Showing papers in "Geophysics in 1994"

Detection of gas in sandstone reservoirs using AVO analysis: A 3-D seismic case history using the Geostack technique

Abstract: The Geostack technique is a method of analyzing seismic amplitude variation with offset (AVO) information. One of the outputs of the analysis is a set of direct hydrocarbon indicator traces called fluid factor traces. The fluid factor trace is designed to be low amplitude for all reflectors in a clastic sedimentary sequence except for rocks that lie off the mudrock line. The mudrock line is the line on a crossplot of P-wave velocity against S-wave velocity on which water-saturated sandstones, shales, and siltstones lie. Some of the rock types that lie off the mudrock line are gas-saturated sandstones, carbonates, and igneous rocks. In the absence of carbonates and igneous rocks, high amplitude reflections on fluid factor traces would be expected to represent gas-saturated sandstones. Of course, this relationship does not apply exactly in nature, and the extent to which the mudrock line model applies varies from area to area. However, it is a useful model in many basins of the world, including the one studied here. Geostack processing has been done on a 3-D seismic data set over the Mossel Bay gas field on the southern continental shelf of South Africa. The authors found that anomalously high amplitude fluid factormore » reflections occurred at the top and base of the gas-reservoir sandstone. Maps were made of the amplitude of these fluid factor reflections, and it was found that the high amplitude values were restricted mainly to the gas field area as determined by drilling. The highest amplitudes were found to be located roughly in the areas of best reservoir quality (i.e., highest porosity) in areas where the reservoir is relatively thick.« less

Anisotropic effective‐medium modeling of the elastic properties of shales

Abstract: Shales are complex porous materials, normally consisting of percolating and interpenetrating fluid and solid phases. The solid phase is generally comprised of several mineral components and forms an intricate and anisotropic microstructure. The shape, orientation, and connection of the two phases control the anisotropic elastic properties of the composite solid. We develop a theoretical framework that allows us to predict the effective elastic properties of shales. Its usefulness is demonstrated with numerical modeling and by comparison with established ultrasonic laboratory experiments. The theory is based on a combination of anisotropic formulations of the self‐consistent (SCA) and differential effective‐medium (DEM) approximations. This combination guarantees that both the fluid and solid phases percolate at all porosities. Our modeling of the elastic properties of shales proceeds in four steps. First, we consider the case of an aligned biconnected clay‐fluid composite composed of ellipsoidal inclusion...

Viscoelastic finite-difference modeling

Abstract: Real earth media disperse and attenuate propagating mechanical waves. This anelastic behavior can be described well by a viscoelastic model. We have developed a finite-difference simulator to model wave propagation in viscoelastic media. The finite-difference method was chosen in favor of other methods for several reasons. Finite-difference codes are more portable than, for example, pseudospectral codes. Moreover, finite-difference schemes provide a convenient environment in which to define complicated boundaries. A staggered scheme of second-order accuracy in time and fourth-order accuracy in space appears to be optimally efficient. Because of intrinsic dispersion, no fixed grid points per wavelength rule can be given; instead, we present tables, which enable a choice of grid parameters for a given level of accuracy. Since the scheme models energy absorption, natural and efficient absorbing boundaries may be implemented merely by changing the parameters near the grid boundary. The viscoelastic scheme is only marginally more expensive than analogous elastic schemes. The efficient implementation of absorbing boundaries may therefore be a good reason for also using the viscoelastic scheme in purely elastic simulations. We illustrate our method and the importance of accurately modeling anelastic media through 2-D and 3-D examples from shallow marine environments.

Nonhyperbolic reflection moveout in anisotropic media

Abstract: The standard hyperbolic approximation for reflection moveouts in layered media is accurate only for relatively short spreads, even if the layers are isotropic. Velocity anisotropy may significantly enhance deviations from hyperbolic moveout. Nonhyperbolic analysis in anisotropic media is also important because conventional hyperbolic moveout processing on short spreads is insufficient to recover the true vertical velocity (hence the depth).We present analytic and numerical analysis of the combined influence of vertical transverse isotropy and layering on long-spread reflection moveouts. Qualitative description of nonhyperbolic moveout on 'intermediate' spreads (offset-to-depth ratio x/z epsilon . With this expansion, we also show that the weak anisotropy approximation becomes inadequate (to describe nonhyperbolic moveout) for surprisingly small values of the anisotropies delta and epsilon .However, the fourth-order Taylor series rapidly loses numerical accuracy with increasing offset. We suggest a new, more general analytical approximation, and test it against several transversely isotropic models. For P-waves, this moveout equation remains numerically accurate even for substantial anisotropy and large offsets. This approximation provides a fast and effective way to estimate the behavior of long-spread moveouts for layered anisotropic models.

