Showing papers in "Geophysics in 1991"
TL;DR: In this paper, a wave-equation traveltime inversion (WT-inversion) method is proposed to perturb the velocity model until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a least squares sense.
Abstract: This paper presents a new traveltime inversion method based on the wave equation. In this new method, designated as wave-equation traveltime inversion (WT), seismograms are computed by any full-wave forward modeling method (we use a finite-difference method). The velocity model is perturbed until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a least squares sense. A gradient optimization method is used and the formula for the Frechet derivative (perturbation of traveltimes with respect to velocity) is derived directly from the wave equation. No traveltime picking or ray tracing is necessary, and there are no high frequency assumptions about the data. Body wave, diffraction, reflection and head wave traveltimes can be incorporated into the inversion. In the high-frequency limit, WT inversion reduces to ray-based traveltime tomography. It can also be shown that WT inversion is approximately equivalent to full-wave inversion when the starting velocity model is 'close' to the actual model.Numerical simulations show that WT inversion succeeds for models with up to 80 percent velocity contrasts compared to the failure of full-wave inversion for some models with no more than 10 percent velocity contrast. We also show that the WT method succeeds in inverting a layered velocity model where a shooting ray-tracing method fails to compute the correct first arrival times. The disadvantage of the WT method is that it appears to provide less model resolution compared to full-wave inversion, but this problem can be remedied by a hybrid traveltime + full-wave inversion method (Luo and Schuster, 1989).
701 citations
TL;DR: In this paper, the shortest traveltime path from one point to another is an approximation to the seismic ray between them, by Fermat's principle, and the shortest path method is an efficient and flexible way to calculate the raypaths and traveltimes of first arrivals to all points in the earth simultaneously.
Abstract: Like the traveling salesman who wants to find the shortest route from one city to another in order to minimize his time wasted on traveling, one can find seismic raypaths by calculating the shortest traveltime paths through a network that represents the earth. The network consists of points that are connected with neighboring points by connections as “long” as the traveltime of a seismic wave along it. The shortest traveltime path from one point to another is an approximation to the seismic ray between them, by Fermat’s principle. The shortest path method is an efficient and flexible way to calculate the raypaths and traveltimes of first arrivals to all points in the earth simultaneously. There are no restrictions of classical ray theory: diffracted raypaths and paths to shadow zones are found correctly. There are also no restrictions to the complexity or the dimensionality of the velocity model. Furthermore, there are no problems with convergence of trial raypaths toward a specified receiver nor with ray...
628 citations
TL;DR: In this article, a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events, nor estimation of these directions.
Abstract: Interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing. A major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated. In this respect, a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events, nor estimation of these directions.The method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly, regardless of the original spatial interval, without any attempt to determine their true dips. The predictability of linear events in the f-x domain allows the missing traces to be expressed as the output of a linear system, the input of which consists of the recorded traces. The interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces.Synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations. Assessment of the method with a real data set shows that the interpolation yields an improved migrated section.
576 citations
TL;DR: In this paper, the magnitude of the grain-scale local flow effect on velocity dispersion in saturated rocks is quantified, by estimating the high-frequency unrelaxed shear and bulk frame moduli, which are then combined with the Biot formulation to predict total dispersion.
Abstract: The magnitude of the grain-scale local flow effect on velocity dispersion in saturated rocks is quantified, by estimating the high-frequency unrelaxed shear and bulk frame moduli, which are then combined with the Biot formulation to predict total dispersion. The method is relatively independent of assumptions about idealized pore geometries and unknown parameters such as pore aspect ratios. The local flow effect depends on the heterogeneity of pore stiffness, in particular the presence of compliant cracks and grain contacts; the pressure dependence of the dry rock properties is shown to contain the essential information about the distribution of pore stiffnesses needed to estimate the high-frequency saturated behavior. To first order, the unrelaxed wet frame compressibility at any given pressure is shown to be approximately the dry frame compressibility at very high pressure; second order corrections add the additional compressibility gained by replacing an amount of mineral equal to the compliant pore volume with fluid. The method predicts that the difference between relaxed and unrelaxed shear compliance is simply proportional to that in bulk. The results for total dispersion (local flow plus Biot) explain quite well the measured P- and S-wave dispersion for a variety of saturated rocks.
