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Showing papers in "Geophysics in 2000"


Journal ArticleDOI
TL;DR: In this paper, a wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media.
Abstract: A wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves, which significantly reduces the computation time compared to the elastic wavefield solutions for exploding‐reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a TI medium are derived. These equations, based on the acoustic assumption (shear wave velocity = 0), are much simpler than their elastic counterparts, yet they yield an accurate description of traveltimes and geometrical amplitudes. Numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex TI models.

500 citations


Journal ArticleDOI
TL;DR: In this article, the authors use the linear slip theory of Schoenberg and co-workers and the models developed by Hudson and Thomsen for pennyshaped cracks to relate the anisotropic parameters to the physical properties of the fracture network and to devise fracture characterization procedures based on surface seismic measurements.
Abstract: The simplest effective model of a formation containing a single fracture system is transversely isotropic with a horizontal symmetry axis (HTI) Reflection seismic signatures in HTI media, such as NMO velocity and amplitude variation with offset (AVO) gradient, can be conveniently described by the Thomsen‐type anisotropic parameters e(V), δ(V), and γ(V) Here, we use the linear slip theory of Schoenberg and co‐workers and the models developed by Hudson and Thomsen for pennyshaped cracks to relate the anisotropic parameters to the physical properties of the fracture network and to devise fracture characterization procedures based on surface seismic measurements Concise expressions for e(V), δ(V), and γ(V) linearized in the crack density, show a substantial difference between the values of the anisotropic parameters for isolated fluid‐filled and dry (gas‐filled) penny‐sh aped cracks While the dry‐crack model is close to elliptical with e(V)≈δ(V), for thin fluid‐filled cracks e(V);≈0 and the absolute value

474 citations


Journal ArticleDOI
TL;DR: Here, a new and much simpler approach to regularized 2-D inversion of magnetotelluric data which uses cheaply computed approximations to the sensitivity matrix to search for a minimum of the penalty functional.
Abstract: There are currently three types of algorithms in use for regularized 2-D inversion of magnetotelluric (MT) data. All seek to minimize some functional which penalizes data misfit and model structure. With the most straight‐forward approach (exemplified by OCCAM), the minimization is accomplished using some variant on a linearized Gauss‐Newton approach. A second approach is to use a descent method [e.g., nonlinear conjugate gradients (NLCG)] to avoid the expense of constructing large matrices (e.g., the sensitivity matrix). Finally, approximate methods [e.g., rapid relaxation inversion (RRI)] have been developed which use cheaply computed approximations to the sensitivity matrix to search for a minimum of the penalty functional. Approximate approaches can be very fast, but in practice often fail to converge without significant expert user intervention. On the other hand, the more straightforward methods can be prohibitively expensive to use for even moderate‐size data sets. Here, we present a new and much m...

405 citations


Journal ArticleDOI
TL;DR: This work investigates the simultaneous migration of shot records using frequency‐domain shot‐record migration algorithms, and introduces a process called phase encoding, which shifts or disperses crossterms between unrelated shot and receiver wavefields.
Abstract: Frequency‐domain shot‐record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computing cost of shot‐record migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade‐off between accuracy and speed. Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency‐domain shot‐record migration algorithms. The difficulty with this approach is the production of so‐called crossterms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the single‐shot‐per‐migration result, we have introduced a process called phase encoding, which shifts or disperses these crossterms. The process of phase encoding...

327 citations


Journal ArticleDOI
TL;DR: Techniques are described for faster training, better overall performance, i.e., generalization, and the automatic estimation of network size and architecture.
Abstract: Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization, and the automatic estimation of network size and architecture.

312 citations


Journal ArticleDOI
TL;DR: In this paper, the linear slip theory was used to obtain simple analytic expressions for the anisotropic coefficients of effective orthorhombic media with a horizontal symmetry plane for naturally fractured reservoirs, under the assumptions of weak anisotropy of the background medium and small compliances of the fractures.
Abstract: Existing geophysical and geological data indicate that orthorhombic media with a horizontal symmetry plane should be rather common for naturally fractured reservoirs. Here, we consider two orthorhombic models: one that contains parallel vertical fractures embedded in a transversely isotropic background with a vertical symmetry axis (VTI medium) and the other formed by two orthogonal sets of rotationally invariant vertical fractures in a purely isotropic host rock. Using the linear‐slip theory, we obtain simple analytic expressions for the anisotropic coefficients of effective orthorhombic media. Under the assumptions of weak anisotropy of the background medium (for the first model) and small compliances of the fractures, all effective anisotropic parameters reduce to the sum of the background values and the parameters associated with each fracture set. For the model with a single fracture system, this result allows us to eliminate the influence of the VTI background by evaluating the differences between t...