The Marmousi experience; velocity model determination on a synthetic complex data set

Abstract: The motivation behind seismic data acquisition and processing is simple—to obtain a depth image of the earth—but performing this process correctly is extremely difficult. A number of well known processing tasks (such as static corrections, deconvolution, multiple elimination, velocity estimation, and migration) have to be executed, and each directly influences the final result. However, the success of the velocity estimation is paramount and critical, and large amounts of man/CPU hours are devoted to it.

Inversion of induced polarization data

Abstract: We present an algorithm for inverting induced polarization (IP) data acquired in a 3-D environment. The algorithm is based upon the linearized equation for the IP response, and the inverse problem is solved by minimizing an objective function of the chargeability model subject to data and bound constraints. The minimization is carried out using an interior-point method in which the bounds are incorporated by using a logarithmic barrier and the solution of the linear equations is accelerated using wavelet transforms. Inversion of IP data requires knowledge of the background conductivity. We study the effect of different approximations to the background conductivity by comparing IP inversions performed using different conductivity models, including a uniform half-space and conductivities recovered from one-pass 3-D inversions, composite 2-D inversions, limited AIM updates, and full 3-D nonlinear inversions of the dc resistivity data. We demonstrate that, when the background conductivity is simple, reasonable IP results are obtainable without using the best conductivity estimate derived from full 3-D inversion of the dc resistivity data. As a final area of investigation, we study the joint use of surface and borehole data to improve the resolution of the recovered chargeability models. We demonstrate that the joint inversion of surface and crosshole data produces chargeability models superior to those obtained from inversions of individual data sets.

Fourier finite-difference migration

Abstract: Many existing migration schemes cannot simultaneously handle the two most important problems of migration: imaging of steep dips and imaging in media with arbitrary velocity variations in all directions. For example, phase‐shift (ω, k) migration is accurate for nearly all dips but it is limited to very simple velocity functions. On the other hand, finite‐difference schemes based on one‐way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events. We propose a new hybrid migration method, named “Fourier finite‐difference migration,” wherein the downward‐continuation operator is split into two downward‐continuation operators: one operator is a phase‐shift operator for a chosen constant background velocity, and the other operator is an optimized finite‐difference operator for the varying component of the velocity function. If there is no variation of velocity, then only a phase‐shift operator will be applied automatically. On the other hand, if there is a strong variatio...

Elastic-wave stimulation of oil production; a review of methods and results

Abstract: Numerous observations accumulated principally during the last 40 years show that seismic waves generated from earthquakes and cultural noise may alter water and oil production In some cases wave excitation may appreciably increase the mobility of fluids The effect of elastic waves on the permeability of saturated rock has been confirmed in numerous laboratory experiments Two related applications have arisen from these findings In the first application, high-power ultrasonic waves are applied for downhole cleaning of the near-wellbore in producing formations that exhibit declining production as a result of the deposition of scales and precipitants, mud penetration, etc In many cases, ultrasound effectively removes the barriers to oil flow into the well The ultrasonic method is reported to be successful in 40-50 percent of the cases studied In the case of successful treatment, the effect of improved permeability may last up to several months Whereas this method has a very local effect, a second application is used to stimulate the reservoir as a whole Here seismic frequency waves are applied at the earth’s surface by arrays of vibroseis-type sources This method has produced promising results; however, further testing and understanding of the mechanisms are necessary