564 citations
TL;DR: In this paper, the authors used simulated annealing to find the critical temperature at which a solid in a heat bath is heated by increasing the temperature, followed by slow cooling until it reaches the global minimum energy state.
Abstract: The seismic inverse problem involves finding a model m that either minimizes the error energy between the data and theoretical seismograms or maximizes the cross-correlation between the synthetics and the observations. We are, however, faced with two problems: (1) the model space is very large, typically of the order of 50 50 ; and, (2) the error energy function is multimodal. Existing calculus-based methods are local in scope and easily get trapped in local minima of the energy function. Other methods such as 'simulated annealing' and 'genetic algorithms' can be applied to such global optimization problems and they do not depend on the starting model. Both of these methods bear analogy to natural systems and are robust in nature. For example, simulated annealing is the analog to a physical process in which a solid in a 'heat bath' is heated by increasing the temperature, followed by slow cooling until it reaches the global minimum energy state where it forms a crystal. To use simulated annealing efficiently for 1-D seismic waveform inversion, we require a modeling method that rapidly performs the forward modeling calculation and a cooling schedule that will enable us to find the global minimum of the energy function rapidly. With the advent of vector computers, the reflectivity method has proved successful and the time of the calculation can be reduced substantially if only plane-wave seismograms are required. Thus, the principal problem with simulated annealing is to find the critical temperature, i.e., the temperature at which crystallization occurs. By initiating the simulated annealing process with different starting temperatures for a fixed number of iterations with a very slow cooling, we noticed that by starting very near but just above the critical temperature, we reach very close to the global minimum energy state very rapidly. We have applied this technique successfully to band-limited synthetic data in the presence of random noise. In most cases we find that we are able to obtain very good solutions using only a few plane wave seismograms.
458 citations
TL;DR: Differential semblance optimization (DSO) as discussed by the authors is an approach to inversion of reflection seismograms which avoids the severe convergence difficulties associated with nonlinear least squares inversion by exploiting both moveout and amplitude characteristics of reflections.
Abstract: Differential semblance optimization (DSO) is an approach to inversion of reflection seismograms which avoids the severe convergence difficulties associated with nonlinear least‐squares inversion. The method exploits both moveout and amplitude characteristics of reflections. We have implemented a version appropriate to plane‐wave (p‐tau) seismograms and layered constant‐density acoustic earth models. Theoretical and numerical analyses of this version of DSO indicate that stable and reasonably accurate estimates of both velocity trend and reflectivity can be derived. To test DSO further, we applied it to a marine data set from the Gulf of Mexico, where the method produced results which compare favorably to well‐log information. The method can be extended to incorporate laterally heterogeneous velocity models.
447 citations
TL;DR: In this paper, the applicability of genetic algorithms to the inversion of plane-wave seismograms was investigated, where a random walk in model space and a transition probability rule were used to help guide their search.
Abstract: Seismic waveform inversion is one of many geophysical problems which can be identified as a nonlinear multiparameter optimization problem. Methods based on local linearization fail if the starting model is too far from the true model. We have investigated the applicability of “Genetic Algorithms” (GA) to the inversion of plane‐wave seismograms. Like simulated annealing, genetic algorithms use a random walk in model space and a transition probability rule to help guide their search. However, unlike a single simulated annealing run, the genetic algorithms search from a randomly chosen population of models (strings) and work with a binary coding of the model parameter set. Unlike a pure random search, such as in a “Monte Carlo” method, the search used in genetic algorithms is not directionless. Genetic algorithms essentially consist of three operations, selection, crossover, and mutation, which involve random number generation, string copies, and some partial string exchanges. The choice of the initial popul...
378 citations
TL;DR: In this paper, an upwind finite-difference method was proposed to solve a conservation law that describes changes in the gradient components of the traveltime field, which is useful both in Kirchhoff migration and modeling and in seismic tomography.
Abstract: Seismic traveltimes can be computed efficiently on a regular grid by an upwind finite‐difference method. The method solves a conservation law that describes changes in the gradient components of the traveltime field. The traveltime field itself is easily obtained from the solution of the conservation law by numerical integration. The conservation law derives from the eikonal equation, and its solution depicts the first‐arrival‐time field. The upwind finite‐difference scheme can be implemented in fully vectorized form, in contrast to a similar scheme proposed recently by Vidale. The resulting traveltime field is useful both in Kirchhoff migration and modeling and in seismic tomography. Many reliable methods exist for the numerical solution of conservation laws, which appear in fluid mechanics as statements of the conservation of mass, momentum, etc. A first‐order upwind finite‐difference scheme proves accurate enough for seismic applications. Upwind schemes are stable because they mimic the behavior of flu...