242 citations


Journal ArticleDOI
TL;DR: You have just joined a new asset team or new company and are handed an area to evaluate, which includes seismic, logs, and a cube of acoustic impedance, which is designed for seismic data.
Abstract: You have just joined a new asset team or new company. You're handed an area to evaluate. The data include seismic, logs, and a cube of acoustic impedance. What do you do with the impedance data? How was it created? What unique information does it provide? What pitfalls and artifacts may be present? How do you interpret this data set on a workstation that is designed for seismic data? How do you report your results to management? Valid questions? Read on. Inversion of seismic data into acoustic impedance (AI) is a rapidly growing field, due primarily to the ease and accuracy of interpretation of the impedance data. The term “inversion” has the potential for a great amount of confusion, as it is used to mean many different things within various branches of geoscience. The discussion in this paper will concentrate on the inversion of poststack seismic traces into acoustic impedance data. Even with this narrower scope, the plethora of programs on the market today makes the comparison of various inversion methodologies and the determination of the quality of your AI cube difficult at best. This paper will provide a description of terminology and a basis for comparison of poststack acoustic impedance inversion products, as well as give the interpreter a methodology for quality control and interpretation of inverted data. Acoustic impedance (AI) is the product of rock density and P -wave velocity. This means that AI is a rock property and not an interface property (e.g., seismic reflection data). As we will illustrate, this distinction is the power of AI. Acoustic impedance inversion is simply the transformation of seismic data into pseudoacoustic impedance logs at every trace. All information in the seismic data is retained. Figure 1 shows an acoustic impedance model and its representation with two imaging techniques. The …

219 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical approach for modeling elastic wave propagation in 2-D and 3-D fully anisotropic media based upon a spectral element method is introduced. But this approach is not suitable for the case of 3D transversely isotropic medium with a symmetry axis tilted relative to the axes of the grid.
Abstract: We introduce a numerical approach for modeling elastic wave propagation in 2-D and 3-D fully anisotropic media based upon a spectral element method. The technique solves a weak formulation of the wave equation, which is discretized using a high-order polynomial representation on a finite element mesh. For isotropic media, the spectral element method is known for its high degree of accuracy, its ability to handle complex model geometries, and its low computational cost. We show that the method can be extended to fully anisotropic media. The mass matrix obtained is diagonal by construction, which leads to a very efficient fully explicit solver. We demonstrate the accuracy of the method by comparing it against a known analytical solution for a 2-D transversely isotropic test case, and by comparing its predictions against those based upon a finite difference method for a 2-D heterogeneous, anisotropic medium. We show its generality and its flexibility by modeling wave propagation in a 3-D transversely isotropic medium with a symmetry axis tilted relative to the axes of the grid.

214 citations


Journal ArticleDOI
TL;DR: In this article, a spectral element method for modeling wave propagation in media with both fluid (acoustic) and solid (elastic) regions, as for instance in offshore seismic experiments, is introduced.
Abstract: We introduce a spectral-element method for modeling wave propagation in media with both fluid (acoustic) and solid (elastic) regions, as for instance in offshore seismic experiments. The problem is formulated in terms of displacement in elastic regions and a velocity potential in acoustic regions. Matching between domains is implemented based upon an interface integral in the framework of an explicit prediction-multicorrection staggered time scheme. The formulation results in a mass matrix that is diagonal by construction. The scheme exhibits high accuracy for a 2-D test case with known analytical solution. The method is robust in the case of strong topography at the fluid-solid interface and is a good alternative to classical techniques, such as finite differencing.

207 citations


PatentDOI
Leonard J. Srnka1
TL;DR: In this paper, the location of and average earth resistivities above, below, and horizontally adjacent to the subsurface geologic formation are first determined using geological and geophysical data in the vicinity of the SINR.
Abstract: A method for surface estimation of reservoir properties, wherein location of and average earth resistivities above, below, and horizontally adjacent to the subsurface geologic formation are first determined using geological and geophysical data in the vicinity of the subsurface geologic formation. Then dimensions and probing frequency for an electromagnetic source are determined to substantially maximize transmitted vertical and horizontal electric currents at the subsurface geologic formation, using the location and the average earth resistivities. Next, the electromagnetic source is activated at or near surface, approximately centered above the subsurface geologic formation and a plurality of components of electromagnetic response is measured with a receiver array. Geometrical and electrical parameter constraints are determined, using the geological and geophysical data. Finally, the electromagnetic response is processed using the geometrical and electrical parameter constraints to produce inverted vertical and horizontal resistivity depth images. Optionally, the inverted resistivity depth images may be combined with the geological and geophysical data to estimate the reservoir fluid and shaliness properties.