3-D resistivity inversion using the finite-element method

Abstract: With the increased availability of faster computers, it is now practical to employ numerical modeling techniques to invert resistivity data for 3-D structure. Full and approximate 3-D inversion methods using the finite-element solution for the forward problem have been developed. Both methods use reciprocity for efficient evaluations of the partial derivatives of apparent resistivity with respect to model resistivities. In the approximate method, the partial derivatives are approximated by those for a homogeneous half-space, and thus the computation time and memory requirement are further reduced. The methods are applied to synthetic data sets from 3-D models to illustrate their effectiveness. They give a good approximation of the actual 3-D structure after several iterations in practical situations where the effects of model inadequacy and topography exist. Comparisons of numerical examples show that the full inversion method gives a better resolution, particularly for the near-surface features, than does the approximate method. Since the full derivatives are more sensitive to local features of resistivity variations than are the approximate derivatives, the resolution of the full method may be further improved when the finite-element solutions are performed more accurately and more efficiently.

Ground‐penetrating radar simulation in engineering and archaeology

Abstract: Forward modeling of ground penetration radar is developed using exact ray-tracing techniques. Structural boundaries for a ground model are incorporated via a discrete grid with interfaces described by splines, polynomials, and in the case of special structures such as circular objects, the boundaries are given in terms of their functional formula. In the synthetic radargram method, the waveform contributions of many different wave types are computed. Using a finely digitized antenna directional response function, the radar cross-section of buried targets and the effective area of the receiving antenna can be statistically modeled. Attenuation along the raypaths is also monitored. The forward models are used: (1) as a learning tool to avoid pitfalls in radargram interpretation, (2) to understand radar signatures measured across various engineering structures, and (3) to predict the response of cultural structures buried beneath important archaeological sites in Japan.

The squirt-flow mechanism: Macroscopic description

Abstract: We introduce a poroelasticity model that incorporates the two most important mechanisms of solid/fluid interaction in rocks: the Biot mechanism and the squirt-flow mechanism. This combined Biot/squirt (BISQ) model relates compressional velocity and attenuation to the elastic constants of the drained skeleton and of the solid phase, porosity, permeability, saturation, fluid viscosity and compressibility, and the characteristic squirt-flow length. Squirt-flow length is a fundamental rock property that does not depend on frequency, fluid viscosity, or compressibility and is determined experimentally. We find that the viscoelastic response of many sandstones is dominated by the squirt-flow component of the BISQ mechanism and that the viscoelastic properties of these rocks can be expressed through a single dimensionless parameter omega R 2 /kappa , where omega is angular frequency, R is the characteristic squirt-flow length, and kappa is hydraulic diffusivity. The Biot mechanism alone does not give an adequate explanation of the observed velocity dispersion and attenuation, and the viscoelastic behavior of many sandstones.

Kirchhoff migration using eikonal equation traveltimes

Abstract: The use of ray shooting followed by interpolation of traveltimes onto a regular grid is a popular and robust method for computing diffraction curves for Kirchhoff migration. An alternative to this method is to compute the traveltimes by directly solving the eikonal equation on a regular grid, without computing raypaths. Solving the eikonal equation on such a grid simplifies the problem of interpolating times onto the migration grid, but this method is not well defined at points where two different branches of the traveltime field meet. Also, computational and data storage issues that are relatively unimportant for performance in two dimensions limit the applicability of both schemes in three dimensions. A new implementation of a gridded eikonal equation solver has been designed to address these problems. A 2-D version of this algorithm is tested by using it to generate traveltimes to migrate the Marmousi synthetic data set using the exact velocity model. The results are compared with three other images: an F-X migration (a standard for comparison), a Kirchhoff migration using ray tracing, and a Kirchhoff migration using traveltimes generated by a commonly used eikonal equation solver. The F-X-migrated image shows the imaging objective more clearly than any of themore » Kirchhoff migrations, and the authors advance a heuristic reason to explain this fact. Of the Kirchhoff migrations, the one using ray tracing produces the best image, and the other two are of comparable quality.« less