293 citations
TL;DR: In this article, the authors show that a dispersive 1-D backward propagation can form the basis of a number of different algorithms for inverse Q filtering, each of which is akin to a particular migration algorithm.
Abstract: Although some attention has been paid to the idea that seismic migration is equivalent to a type of deconvolution (of the spatial wavelet), less thought has been given to the opposite perspective: that deconvolution (of the earth Q filter) might itself be equivalent to a form of migration. The key point raised in this paper is that a dispersive 1-D backward propagation can form the basis of a number of different algorithms for inverse Q filtering, each of which is akin to a particular migration algorithm. An especially efficient algorithm can be derived by means of a coordinate transformation equivalent to that in the Stolt frequency-wavenumber migration.This fast algorithm, valid for Q constant with depth, can be extended to accommodate depth-variable Q by cascading a series of constant Q compensations, as in cascaded migration. By combining a cascaded phase compensation with a windowed approach to amplitude compensation, we obtain an algorithm that is sufficiently efficient to be used routinely for prestack data processing. Data examples compare the results of conventional processing with the more stable phase treatment that can be obtained by including prestack inverse Q filtering in the processing.
244 citations
TL;DR: In this article, the boundary conditions for elastic waves are developed for elastic wave motions in unbounded spatial domains based on compositions of simple first-order differential operators, which can be applied without modification to problems in both two and three dimensions.
Abstract: Absorbing boundary conditions are needed for computing numerical models of wave motions in unbounded spatial domains. The boundary conditions developed here for elastic waves are generalizations of ones developed earlier for acoustic waves. These conditions are based on compositions of simple first-order differential operators. The formulas can be applied without modification to problems in both two and three dimensions. The boundary conditions are stable for all values of the ratio of P-wave velocity to S-wave velocity, and they are effective near a free surface and in a horizontally stratified medium. The boundary conditions are approximated with simple finite-difference equations that use values of the solution only along grid lines perpendicular to the boundary. This property facilitates implementation, especially near a free surface and at other corners of the computational domain.
229 citations
TL;DR: In this article, a practical algorithm for inverting gridded resistivity data for three-dimensional structure and applied it to data from an experiment designed to detect leaks from ponds.
Abstract: We have developed a practical algorithm for inverting gridded resistivity data for three‐dimensional structure and applied it to data from an experiment designed to detect leaks from ponds This method yields relatively accurate reconstructions of structure when applied to synthetic data, but lateral contrasts in resistivity are mapped much more accurately than are vertical contrasts The best results are obtained when transmitting electrodes are located directly above the suspected leak Application to real data yields results which are consistent with well data and an adjacent Schlumberger sounding
TL;DR: In this paper, the authors consider the case of monochromatic illumination of a region consisting of small perturbations to a homogeneous background, and compare the two reconstruction algorithms to reveal the effect of neglecting scattering.
Abstract: Tomographic imaging is now in widespread use in geophysical inversion. Most early work in this field used the ray approximation to wave propagation, but more recently scattering effects have been addressed via the formalism of diffraction tomography. However, if the correct image cannot be adequately represented as a perturbation of a simple background, this may demand considerably more computational resources than ray tomography. Therefore it is of some interest to determine the scalelength of variation below which scattering cannot be neglected, so that ray tomography is no longer reliable. In the hypothetical case of monochromatic illumination of a region consisting of small perturbations to a homogeneous background, the way in which the two reconstruction algorithms map the data into the Fourier components of the object may be directly compared to reveal the effect of neglecting scattering. These mappings begin to differ significantly at a wave‐number corresponding to the first Fresnel zone radius; it...
TL;DR: In this article, it was shown that, regardless of frequency, it is safe to ignore the electrokinetic losses when the electrolyte molarity is on the order of 0.1 M or greater.