205 citations


Journal ArticleDOI
TL;DR: In this article, a theoretical rock-physics model was applied to 2D Blake Ridge marine seismic data to determine gas hydrate and free-gas saturation, and the model was used to estimate porosity and saturation from interval velocity.
Abstract: Marine seismic data and well‐log measurements at the Blake Ridge offshore South Carolina show that prominent seismic bottom‐simulating reflectors (BSRs) are caused by sediment layers with gas hydrate overlying sediments with free gas. We apply a theoretical rock‐physics model to 2-D Blake Ridge marine seismic data to determine gas‐hydrate and free‐gas saturation. High‐porosity marine sediment is modeled as a granular system where the elastic wave velocities are linked to porosity; effective pressure; mineralogy; elastic properties of the pore‐filling material; and water, gas, and gas‐hydrate saturation of the pore space. To apply this model to seismic data, we first obtain interval velocity using stacking velocity analysis. Next, all input parameters to the rock‐physics model, except porosity and water, gas, and gas hydrate saturation, are estimated from geologic information. To estimate porosity and saturation from interval velocity, we first assume that the entire sediment does not contain gas hydrate o...

Journal ArticleDOI
TL;DR: In this paper, the wave velocities of ice and gas hydrate-bearing sediments were obtained as a function of concentration and temperature. And the reflection coefficients were computed with a viscoelastic single-phase constitutive model.
Abstract: We obtain the wave velocities of ice‐ and gas hydrate‐bearing sediments as a function of concentration and temperature. Unlike previous theories based on simple slowness and/or moduli averaging or two‐phase models, we use a Biot‐type three‐phase theory that considers the existence of two solids (grain and ice or clathrate) and a liquid (water), and a porous matrix containing gas and water. For consolidated Berea sandstone, the theory underestimates the value of the compressional velocity below 0°C. Including grain‐ice interactions and grain cementation yields a good fit to the experimental data. Strictly speaking, water proportion and temperature are closely related. Fitting the wave velocity at a given temperature allows the prediction of the velocity throughout the range of temperatures, provided that the average pore radius and its standard deviation are known. The reflection coefficients are computed with a viscoelastic single‐phase constitutive model. The analysis is carried out for the top and botto...

Journal ArticleDOI
TL;DR: Electrical resistance tomography (ERT) as mentioned in this paper is a method that calculates the subsurface distribution of electrical resistivity from a large number of resistance measurements made from electrodes using electrodes on the ground surface or in boreholes.
Abstract: Electrical resistance tomography (ERT) is a method that calculates the subsurface distribution of electrical resistivity from a large number of resistance measurements made from electrodes. For in-situ applications, ERT uses electrodes on the ground surface or in boreholes. It is a relatively new imaging tool in geophysics. The basic concept was first described by Lytle and Dines as a marriage of traditional electrical probing (introduced by the Schlumberger brothers) and the new data inversion methods of tomography. Development of both the theory and practice of ERT was confined mostly to the late 1980s and the 1990s. Tomographic inversion added important new capabilities as it was more general, accurate, and rigorous at spatial imaging of geophysical electrical resistance data than earlier pseudosection or curve fitting methods. An early application of geophysical ERT was to image laboratory core samples under test but practical field scale use of ERT was delayed by the lack of suitable measurement and test equipment. ERT requires the same four electrode resistance measurement used by the Schlumberger brothers (two electrodes to inject current and two other electrodes to measure the resulting potential); however, tomography requires addressing tens or hundreds of electrodes and making hundreds or thousands of such measurements in a timely fashion. Clearly, the available manual measurement systems that were designed for one, or perhaps a few measurements at a time, were not practical for ERT. High-speed, automated systems were needed.