Comparison of AVO indicators: A modeling study

Abstract: A worldwide collection of 25 sets of velocity and density measurements from adjacent shales, brine sands, and gas sands was acquired with full-waveform sonic, dipole sonic, and conventional well logging devices and/or in the laboratory. These data provide theoretical shale over brine-sand and shale over gas­ sand P-wave and S-wave normal-incidence reflection coefficients (R p and R s ), AVO intercepts (A), AVO gradients (B), the AVO indicators R p - R s (reflection coefficient difference), and A * B (AVO product). The reflection coefficient difference is found to be a more universal indicator than the AVO product in clastic stratigraphic intervals. For shale over brine-sand re­ flections, the average R p - R s tends to be near zero and relatively invariant with depth. Irrespective of gas-sand impedance, R p - R s is always negative for shale over reservoir quality gas-sand reflections and more negative than for the corresponding brine-sand reflections. In comparison, the AVO product may be positive, near zero, or negative for gas-sands depend­ ing on the impedance contrast with the overlying shale. These measurements also verify that R p - R s is well approximated by a simple linear combination of A and B.

A theory of normal moveout

Abstract: Three geophysical principles are shown to be sufficient to determine the most general, practical normal moveout (NMO) equation. The principles are reciprocity in a common midpoint (CMP) gather, finite slowness, and exact constant velocity limit. The resulting equation is the shifted hyperbola NMO equation that has three parameters. Comparisons at both near and far offsets between the shifted hyperbola NMO equation and the results for layered media assign geophysical meaning to the parameters. Two of the parameters, zero offset time and NMO velocity, are constants and control the very near offset behavior. The third parameter is dimensionless and controls the far offset behavior of the NMO curve, but it may be a function of offset so as to exactly fit any traveltime curve. The parameters may be found by a linear least-squares fit to data. The theory applies to all offsets for nonturning wave reflections in an isotropic earth for both P-waves and converted (P - SV) waves.

Ground-penetrating radar monitoring of a controlled DNAPL release; 200 MHz radar

Abstract: A controlled release of tetrachloroethylene was performed in a saturated, natural sandy aquifer to evaluate the effectiveness of various geophysical techniques for detecting and monitoring dense nonaqueous phase liquids (DNAPLs) in the subsurface. Tetrachloroethylene, typical of most DNAPLs, has a low relative dielectric permittivity (2.3), which contrasts with the high relative permittivity (80) of the pore water it displaces, making it a potential target for detection by ground-penetrating radar (GPR). GPR data were acquired using 200 MHz antennas.Radar sections collected at different times over the same spatial location clearly show the changes induced by the movement of DNAPL in the subsurface. Temporal changes can be examined through the evolution of a radar data trace collected at a single spatial location. Normal moveout analysis of commonmidpoint (CMP) data demonstrates induced changes in electromagnetic (EM) wave velocities of up to 30 percent caused by the presence of DNAPL. The distribution of DNAPL can be mapped in three dimensions at different times using a network of 16 radar lines.The 200 MHz GPR proved to be an effective technique for monitoring the movement of DNAPL in the subsurface. Direct detection of DNAPLs by radar is also feasible in this simple environment.

Constant Q attenuation of subsurface radar pulses

Abstract: Q is a measure of the energy stored to the energy dissipated in a propagating wave and can be estimated from the ratio of attenuation and frequency. For seismic waves, Q has been found to be essentially independent of frequency. As a result, attenuation is an approximately linear function of frequency and the impulse response function of the earth. Hence, the distortion of a seismic pulse as it propagates can be described by a single parameter. Laboratory measurements show that the attenuation of radio waves in some geological materials can also be approximated by a linear function of frequency over the bandwidths of typical subsurface radar pulses. We define a new parameter Q* to describe the slope of this linear region. The impulse response of the transfer function for a given value of Q* differs from that of the same value of Q only in total amplitude. Thus the change of shape of a radar pulse as it travels through these materials can also be described by a single parameter. The constant Q* model succe...

3-D elastic modeling with surface topography by a Chebychev spectral method

Abstract: The 3-D numerical Chebychev modeling scheme accounts for surface topography. The method is based on spectral derivative operators. Spatial differencing in horizontal directions is performed by the Fourier method, whereas vertical derivatives are carried out by a Chebychev method that allows for the incorporation of boundary conditions into the numerical scheme. The method is based on the velocity‐stress formulation. The implementation of surface topography is done by mapping a rectangular grid onto a curved grid. Boundary conditions are applied by means of characteristic variables. The study of surface effects of seismic wave propagation in the presence of surface topography is important, since nonray effects such as diffractions and scattering at rough surfaces must be considered. Several examples show this. The 3-D modeling alogrithm can serve as a tool for understanding these phenomena since it computes the full wavefield.