Abstract: When a fluid electrolyte moves relative to a solid, an electric field is generated that migrates ions and thus dissipates energy. This 9electrokinetic9 dissipation is theoretically compared to the viscous shear dissipation for fluid flow generated by a fixed time harmonic pressure gradient in a planar quartz duct. It is shown that, regardless of frequency, it is safe to ignore the electrokinetic losses when the electrolyte molarity is on the order of 0.1 M or greater. For low molarity electrolytes (10 (super -3) M), however, the electrokinetic losses do become significant compared to the viscous losses for flow in sufficiently tight pores. The ratio of electrokinetic dissipation D E to viscous dissipation D V is always a maximum when the electrokinetic radius (the duct half-width divided by the Debye length) is nearly equal 1.5. The maximum value of D E /D V does not exceed 0.5 for the NaCl, KCl, and quartz systems considered.The generated electric field pushes on the excess ions in the duct in a direction opposite to the applied pressure gradient, thus giving rise to an apparent viscosity enhancement. This enhancement is E /D V ratio. Indeed, the central effect of a large D E /D V ratio is that the amount of relative fluid flow is reduced, and thus, the amount of wave attenuation is reduced.
TL;DR: In this article, the authors derived exact formulas for two elastic parameters needed to describe wave propagation in a conglomerate of two porous phases, which are properties of the composite solid frame (drained of fluid) and are shown here to be completely determined in terms of the bulk moduli associated with the two solid constituents, the main moduli of the drained conglomerate and the drained phases, and the porosities in each phase.
Abstract: Wave propagation in fluid-filled porous media is governed by Biot's equations of poroelasticity. Gassmann's relation gives an exact formula for the poroelastic parameters when the porous medium contains only one type of solid constituent. The present paper generalizes Gassmann's relation and derives exact formulas for two elastic parameters needed to describe wave propagation in a conglomerate of two porous phases. The parameters were first introduced by Brown and Korringa when they derived a generalized form of Gassmann's equation for conglomerates. These elastic parameters are the bulk modulus K s associated with changes in the overall volume of the conglomerate and the bulk modulus K (sub phi ) associated with the pore volume when the fluid pressure (p f ) and confining pressure (p) are increased, keeping the differential pressure (p d = p - p f ) fixed. These moduli are properties of the composite solid frame (drained of fluid) and are shown here to be completely determined in terms of the bulk moduli associated with the two solid constituents, the bulk moduli of the drained conglomerate and the drained phases, and the porosities in each phase. The pore structure of each phase is assumed uniform and smaller than the grain size in the conglomerate. The relations found are completely independent of the pore microstructure and provide a means of analyzing experimental data.The key idea leading to the exact results is this: Whenever two scalar fields (in our problem p f and p d ) can be independently varied in a linear composite containing only two constituents, there exists a special value gamma of the increment ratio for these two fields corresponding to an overall expansion or contraction of the medium with no change of relative shape. This fact guarantees that a set of consistency relations exists among the constituent moduli and the effective moduli, which then determines all but one of the effective constants. Thus, K s and K (sub phi ) are determined in terms of the drained frame modulus K and the constituents' moduli. Because the composite is linear, the coefficients found for the special value of the increment ratio are also the exact coefficients for an arbitrary ratio. Since modulus K is commonly measured while the other two are not, these exact relations provide a significant advance in our ability to predict the response of porous materials to pressure changes.It is also shown that additional results (such as rigorous bounds on the parameters) may be easily obtained by exploiting an analogy between the equations of thermoelasticity and those of poroelasticity. The method used to derive these results may also be used to find exact expressions for three component composite porous materials when thermoelastic constants of the components and the composite are known.
TL;DR: In this article, an outcropping hemispherical inhomogeneity embedded in a two-dimensional (2D) earth is used to model the effects of three-dimensional near-surface electromagnetic (EM) "static" distortion.
Abstract: An outcropping hemispherical inhomogeneity embedded in a two‐dimensional (2-D) earth is used to model the effects of three‐dimensional (3-D) near‐surface electromagnetic (EM) “static” distortion. Analytical solutions are first derived for the galvanic electric and magnetic scattering operators of the heterogeneity. To represent the local distortion by 3-D structures of fields which were produced by a large‐scale 2-D structure, these 3-D scattering operators are applied to 2-D electric and magnetic fields derived by numerical modeling to synthesize an MT data set. Synthetic noise is also included in the data. These synthetic data are used to study the parameters recovered by several published methods for decomposing or parameterizing the measured MT impedance tensor. The stability of these parameters in the presence of noise is also examined. The parameterizations studied include the conventional 2-D parameterization (Swift, 1967), Eggers’s (1982) and Spitz’s (1985) eigenstate formulations, LaTorraca et al...