Journal ArticleDOI
TL;DR: Tensor Euler deconvolution has been developed to help interpret gravity tensor gradient data in terms of 3-D subsurface geological structure as discussed by the authors, which has been tested on point, prism, and cylindrical mass models using line and gridded data forms.
Abstract: Tensor Euler deconvolution has been developed to help interpret gravity tensor gradient data in terms of 3-D subsurface geological structure. Two forms of Euler deconvolution have been used in this study: conventional Euler deconvolution using three gradients of the vertical component of the gravity vector and tensor Euler deconvolution using all tensor gradients. These methods have been tested on point, prism, and cylindrical mass models using line and gridded data forms. The methods were then applied to measured gravity tensor gradient data for the Eugene Island area of the Gulf of Mexico using gridded and ungridded data forms. The results from the model and measured data show significantly improved performance of the tensor Euler deconvolution method, which exploits all measured tensor gradients and hence provides additional constraints on the Euler solutions.

Journal ArticleDOI
TL;DR: In this paper, the authors determined P- and S-wave velocity depth profiles in shallow, unconsolidated beach sand by analyzing three-component surface seismic data and attributed this discrepancy to the angularity of the sand grains.
Abstract: We determined P- and S-wave velocity depth profiles in shallow, unconsolidated beach sand by analyzing three-component surface seismic data. P- and S-wave velocity profiles were calculated from traveltime measurements of vertical and tangential component seismograms, respectively. The results reveal two discrepancies between theory and data. Whereas both velocities were found to be proportional to the pressure raised to the power of 1/6, as predicted by the Hertz-Mindlin contact theory, the actual values of the velocities are less than half of those calculated from this theory. We attribute this discrepancy to the angularity of the sand grains. Assuming that the average radii of curvature at the grain contacts are smaller than the average radii of the grains, we modify the Hertz-Mindlin theory accordingly. We found that the ratio of the contact radius to the grain radius is about 0.086. The second disparity is between the observed Poisson’s ratio of 0.15 and the theoretical value (0.008 for random pack of quartz spheres). This discrepancy can be reconciled by assuming slip at the grain contacts. Because slip decreases the shearing between grains, Poisson’s ratio increases.

Journal ArticleDOI
TL;DR: In this paper, the authors rework the total current conductivity function introduced in a previous paper, related to electrical polarization of rocks in the frequency range of 1 MHz to 10−3 Hz, and replace the original five parameters in this function with new ones, which from the beginning have clear petrophysical and electrochemical meanings and well defined ranges of variation.
Abstract: The author reworks his total current conductivity function introduced in a previous paper, related to electrical polarization of rocks in the frequency range of 1 MHz to 10−3 Hz. The original five parameters in this function are replaced by new ones, which from the beginning have clear petrophysical and electrochemical meanings and well‐defined ranges of variation. Some classical models are derived as particular cases of it. The main existing models proposed to describe induced polarization (IP) are analyzed, and most of them are grouped together under a common circuit analog representation and a respective generating function. A circuit analog is assigned to each model. The multi‐Cole‐Cole model circuit analog reveals intrinsic constraints involving the values of its circuit elements. Because of these constraint relations and the relaxation times ratio (τ1/τ2)—usually many orders of magnitude from unity—the model has no physical validation to represent single‐phase material systems (in the sense of the p...

Journal ArticleDOI
TL;DR: In this paper, a joint inversion of surface and borehole data is proposed to reduce the nonuniqueness of the inversion with respect to the distance between the source and observation locations.
Abstract: The inversion of magnetic data is inherently nonunique with respect to the distance between the source and observation locations. This manifests itself as an ambiguity in the source depth when surface data are inverted and as an ambiguity in the distance between the source and boreholes if borehole data are inverted. Joint inversion of surface and borehole data can help to reduce this nonuniqueness. To achieve this, we develop an algorithm for inverting data sets that have arbitrary observation locations in boreholes and above the surface. The algorithm depends upon weighting functions that counteract the geometric decay of magnetic kernels with distance from the observer. We apply these weighting functions to the inversion of three‐component magnetic data collected in boreholes and then to the joint inversion of surface and borehole data. Both synthetic and field data sets are used to illustrate the new inversion algorithm. When borehole data are inverted directly, three‐component data are far more usefu...

