhalifah Tariq
Published: October 2002

Nearly all dip‐moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero‐offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale’s v(z) ray‐tracing‐based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray‐tracing procedure crafted for anisotropic media, I modify some aspects of their DMO so that it can work for v(z) anisotropic media. DMO impulse responses in typical transversely isotropic (TI) models (such as those associated with shales) deviate substantially from the familiar elliptical shape associated with responses in homogeneous isotropic media (to the extent that triplications arise even where the medium is homogeneous). Such deviations can exceed those caused by vertical inhomogeneity, thus emphasizing the importance of taking anisotropy into account in DMO processing. For isotropic or elliptically anisotropic media, the impulse response is an ellipse; but as the key anisotropy parameter η varies, the shape of the response differs substantially from elliptical. For typical η > 0, the impulse response in TI media tends to broaden compared to the response in an isotropic homogeneous medium, a behavior opposite to that encountered in typical v(z) isotropic media, where the response tends to be squeezed. Furthermore, the amplitude distribution along the DMO operator differs significantly from that for isotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common‐midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale‐induced anisotropy.
An iterative algorithm for conductivity image reconstruction from crosswell EM measurements
Authors: Zhang Yong C. , Liu Ce , Shen Liang C.
Published: October 2002

An efficient iterative modeling and inversion algorithm is developed to reconstruct conductivity images using data obtained from crosswell electromagnetic measurements. The forward modeling uses a distorted Born approximation, in which cylindrical conductivity distributions are considered to be deviations from a 1-D background conductivity. The inversion algorithm employs a constrained optimization method to achieve maximum stability when noise is present. Both synthetic and field‐measured data are inverted in this paper. The method developed starts with an estimated homogeneous formation and reconstructs a 1-D conductivity image; the 2-D image reconstruction uses the reconstructed 1-D image as the initial input in the inversion process. Conductivity tomographs of two synthetic models and of the Devine Test Site are presented. The operating frequency used in the examples is 512 Hz and a range of [Formula: see text] is imaged. The images reconstructed for the tested cases show a satisfactory agreement with the known geological properties.
3-D seismic evidence of the effects of carbonate karst collapse on overlying clastic stratigraphy and reservoir compartmentalization
Authors: Hardage B. A. , Carr D. L. , Lancaster D. E. , Simmons J. L. , Elphick R. Y. , Pendleton V. M. , Johns R. A.
Published: October 2002

A multidisciplinary team, composed of stratigraphers, petrophysicists, reservoir engineers, and geophysicists, studied a portion of Boonsville gas field in the Fort Worth Basin of north‐central Texas to determine how modern geophysical, geological, and engineering techniques can be combined to understand the mechanisms by which fluvio‐deltaic depositional processes create reservoir compartmentalization in a low‐ to moderate‐accommodation basin. An extensive database involving well logs, cores, production, and pressure data from more than 200 wells, [Formula: see text] [Formula: see text] of 3-D seismic data, vertical seismic profiles (VSPs), and checkshots was assembled to support this investigation. We found the most important geologic influence on stratigraphy and reservoir compartmentalization in this basin to be the existence of numerous karst collapse chimneys over the [Formula: see text] [Formula: see text] area covered by the 3-D seismic grid. These near‐vertical karst collapses originated in, or near, the deep Ordovician‐age Ellenburger carbonate section and created vertical chimneys extending as high as 2500 ft (610 m) above their point of origin, causing significant disruptions in the overlying clastic strata. These karst disruptions tend to be circular in map view, having diameters ranging from approximately 500 ft (150 m) to as much as 3000 ft (915 m) in some cases. Within our study area, these karst features were spaced 2000 ft (610 m) to 6000 ft (1830 m) apart, on average. The tallest karst collapse zones reached into the Middle Pennsylvanian Strawn section, which is some 2500 ft (760 m) above the Ellenburger carbonate where the karst generation began. We used 3-D seismic imaging to show how these karst features affected the strata above the Ellenburger and how they have created a well‐documented reservoir compartment in the Upper Caddo, an upper Atoka valley‐fill sandstone that typically occurs 2000 ft (610 m) above the Ellenburger. By correlating these 3-D seismic images with outcrops of Ellenburger karst collapses, we document that the physical dimensions (height, diameter, cross‐sectional area) of the seismic disruptions observed in the 3-D data equate to the karst dimensions seen in outcrops. We also document that this Ellenburger carbonate dissolution phenomenon extends over at least 500 mi (800 km), and by inference we suggest karst models like we describe here may occur in any basin that has a deep, relatively thick section of Paleozoic carbonates that underlie major unconformities.
Implementation of 3-D prestack Kirchhoff migration, with application to data from the Ouachita frontal thrust zone
Authors: Epili Duryodhan , McMechan George A.
Published: October 2002