TL;DR: In this article, an iterative, modified least squares inversion based on a finite element forward solution of Laplace's equation is proposed for determining the electrical resistivity distribution in a volume from discrete measurements made within the volume or on its surface.
Abstract: Electrical resistivity tomography (ERT) is a method for determining the electrical resistivity distribution in a volume from discrete measurements of current and voltage made within the volume or on its surface. We have developed an ERT algorithm that is an iterative, modified least squares inversion, based on a finite element forward solution of Laplace’s equation. We report the results of tests on this algorithm designed to determine how resistance measurements made from two boreholes may be used to image the resistivity distribution between them. A number of simple but geophysically significant structures are modeled. These include a single isolated block anomaly, two layers, a thin isolated continuous layer, and a vertical band. The main features of most resistivity models were identifiable in the reconstructions. Limited data accuracy and noise were simulated and found to cause a deterioration of the image. However, even with measurements of only one significant figure accuracy, the algorithm converg...
TL;DR: In this paper, a new wellbore seismic technique uses the vibrations produced by a drill bit while drilling as a downhole seismic energy source, which is described as "inverse" VSP because the source and receiver positions of conventional VSP are reversed.
Abstract: A new wellbore seismic technique uses the vibrations produced by a drill bit while drilling as a downhole seismic energy source. The technique is described as 'inverse' VSP because the source and receiver positions of conventional VSP are reversed. No downhole instrumentation is required to obtain the data and the data recording does not interfere with the drilling process. These characteristics offer a method by which borehole seismic data can be acquired, processed, and interpreted while drilling. Interchanging the conventional VSP source and receiver positions improves the efficiency of recording multioffset surveys for imaging a 3-D data volume in the borehole vicinity. The continuous signals generated by the drill bit are recorded by a pilot sensor attached to the top of the drillstring and by receivers located at selected positions around the borehole. The pilot signal is crosscorrelated with the receiver signals to compute traveltimes of the arrivals and to attenuate incoherent noise. Deconvolution and time shifts of the pilot signal compensate for the effects of propagation from the drill bit to the top of the drillstring. By repeating this process for an interval of the well, a VSP-equivalent data set is generated. Results from a test well demonstrate that the processed drill-bit data are comparable to conventional VSP data.
TL;DR: In this paper, the two techniques which may be best for this search are a ground-penetrating radar survey and a soil conductivity survey, with its capability for estimating the depth and shape of buried objects, are presented.
Abstract: Over the decades, grave markers in old cemeteries have been lost. Geophysical exploration can sometimes locate the unmarked burials. The two techniques which may be best for this search are a ground‐penetrating radar survey and a soil conductivity survey. A ground‐penetrating radar survey, with its capability for estimating the depth and shape of buried objects, is particularly suitable. With an electromagnetic induction survey, the disturbed soil in the grave shaft can sometimes be detected as a change in electrical conductivity. Both of these surveys also can locate large metal objects. These surveys have limitations. At some sites, the radar cannot profile deeply enough; at others, the soil strata are so complex that graves cannot be distinguished. A conductivity survey can be degraded by metallic trash and other small objects in the topsoil; it can give the best results where the earth is distinctly stratified. Results from nine surveys are illustrated here. The sites are all in the U.S.A. and the gra...
TL;DR: In this article, a new integro-difference formulation for evaluating surface charge has been adopted in favor of true surface integrations over the source cells with potential differencing across the field cells in the 3D body.
Abstract: Recent progress in integral equation modeling of three‐dimensional magnetotelluric responses includes the ability to simulate 3-D structures which outcrop (excluding topography), which transect layer interfaces, and which extend indefinitely in one or more directions. The most important factor in achieving this capability is an accurate treatment of the electric surface charge. In particular, a previous integro‐difference formulation for evaluating charges has been abandoned in favor of true surface integrations over the source cells with potential differencing across the field cells in the 3-D body. The new procedure constitutes a good approximation to Galerkin’s method while preserving internal consistency in terms of pulse basis functions. To verify outcropping structures, juxtaposed conductive and resistive prisms at the surface are simulated and compared to 2-D results. An elongate version of the 3-D model shows good agreement with both transverse electric and transverse magnetic modes of the 2-D res...