Generalized compact gravity inversion

Abstract: Extending the compact gravity inversion technique by incorporating a priori information about the maximum compactness of the anomalous sources along several axes provides versatility. Thus, the method may also incorporate information about limits in the axes lengths or greater concentration of mass along one or more directions. The judicious combination of different constraints on the anomalous mass distribution allows the introduction of several kinds of a priori information about the (arbitrary) shape of the sources. This method is particularly applicable to constant, linear density sources such as mineralizations along faults and intruded sills, dikes, and laccoliths in a sedimentary basin. The correct source density must be known with a maximum uncertainty of 40 percent; otherwise, the inversion produces thicker bodies for densities smaller than the true value and vice-versa. Because of the limitations of the inverse gravity problem, the proposed technique requires an empirical technique to analyze the sensitivity of solutions to uncertainties in the a priori information. The proposed technique is based on a finite number of acceptable solutions, presumably representative of the ambiguity region. By using standard statistical techniques, each parameter is assigned a coefficient measuring its uncertainty. The known hematite and magnetite ore body shape, in the vicinity of Iron Mountain, MO, was reproduced quite well using this inversion technique.

Do traveltimes in pulse‐transmission experiments yield anisotropic group or phase velocities?

Abstract: The elastic properties of layered rocks are often measured using the pulse through-transmission technique on sets of cylindrical cores cut at angles of 0, 90, and 45 degrees to the layering normal (e.g., Vernik and Nur, 1992; Lo et al., 1986; Jones and Wang, 1981). In this method transducers are attached to the flat ends of the three cores (see Figure 1), the first-break traveltimes of P, SV, and SH-waves down the axes are measured, and a set of transversely isotropic elastic constants are fit to the results. The usual assumption is that frequency dispersion, boundary reflections, and near-field effects can all be safely ignored, and that the traveltimes measure either vertical anisotropic group velocity (if the transducers are very small compared to their separation) or phase velocity (if the transducers are relatively wide compared to their separation) (Auld, 1973).

3-D elastic prestack, reverse-time depth migration

Abstract: By combining and extending previous algorithms for 2-D prestack elastic migration and 3-D prestack acoustic migration, a full 3-D elastic prestack depth migration algorithm is developed. Reverse-time extrapolation of the recorded data is by 3-D elastic finite differences; computation of the image time for each point in the 3-D volume is by 3-D acoustic finite differences. The algorithm operates on three-component, vector-wavefield common-source data and produces three-component vector reflectivity distributions. Converted P-to-S reflections are automatically imaged with the primary P-wave reflections. There are no dip restrictions as the full wave equation is used. The algorithm is illustrated by application to synthetic data from three models; a flat reflector, a dipping truncated wedge overlying a flat reflector, and the classical French double dome and fault model.

Borehole flexural modes in anisotropic formations

Abstract: A perturbation method of solution is an efficient way of analyzing elastic wave propagation along a borehole in anisotropic formations. The perturbation model allows us to calculate changes in the modal dispersion curves caused by the differences in elastic constants between the anisotropic formation of interest and a reference, or unperturbed, isotropic formation. The equivalent isotropic constants in the reference formation are obtained from the appropriate compressional‐and shear‐wave velocities for the selected propagation and polarization directions of the flexural mode. This choice of the unperturbed solution means that the required perturbation is minimal, resulting in enhanced accuracy of the perturbed solution. Computational results are presented for the dispersion curves of borehole flexural waves in a transversely isotropic (TI) formation as a function of borehole deviation from the TI symmetry axis. In addition, radial distributions of displacement and stress fields associated with the flexura...