A 3-D prestack Kirchhoff migration is implemented and successfully applied to a 3-D data set from the Ouachita frontal thrust zone in southeastern Oklahoma. The algorithm uses data decomposition and operates efficiently both in multiprocessor vector and parallel environments. Image time maps are precomputed once for each survey point, regardless of how many times it is a source or receiver, and stored in random access disk files. These files, and the data traces, are read asynchronously during migration. Image time computation is done by two‐point ray tracing to avoid interpolation between irregularly spaced rays or points on wavefronts. The same software can be used to depth migrate all input data geometries (stacked sections, common‐source or common‐receiver, or common‐offset or common‐midpoint gathers). The output images from the Ouachita field data show structural closure on folded thrust sheets of Wapanucka limestone, and repetition of lithology caused by lateral displacement on the thrusts.
Pitfalls of using conventional and discrete Radon transforms on poorly sampled data
Authors: Marfurt Kurt J. , Schneider Robert V. , Mueller Michael C.
Published: October 2002

The least‐square discrete Radon transform (DRT) is currently one of the most popular methods used in the suppression of multiples and other coherent noise events on irregularly sampled data gathers used for prestack true amplitude analysis. Unfortunately, in the absence of a priori information, this technique suffers from the same aliasing problems as Fourier and conventional (τ, p) methods. Although the DRT is able to reconstruct the original image more accurately than conventional (τ, p) transforms, a harmful by‐product is an increase in the amplitude of aliased events in the transform domain. In particular, the DRT will boost the amplitude of the aliases of true events that fall outside the p analysis window to help reconstruct the input data. These amplified aliases degrade signal periodicity in the (τ, p) domain. If muted, they can destroy subtle amplitude changes necessary for amplitude variation with offset (AVO) analysis. At the very least, one should carefully evaluate the choice of analysis window and mutes when designing a filter in the (τ, p) domain. Alternatively, one can exploit additional a priori information based on semblance. Iterative application of the DRT and mutes can also be used to suppress aliased events further.
High resolution of glacial ice stratigraphy: A ground‐penetrating radar study of Pegasus Runway, McMurdo Station, Antarctica
Authors: Arcone Steven A.
Published: October 2002

Ground‐penetrating radar (GPR) has been used to detect areas of present or potential structural weakness beneath a 3.2-km snow‐covered ice runway on the Ross Ice Shelf, Antarctica. The bandwidths of the transmitted wavelets were centered near 500 MHz. The data show many horizons up to tens of meters long and occurring to about a 9-m depth, below which a brine intrusion limits penetration. The horizons are interpreted as discrete scatterers because of their diffraction nature and loss of higher frequencies with depth. The presence of porous ice or dispersed water is interpreted from wavelet phase. The water may be associated with apparent deepening and fading of the brine horizon. If the above interpretation is correct, water occurs at depths to 3.5 m and extends as much as 40 m horizontally, which is greater and deeper than known previously. At 3.5 m depth, the water may be adsorbed on mineral particles rather than remain free. Migration of the diffractions with a single‐layer migration scheme shows all horizons above the brine layer to be small dielectric perturbations within the ice. Stacking and Hilbert transformation of the data reveal slight folding along the length of the runway. Loss of high‐frequency amplitude in the wavelets suggests that higher frequency radar might improve resolution only in the top few meters.
A simultaneous inversion of seismic traveltimes and amplitudes for velocity and attenuation
Authors: Vasco Don W. , Peterson John E. , Majer Ernest L.
Published: October 2002

It is possible to efficiently use traveltime and amplitude information to infer variations in velocity and Q. With little additional computation, terms accounting for source radiation pattern and receiver coupling may be included in the inversion. The methodology is based upon a perturbation approach to paraxial ray theory. The perturbation approach linearizes the relationship between velocity deviations and traveltime and amplitude anomalies. Using the technique, we infer the velocity and attenuation structure at a fractured granitic site near Raymond, California. A set of four well pairs are examined and each is found to contain two zones of strong attenuation. The velocity variations contain an upper low velocity region corresponding to the uppermost attenuating zone. The location of these zones agrees with independent well‐log and geophysical data. The velocity and attenuation anomalies appear to coincide with extensively fractured sections of the borehole and may indicate fracture zones rather than individual fractures.
Solving 1-D inverse problems by Chebyshev polynomial expansion
Authors: Grechka Vladimir Y. , McMechan George A. , Volovodenko Vitaly A.
Published: October 2002