TL;DR: In this paper, the authors measured compressional velocities of two water saturated sandstones having a range of porosities Phi (2 to 36 percent), permeabilities K (0.001 to 306 mD) and clay contents C (negligible to 30 percent) under varying confining and pore fluid pressures (up to 40 MPa).
Abstract: Compressional velocities V P were measured in laboratory samples at ultrasonic frequencies (0.5-1.5 MHz) and under varying confining and pore fluid pressures (up to 40 MPa). Forty-two water saturated sandstones having a range of porosities Phi (2 to 36 percent), permeabilities K (0.001 to 306 mD) and clay contents C (negligible to 30 percent) were studied. I found that at 40 MPa the compressional velocity is inversely proportional to clay content. P-wave velocity decreases with increasing porosity, but the scatter is large even at very high pressures. The velocity-porosity scatter is reduced when the clay content is included. The dependence of V P on permeability for a wide range of porosities (6 to 36 percent) is indeterminable due to a large scatter. When the rocks are grouped into identical porosities the scatter is reduced and V P increases with decreasing clay content and increasing permeability. However, the effect of permeability alone on V P was found to be negligible in rocks with identical porosity, lithology, and negligible or similar clay content. Hence, the velocity-permeability relationship is controlled by the velocity-clay content and permeability-clay content interrelations.For all samples, the compressional-wave velocity V P in km/s at ultrasonic frequencies and 40 MPa is related to porosity Phi (fractional), clay content C (fractional) and permeability K (millidarcy) by V P = 5.66 - 6.11Phi - 3.53C + 0.0007K, r = 0.96 where r is the correlation coefficient. The relationship shows empirically that the permeability effect is very small compared to that of porosity and clay content.By calculating the elastic moduli, I extrapolated from ultrasonic to seismic frequencies and obtained V (sub P(seismic)) = 5.27 - 5.4Phi - 2.54C + 0.001K, r = 0.93 for porosities 6-36 percent.
TL;DR: In this paper, an industrial laminate, Phenolic CE, is shown to possess seismic anisotropy, which is characteristic of orthorhombic symmetry, i.e., that the material has three mutually orthogonal axes of two-fold symmetry.
Abstract: An industrial laminate, Phenolic CE, is shown to possess seismic anisotropy. This material is composed of laminated sheets of canvas fabric, with an approximately orthogonal weave of fibers, bonded with phenolic resin. It is currently being used in scaled physical modeling studies of anisotropic media at The University of Calgary. Ultrasonic transmission experiments using this material show a directional variation of compressional- and shear-wave velocities and distinct shear-wave birefringence, or splitting. Analysis of group-velocity measurements taken for specific directions of propagation through the material demonstrates that the observed anisotropy is characteristic of orthorhombic symmetry, i.e., that the material has three mutually orthogonal axes of two-fold symmetry. For P waves, the observed anisotropy in symmetry planes varies from 6.3 to 22.4 percent, while for S waves it is observed to vary from 3.5 to 9.6 percent.From the Kelvin-Christoffel equations, which yield phase velocities given a set of stiffness values, expressions are elaborated that yield the stiffnesses of a material given a specified set of group-velocity observations, at least three of which must be for off-symmetry directions.
TL;DR: In this article, the authors used a conventional partial curve-matching method to obtain initial model parameters, which were used in a computer program to obtain final parameters, based on the model obtained, aquifer hydraulic conductivity and transmissivity were calculated.
Abstract: Seventeen Schlumberger vertical electrical soundings (VES) were carried out in parts of the Umuahia area of Nigeria, using a maximum current electrode separation of 1 km. The data were interpreted using a conventional partial curve‐matching method to obtain initial model parameters, which were used in a computer program to obtain final parameters. Three soundings were made at existing boreholes for comparison. Aquifer parameters of hydraulic conductivity and transmissivity were obtained by analyzing pumping test data from existing boreholes. The results of the interpretation revealed three distinct geoelectric layers overlying a conductive geoelectric basement. Based on the model obtained, aquifer hydraulic conductivity and transmissivity were calculated. The hydraulic conductivity calculated agreed closely with that determined from pumping test data. The results of the present study also indicate that the entire area is divided into two zones, each of which is homogeneous in hydraulic properties and wate...
TL;DR: In this article, the authors used the velocity estimates from tomography as a reference model for a numerical propagation of the time reversed data and used the backpropagated wave fields to provide images of the discontinuities in the velocity field.