Hydrocarbon‐generation‐induced microcracking of source rocks

Abstract: Laboratory measurements of ultrasonic velocity and anisotropy in kerogen-rich black shales of varying maturity suggest that extensive, bedding-parallel microcracks exist in situ in most mature source rocks undergoing the major stage of hydrocarbon generation and migration. Given the normal faulting regime with the vertical stress being the maximum principal stress typical of most sedimentary basins, this microcrack alignment cannot be accounted for using simplified fracture mechanics concepts. This subhorizontal microcrack alignment is consistent with (1) a model of local principal stress rotation and deviatoric stress reduction within an overpressured formation undergoing hydrocarbon generation, and with (2) a strong mechanical strength anisotropy of kerogen-rich shales caused by bedding-parallel alignment of kerogen microlayers. Microcracks originate within kerogen or at kerogen-illite interfaces when pore pressure exceeds the bedding-normal total stress by only a few MPa due to the extremely low-fracture toughness of organic matter. P-wave and, especially, S-wave anisotropy of the most mature black shales, measured as a function of confining pressure, indicate the effective closure pressure of these microcracks in the range from 10 to 25 MPa. Estimates of pore pressure cycles in the matrix of the active hydrocarbon-generating/expelling part of the source rock formation show that microcracks can be maintained openmore » over the sequence of these cycles and hence be detectable via high-resolution in-situ sonic/seismic studies.« less

Modeling of streaming potential responses caused by oil well pumping

Abstract: The occurrence of streaming potentials is directly related to movement of fluids in the subsurface. To investigate whether streaming potential measurements in boreholes and at the surface can be used to monitor subsurface flow and detect subsurface flow patterns in oil reservoirs, we model streaming potential responses caused by oil well pumping in monitoring wells and at the earth's surface. Since the model parameters: permeabilities, cross‐coupling properties, and electric conductivities depend on a few basic rock‐physics parameters such as brine conductivity, amount of water saturation, and porosity, the model parameters are evaluated self‐consistently using rock‐physics models. Using a threedimensional, (3-D) finite‐difference algorithm, the governing differential equations that are drawn from nonequilibrium thermodynamics are solved numerically in three self‐consistent steps: solution of the hydraulic problem, computation of the streaming current sources based on the principle of conservation of char...

The influence of clay content, salinity, stress, and wettability on the dielectric properties of brine-saturated rocks; 10 Hz to 10 MHz

Abstract: Complex impedance measurements have been performed on 14 shaly sand samples, Berea sandstone, and Ottawa sand-bentonite packs in a frequency range of 10 Hz to 10 MHz, using both the two- and four-electrode techniques. Measurements have been conducted at an effective radial stress varying from ambient pressure to 4000 psi for brine-saturated oil-wet and water-wet samples.The dielectric permittivity is found to correlate with the clay volume fraction, the cation exchange capacity, and electrochemical potential of the rock samples and to depend strongly on the salinity of the brine used. Stress and wettability are shown to have a small influence on the dielectric constant of fully brine-saturated rocks. A lower critical frequency is found to characterize the geometry of the pore space. Empirical correlations between the dielectric constant, frequency, permeability, cation exchange capacity, and porosity are presented for the shaly sands used in this study. These correlations provide a means of estimating important petrophysical parameters such as the permeability and the clay content from a nondestructive complex impedance sweep of shaly sands fully saturated with brine.

Pore fluid effects on seismic velocity in anisotropic rocks

Abstract: A simple new technique predicts the high‐ and low‐frequency saturated velocities in anisotropic rocks entirely in terms of measurable dry rock properties without the need for idealized crack geometries. Measurements of dry velocity versus pressure and porosity versus pressure contain all of the necessary information for predicting the frequency‐dependent effects of fluid saturation. Furthermore, these measurements automatically incorporate all pore interaction, so there is no limitation to low crack density. The velocities are found to depend on five key interrelated variables: frequency, the distribution of compliant crack‐like porosity, the intrinsic or noncrack anisotropy, fluid viscosity and compressibility, and effective pressure. The sensitivity of velocities to saturation is generally greater at high frequencies than low frequencies. The magnitude of the differences from dry to saturated and from low frequency to high frequency is determined by the compliant or crack‐like porosity. Predictions of s...