Seismic wave propagation described by differential equations with variable coefficients may be solved by the Chebyshev polynomial expansion method (CPEM). This method approximates a model and forward solutions by orthonormal Chebyshev polynomials. The CPEM provides an alternative to the usual formulation. In CPEM, the model is approximated globally and the forward solutions can explicitly depend on the parameters of the model. The former ensures that a smooth model is produced by inversion. The latter produces partial derivatives of the forward solutions directly with respect to the model parameters, which streamlines the inversion and also gives a quantitative tool for determining the feasibility of inversion in the presence of noise (by singular value decomposition). Two examples of inversion demonstrate the potential of the CPEM. The first is nonlinear inversion for velocity and density using borehole SH‐wave data. The second is linear inversion for interval velocities from rms velocity data. Estimation of interval velocity from stacking velocity is illustrated using field data from the Gulf of Mexico.
Outcrop topography as a proxy of acoustic impedance in synthetic seismograms
Authors: Stafleu Jan , Schlager Wolfgang , Everts Arnout J. W. , Kenter Jeroen A. M. , Blommers Geert , van Voorden Anton
Published: October 2002

Two‐dimensional seismic models of geologic data are usually based on simplified impedance functions: large “seismic‐scale” lithologic blocks exhibit uniform impedance values, and abrupt changes in impedance occur at the boundaries of these lithologic blocks. For outcrop‐based seismic models, erosional slope topography may be one possible proxy for impedance that is relatively easy to measure in outcrop. In this paper, we use terrestrial photogrammetric techniques to establish the relationship between outcrop topography, expressed as the rock slope angle, and impedance for a marl‐limestone terrain in the Vercors, southeast France. The photogrammetric surveys were combined with sedimentologic descriptions and petrophysical measurements (including P‐wave velocity, bulk‐density, clay content, and porosity). The slope angle along a particular vertical profile was then converted into a pseudoimpedance log, which was subsequently used to construct 1-D synthetic seismograms. A comparison of these new seismograms with published seismic models of the same area revealed the benefits of the new approach, in particular for seismic modeling using high‐frequency source wavelets.
Nonlinear wave propagation in sandstone: A numerical study
Authors: Cheng Ningya
Published: October 2002

Elastic nonlinear effects in rocks are observed widely in laboratory experiments. For example, Toksöz et al. (1976) measured the pressure dependence of wave speed in the rocks. In crystalline rock and sandstone, Johnson et al. (1987) and Johnson and Shankland (1989) have demonstrated the nonlinear generation of elastic waves. The importance of nonlinear effects in seismic waves in the earth in regard to models of the source is given in Johnson and McCall (1994). The evolution of the harmonic spectrum of a single frequency wave propagated in Berea Sandstone was shown in Meegan et al. (1993). The structural defects contained in rock, such as microcracks and grain‐to‐grain contacts, give rise to this strong elastic nonlinearity (e.g., Gist, 1994). A new theoretical model is developed in McCall and Guyer (1994) to describe elastic behavior of hysteretic nonlinear materials, such as rock. In general, the third‐order elastic constants of the rocks have much larger values than ordered solids.
3-D microearthquake attenuation tomography at the Northwest Geysers geothermal region, California
Authors: Romero Arturo E. , McEvilly Thomas V. , Majer Ernest L.
Published: October 2002

We present the results of the modeling of a 3-D differential attenuation structure [Formula: see text] beneath the Northwest Geysers geothermal field. A set of 480 high‐quality microearthquakes distributed evenly throughout the field and with a minimum of 10 P‐wave arrivals was selected for the study. We constructed spectral ratios by dividing each spectrum with a reference spectrum from each observing station. The reference spectrum was derived from the average spectrum of all events that were recorded at that station to correct for the strong site dependence of the observed spectra. We then estimated the differential attenuation operator from the slopes of the spectral ratios. The velocity models and the raypaths for all events are known from a previous velocity inversion study. The inversion for the differential attenuation structure was carried out using a modified progressive inversion method. The observed [Formula: see text] structure correlates well with mapped geologic units. High [Formula: see text] and lower velocities correlate with Franciscan melange, while lower attenuation and higher velocities correspond to metagraywacke units. High P‐wave [Formula: see text] also underlies the southern region between 2 and 3 km depth where low [Formula: see text] values suggest undersaturation of the reservoir rocks. Most of the steam entries also occur within this region and probably delineate the steam reservoir. These anomalies may be explained by high rock temperatures and the presence of steam and other gases.
Acoustic evidence of mechanical damage surrounding stressed boreholes
Authors: Winkler Kenneth W.
Published: October 2002