Abstract: Traveltime tomography is an appropriate method for estimating seismic velocity structure from arrival times. However, tomography fails to resolve discontinuities in the velocities. Wave‐equation techniques provide images using the full wave field that complement the results of traveltime tomography. We use the velocity estimates from tomography as a reference model for a numerical propagation of the time reversed data. These “backpropagated” wave fields are used to provide images of the discontinuities in the velocity field. The combined use of traveltime tomography and wave‐equation imaging is particularly suitable for forming high‐resolution geologic images from multiple‐source/multiple‐receiver data acquired in borehole‐to‐borehole seismic surveying. In the context of crosshole imaging, an effective implementation of wave‐equation imaging is obtained by transforming the data and the algorithms into the frequency domain. This transformation allows the use of efficient frequency‐domain numerical propagat...
TL;DR: In this paper, the authors investigated the reasons for the very low permeability, less than 10-20m2 (10 nD), exhibited by many tight shales, and found that the flow path consists of a network of very tortuous pores with small diameters, of the order of 8-16 nm.
Abstract: Permeability, porosity, formation factor, mercury porosimetry, and stress‐strain measurements were made on 10 shale samples taken at depths between 4500 m and 5600 m in three wells on the Scotian shelf. The purpose was to obtain shale permeability values for quantitative sedimentary basin modeling and to investigate the reasons for the very low permeabilities, less than 10-20m2 (10 nD), exhibited by many tight shales. Permeabilities of 10-22-7×10-22m2 (0.1-0.7nD) and porosities of 0.9–9.2 percent were measured. The results suggest that the extremely low permeabilities occur because the flow path consists of a network of very tortuous pores (true tortuosity = 3.3) with small diameters, of the order of 8–16 nm. Presence of calcite and dolomite apparently is associated with reduced porosity, possibly a result of blocking of the pores, while kaolinite shows the reverse trend.
TL;DR: In this paper, a sampling strategy is proposed for a fixed azimuth while the take-off angle is automatically adjusted in order to have a roughly homogeneous spacing between end points of the rays.
Abstract: Procedures for accurate ray tracing in complex three-dimensional media with interfaces are proposed. The ray tracing equations and the associated paraxial linear equations are solved either by a numerical solver or by an analytical perturbation approach. Interfaces are described with an explicit representa tion or an implicit representation using B-spline inter polation. For the implicit representation, we exploit two important properties of B-splines, the convex hull and subdivision properties, in order to determine the intersection of the ray with the interface. At the free surface where the recording system is located, a sampling strategy is proposed: limits of branches at caustics, shadow zones, and medium boundaries are detected for a fixed azimuth while the take-off angle is automatically adjusted in order to have a roughly homogeneous spacing between end points of the rays. The same strategy is also possible for a fixed take-off angle. The assumed continuity of the traveltime surface between two adjacent azimuths enables one to obtain the initial condition of a ray arriving at any station located on the portion of surface delimited by these two azimuths. This procedure al lows for the classification of rays arriving at a given station as we show on different synthetic examples.
TL;DR: Complex resistivity measurements were performed on 22 saturated samples (sandstones, slate, shale, and granites) at room temperature and pressure over a frequency range from 1 Hz to 5 MHz, using a two-terminal sample holder as discussed by the authors.
Abstract: Complex resistivity measurements were performed on 22 saturated samples (sandstones, slate, shale, and granites) at room temperature and pressure over a frequency range from 1 Hz to 5 MHz, using a two‐terminal sample holder Although low‐frequency measurements (from 1 Hz to 1–10 kHz) are perturbed by electrode polarization phenomena, we observed classical behavior for 20 samples, ie, behavior that can be fitted to a Cole and Cole response function, and different behavior for the other two (two slates) These two last samples exhibit an almost constant imaginary part of the complex resistivity Since the frequency dependence is caused by interfacial effects, it is possible to characterize the internal surface area from electrical measurements We use models developed by Le Mehaute and Crepy (1983) and Po Zen Wong (1987) to calculate the fractal dimension d of the internal surface area from experimental data An independent measurement confirms that the specific surface area correlates with d The two mod
TL;DR: In this article, a closed-form formula for the curvature correction is derived for which the calculated values differ from those published by Swick by more than 0.5 mGal for high elevations.