Interpreting laboratory velocity measurements in partially gas-saturated rocks

Abstract: It is an old problem in rock physics that the saturation dependence of high-frequency laboratory velocities does not match the Biot-Gassmann theory commonly used to predict the effects of gas on seismic velocities. A new interpretation of laboratory velocity data shows that the saturation dependence is controlled by two previously published high-frequency acoustic mechanisms: (1) a gas pocket model that describes pressure equilibration between liquid and gas-saturated regions of the pore space, and (2) local fluid flow, induced by pressure equilibration in pores with different aspect ratios. When these two mechanisms are added to Biot theory, the result describes published velocity versus gas saturation data for a wide range of rock types. These two mechanisms are negligible at the lower frequencies of seismic data, so the saturation dependence of laboratory velocities cannot be used to predict the saturation dependence at seismic frequencies. The one laboratory measurement that is relevant for predicting the seismic velocity is the ultrasonic velocity of the dry rock. The dry-rock velocities should be used in the Biot-Gassmann theory to predict the full saturation dependence of the seismic velocities.

Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks

Abstract: Seismic velocities in rocks at ultrasonic frequencies depend not only on the degree of saturation but also on the distribution of the fluid phase at various scales within the pore space. Two scales of saturation heterogeneity are important: (1) saturation differences between thin compliant pores and larger stiffer pores, and (2) differences between saturated patches and undersaturated patches at a scale much larger than any pore. We propose a formalism for predicting the range of velocities in partially saturated rocks that avoids assuming idealized pore shapes by using measured dry rock velocity versus pressure and dry rock porosity versus pressure. The pressure dependence contains all of the necessary information about the distribution of pore compliances for estimating effects of saturation at the finest scales where small amounts of fluid in the thinnest, most compliant parts of the pore space stiffen the rock in both compression and shear (increasing both P- and S-wave velocities) in approximately the same way that confining pressure stiffens the rock by closing the compliant pores. Large-scale saturation patches tend to increase only the high-frequency bulk modulus by amounts roughly proportional to the saturation. The pore-scale effects will be most important at laboratory and logging frequencies when pore-scale pore pressure gradients are unrelaxed. The patchy-saturation effects can persist even at seismic field frequencies if the patch sizes are sufficiently large and the diffusivities are sufficiently low for the larger-scale pressure gradients to be unrelaxed.

SEG/EAEG 3-D modelling project; 2nd update

Abstract: The first update for the SEG/EAEG 3-D Modeling Project appeared in the February issue of TLE and the March issue of First Break. Our goal is to design salt and overthrust 3-D models and then simulate realistic 3-D surveys based on those models. Given the project’s significance and scope, we plan frequent progress reports. In conjunction with this goal and to solicit input, we have made recent presentations at SEG Cairo, the SEG/EAEG Summer Research Workshop in The Netherlands, the Stanford Exploration Project, and the Center for Wave Phenomena at the Colorado School of Mines.

Scale effects on velocity dispersion: From ray to effective medium theories in stratified media

Abstract: Wave propagation in stratified media may be explained by ray theory, effective medium theory, or scattering theory depending on the scales of wavelength and layer spacing. To effectively integrate and use seismic data at different frequencies and widely varying scales, it is essential to understand the domain of applicability of long and short wavelength behavior and the transition between them. A joint experimental and theoretical study was conducted to investigate velocity behavior at the transition from ray theory to effective medium theory in stratified media. Velocity measurements were performed at 50 and 500 kHz on periodic media composed of steel and plastic discs. The ratio of wavelength to layer spacing, λ/d, spanned more than two orders of magnitude between 0.1 and 50, and the volume fraction of steel ranged from 9 to 89 percent by volume. Our results confirm that velocities in stratified media depend on composition and are controlled by the ratio of wavelength to layer spacing. Velocities in th...

Finite-difference solution of the eikonal equation using an efficient, first-arrival, wavefront tracking scheme

Abstract: First‐break traveltimes can be accurately computed by the finite‐difference solution of the eikonal equation using a new corner‐node discretization scheme. It offers accuracy advantages over the traditional cell‐centered node scheme. A substantial efficiency improvement is achieved by the incorporation of a wavefront tracking algorithm based on the construction of a minimum traveltime tree. For the traditional discretization scheme, an accurate average value for the local squared slowness is found to be crucial in stabilizing the numerical scheme for models with large slowness contrasts. An improved method based on the traditional discretization scheme can be used to calculate traveltimes in arbitrarily varying velocity models, but the method based on the corner‐node discretization scheme provides a much better solution.