Laboratory experiments demonstrate that acoustic waveforms recorded in a borehole provide evidence of stress‐induced mechanical damage in surrounding rock. In the experiments, external uniaxial stress was applied perpendicular to the borehole. Stress concentrations near the borehole wall caused velocities of refracted compressional‐wave to vary with azimuth. Low velocities occurred in zones of tensile stress, and high velocities occurred in zones of compressive stress. Velocity variations are on the order of 10%. At high values of externally applied uniaxial stress, rock exceede its yield strength and permanent damage developed. This damage decreased the measured velocities by approximately 10%, especially in the zones of compressive stress concentration. The heterogenous nature of the velocities surrounding the borehole resulted in low‐velocity channels parallel to the borehole wall, caused either by tensile stress concentrations or by mechanical damage. These low‐velocity channels may be responsible for high‐amplitude “bright‐spots” that appear on variable density plots of azimuthal waveform scans. The amplitude increases can be on the order of 500% and are associated with low‐velocity zones, not with decreased attenuation. The hypothezised mechanism is acoustic focusing, whereby velocity gradients refract acoustic waves back towards the borehole.
The subsurface structure of the Chalco sub‐basin (Mexico City) inferred from geophysical data
Authors: Campos‐Enríquez J. O. , Delgado‐Rodríguez O. , Chávez‐Segura R. , Gómez‐Contreras P. , Flores‐Márquez E. L. , Birch F. S.
Published: October 2002

The Chalco sub‐basin, the hydrogeological reserve of Mexico City, is located in the southern portion of Mexico City's basin, an intramontane valley located at 2200 m a.s.l. in the Trans‐Mexican Volcanic Belt (Central Mexico). Several geophysical studies (dc resistivity, seismic refraction, gravity, well‐logging) have been conducted in this area. The objectives of these independent surveys were different and of regional and local scopes. This study represents the first comprehensive effort to assimilate and interpret the data available to date from the area of the Chalco sub‐basin and to infer its main basinal characteristics. According to the topography we obtained of the basement, a northeast‐southwest structural high separates the sub‐basin into two portions. The western portion is asymmetric and deeper than the eastern one. An east‐west half graben‐like structure is located in the western portion. This structure could make possible an east‐west fluid flow at depth, and it also implies a differential subsidence. It was also possible to establish the stratigraphy of the volcano‐sedimentary infill. The gravity models give the interface: (1) between lacustrine sediments (aquitard) and the granular aquifer and (2) between the granular aquifer and the basaltic container. The resistivity boundaries correspond to the contact zone between saline and fresh water in the aquitard and semiconfined aquifer respectively, and they correlate with the existence of a vertical flow of saline fluids from the aquitard to the aquifer. The estimate of the volume of fluids contained in the granular aquifer range between 2 and [Formula: see text].
Instantaneous slowness versus depth functions
Authors: Al‐Chalabi M.
Published: October 2002

Slowness versus depth functions offer a versatile complement to velocity versus depth functions. Obtaining the time‐depth relationship, which is essential for time to depth conversion, is greatly facilitated by the convenient mathematical form of the slowness versus depth functions. This feature allows them to be used to provide an accurate description of a wide range of forms of slowness (hence, velocity) variation with depth. Examples of polynomial and asymptotic slowness versus depth functions are given. As in the case of velocity versus depth functions, the applicability of some function forms (such as high‐order polynomials) may diminish rapidly outside the depth range over which the function is derived.
Seismic attenuation in finely layered porous rocks: Effects of fluid flow and scattering
Authors: Gurevich Boris , Zyrianov Vadim B. , Lopatnikov Sergey L.
Published: October 2002