Abstract: The complete Bouguer reduction includes, in addition to the simple Bouguer slab correction (Bullard A), both curvature (Bullard B) and terrain (Bullard C) corrections. A new closed‐form formula for the curvature correction is derived for which the calculated values differ from those published by Swick by more than 0.5 mGal for high elevations. These corrections reduce those of an infinite slab (Bullard A) to that of a spherical cap having a surface radius of 166.7 km. The spherical cap produces a lesser effect than the infinite slab because of the “truncation” of that part of the slab above the earth and extending to infinity, but it produces a greater effect than the slab because of subslab earth resulting from curvature. The physical significance of the correction lies in the combination of these two differences, which are each a function of elevation. The Bullard B surface radius (166.7 km: outer radius of the Hayford‐Bowie system) is reaffirmed by the exact formula to be appropriate for exploration su...
TL;DR: In this article, the resistivity of three sandstone samples collected during imbibition (increasing Sw) and drainage (decreasing Sw) show pronounced hysteresis in resistivity throughout much of the saturation range.
Abstract: Laboratory measurements of the resistivity of three sandstone samples collected during imbibition (increasing Sw) and drainage (decreasing Sw) show pronounced hysteresis in resistivity throughout much of the saturation range. The variation in resistivity can be related to changes in pore-scale fluid distribution caused by changes in saturation history. The form of the hysteresis is such that resistivity measured during imbibition is consistently less than that measured, at the same saturation, during drainage. This can be attributed to the presence of conduction at the air/ water interface in partially saturated samples; an effect that is enhanced by fluid geometries associated with the imbibition process. The results of this study suggest that the dependence of geophysical data on saturation history should be considered when interpreting data from the unsaturated zone.
TL;DR: In this article, a regional residual separation method for gravity data is proposed, which uses a robust procedure to determine the coefficients of a polynomial fitted to the observations and minimizes the influence of the residual field in the fitted surface.
Abstract: Standard polynomial fitting methods are inconsistent in their formulation. The regional field is approximated by a polynomial fitted to the observed field. As a result, in addition to the nonuniqueness in the definition of the regional field, the fitted polynomial is strongly influenced by the residual field (observed field minus regional field). We present a regional‐residual separation method for gravity data which uses a robust procedure to determine the coefficients of a polynomial fitted to the observations. Under the hypothesis that the regional can be modeled correctly by the polynomial surface, the proposed method minimizes the influence of the residual field in the fitted surface. The proposed method was applied to real gravity data from Ceara state, Brazil, and produced information on zones of possible crustal thickening and the occurrence of lower‐crustal granulitic rocks thrust into the shallow subsurface.
TL;DR: In this article, an adaptation of the Macnae-Lamontagne method allows transform of airborne step-response electromagnetic (EM) data to a conductivity-depth image based on a nonlinear transformation of the amplitude of measured response at each delay time to an apparent mirror image depth.
Abstract: An adaptation of the Macnae-Lamontagne method allows transform of airborne step-response electromagnetic (EM) data to a conductivity-depth image. The algorithm is based on a nonlinear transformation of the amplitude of the measured response at each delay time to an apparent mirror image depth. Using matrix algebra, the set of mirror image depth-delay time data pairs can then be used to derive a conductivity section. Data can be efficiently processed on a personal computer at rates faster or comparable to the rate required for collection. Stable conductivity fitting as a function of depth is obtained by damping the matrix inversion by specification of the first- and second-derivative smoothness weights of the fitted conductivity-depth sounding. Damping parameters may be either fixed or varied along the profile; their choice can be constrained by geologic control. Stability of the process is enhanced by accounting for the transmitter and receiver tilts.The mirror image depth-delay time data can also be used directly with simple regression to obtain the best-fitting thin-sheet and half-space models. With one novel assumption, the thin-sheet model can be converted to a thick-sheet overburden model without prespecification of either its conductivity or thickness. Depending on the geology, these simple models may prove quite useful.The conductivity imaging algorithm has been applied to a test data set collected with the SPECTREM system. The stability and speed of the imaging process were confirmed and have demonstrated airborne EM sounding to depths well over 400 m in an area with quite conductive sediments. Comparing the results with a better resolved image obtained from ground UTEM data shows that the airborne data can adequately define the geometry of the uppermost conductor encountered in the section. The geophysical results are consistent with geologic control and measurements of resistivity obtained from well logs.