Scattering caused by fine layering is known to play an important role in seismic attenuation. If the rock is also porous and permeable, additional attenuation can be caused by a flow of the pore fluid induced by the passing wave (see e.g., White, 1983). At frequencies higher than 100 kHz, standard Biot's attenuation (Biot, 1962; Bourbié et al., 1987) may also contribute to the overall attenuation in a layered poroelastic rock. While standard Biot's attenuation has been well known for decades, the effects of scattering by fine layering and interlayer flow have been studied extensively both theoretically and numerically in recent years. However, in all theoretical approaches proposed thus far, these effects have been treated separately: scattering was studied for purely elastic rocks (Burridge and Chang, 1989; Shapiro et al. 1994), while attenuation caused by interlayer flow was considered either for periodically stratified media that causes no scattering (Norris, 1993) or for frequencies at which scattering is negligible (Gurevich and Lopatnikov, 1995).
Resistivity of partially saturated carbonate rocks with microporosity
Authors: Sen Pabitra N.
Published: October 2002

Simple Archie's relations relate average conductivity to average porosity and average saturation, and seem to work when the fluctuations of local porosity and local saturation are small. In general, carbonates are extremely inhomogeneous and Archie's relations fail—the saturation exponent n can depend on saturation itself, and n can be anomalously large or small. The resistivity of rocks with a mixture of micropores, macropores, and vugs is computed using effective medium theories. Quantitative mathematical modeling is used to study the influence of textural details. Geometries that lead to an anomalously high value of saturation exponent are contrasted with those with an anomalously low value of saturation exponent. The resistivity becomes anomalously large when the conducting water phase is trapped in isolated regions. The resistivity becomes insensitive to the volume fraction of water if the configuration of the major current‐carrying paths changes little with saturation. Simple examples with differences in wettability are considered.
Square array resistivity anomalies and inhomogeneity ratio calculated by the finite‐element method
Authors: Tsokas Gregory N. , Tsourlos Panagiotis I. , Szymanski John E.
Published: October 2002

In this work the square array configuration is studied. As with any four‐electrode measuring configuration, three different resistances can be measured directly and, in particular, by using the square array these resistance values can be used to obtain a measure of the apparent anisotropy: this is the so‐called azimuthal inhomogeneity ratio (AIR). The AIR is used widely to derive information regarding the directional variation of the subsurface resistivity. Similar types of information can be obtained using any collinear array but would need to be used in a crossed mode. This gives an operational advantage to the square array. Here, the AIR and the square α and β apparent resistivities have been calculated for a number of simple subsurface models. Moreover, the apparent resistivity responses for several different linear arrays were calculated to allow useful comparisons. The forward modeling has been carried out via a 2.5-D finite‐element scheme and an existing approach has been modified in order to calculate the potential variations parallel to the strike direction. Here, the use of AIR as a pattern recognition tool is investigated. The AIR anomalies are shown to delineate the edges of the targets successfully, retaining the same pattern when the model was shifted in depth, and indicating a satisfactory resolving ability. The AIR can be used as complementary information to the apparent resistivity measures and can improve the interpretation. However, careful consideration has to be given to the data noise.
Fracture detection using crosswell and single well surveys
Authors: Majer Ernest L. , Peterson John E. , Daley Thomas , Kaelin Bruno , Myer Larry , Queen John , D'Onfro Peter , Rizer William
Published: October 2002

We recorded high‐resolution (1 to 10 kHz), crosswell and single well seismic data in a shallow (15 to 35 m), water‐saturated, fractured limestone sequence at Conoco's borehole test facility near Newkirk, Oklahoma. Our objective was to develop seismic methodologies for imaging gas‐filled fractures in naturally fractured gas reservoirs. The crosswell (1/4 m receiver spacing, 50 to 100 m well separation) surveys used a piezoelectric source and hydrophones before, during, and after an air injection that we designed to displace water from a fracture zone. Our intent was to increase the visibility of the fracture zone to seismic imaging and to confirm previous hydrologic data that indicated a preferred pathway. For the single well seismic imaging (a piezoelectric source and an eight‐element hydrophone array at 1/4 m spacing), we also recorded data before and after the air injection. The crosswell results indicate that the air did follow a preferred pathway that was predicted by hydrologic modeling. In addition, the single well seismic imaging using vertical common depth‐point (CDP) gathers indicated an anomaly consistent with the anomaly location of crosswell and hydrologic inversion results. Following the field tests, a slant well was drilled and cored to confirm the existence and nature of the rock associated with the seismic anomalies. A vertical fracture was intersected within less than 1 m of where the seismic results had predicted.