Journal ArticleDOI
TL;DR: In this article, the authors define the Kirchhoffer model as the mathematical transpose of the kirchhoff migration, and propose an algorithm that only models the events that kirkhoff migration can image.
Abstract: Because of its computational efficiency, prestack Kirchhoff depth migration is currently one of the most popular algorithms used in 2-D and 3-D subsurface depth imaging. Nevertheless, Kirchhoff algorithms in their typical implementation produce less than ideal results in complex terranes where multipathing from the surface to a given image point may occur, and beneath fast carbonates, salt, or volcanics through which ray‐theoretical energy cannot penetrate to illuminate underlying slower‐velocity sediments. To evaluate the likely effectiveness of a proposed seismic‐acquisition program, we could perform a forward‐modeling study, but this can be expensive. We show how Kirchhoff modeling can be defined as the mathematical transpose of Kirchhoff migration. The resulting Kirchhoff modeling algorithm has the same low computational cost as Kirchhoff migration and, unlike expensive full acoustic or elastic wave‐equation methods, only models the events that Kirchhoff migration can image. Kirchhoff modeling is also...

Journal ArticleDOI
TL;DR: In this paper, the authors exploit the numerical structure of the finite element method, modern sparse matrix technology, and source-receiver reciprocity to develop an algorithm that explicitly calculates the Jacobian matrix at only the cost of a forward model solution.
Abstract: Linearized inversion of surface seismic data for a model of the earth’s subsurface requires estimating the sensitivity of the seismic response to perturbations in the earth’s subsurface. This sensitivity, or Jacobian, matrix is usually quite expensive to estimate for all but the simplest model parameterizations. We exploit the numerical structure of the finite‐element method, modern sparse matrix technology, and source‐receiver reciprocity to develop an algorithm that explicitly calculates the Jacobian matrix at only the cost of a forward model solution. Furthermore, we show that we can achieve improved subsurface images using only one inversion iteration through proper scaling of the image by a diagonal approximation of the Hessian matrix, as predicted by the classical Gauss‐Newton method. Our method is applicable to the full suite of wave scattering problems amenable to finite‐element forward modeling. We demonstrate our method through some simple 2‐D synthetic examples.

Journal ArticleDOI
A. Abdel Aal1, A. El Barkooky1, M. Gerrits1, Hans-Jurg Meyer1, M. Schwander1, H. Zaki1 
TL;DR: The Northeast Mediterranean Deepwater Area (41 500 km2) was awarded to Shell Egypt in July 1998 and operations started on 1 February 1999 to acquire a 7000-km, 2D (6-km cable, 8 s, 120-fold) seismic survey as discussed by the authors.
Abstract: The Northeast Mediterranean Deepwater Area (41 500 km2) was awarded to Shell Egypt in July 1998. Operations started on 1 February 1999 to acquire a 7000-km, 2-D (6-km cable, 8 s, 120-fold) seismic survey. Key pre-1999 data included a 1500-km 2-D seismic (1973 vintage). In December 1999 Exxon Exploration and Production, Egypt acquired a 25% interest in the concession.

Journal ArticleDOI
TL;DR: Linearized methods are presented for appraising resolution and parameter accuracy in images generated with 2-D and 3-D nonlinear electromagnetic (EM) inversion schemes and an iterative statistical method yields accurate estimates of the model covariance matrix.
Abstract: Linearized methods are presented for appraising resolution and parameter accuracy in images generated with 2-D and 3-D nonlinear electromagnetic (EM) inversion schemes. When direct matrix inversion is used, the model resolution and a posteriori model covariance matrices can be calculated readily. By analyzing individual columns of the model resolution matrix, the spatial variation of the resolution in the horizontal and vertical directions can be estimated empirically. Plotting the diagonal of the model covariance matrix provides an estimate of how errors in the inversion process, such as data noise and incorrect a priori assumptions, map into parameter error and thus provides valuable information about the uniqueness of the resulting image. Methods are also derived for image appraisal when the iterative conjugate gradient technique is applied to solve the inverse. An iterative statistical method yields accurate estimates of the model covariance matrix as long as enough iterations are used. Although determining the entire model resolution matrix in a similar manner is computationally prohibitive, individual columns of this matrix can be determined. Thus, the spatial variation in image resolution can be determined by calculating the columns of this matrix for key points in the image domain and then interpolating between. Examples of the image analysis techniques are provided on 2-D and 3-D synthetic crosswell EM data sets as well as a field data set collected at Lost Hills oil field in central California.

Journal ArticleDOI
TL;DR: In this paper, a staggered-grid finite-difference method for simulating electromagnetic induction in a fully 3D anisotropic medium is presented, where the electrical conductivity of the formation is represented as a full 3£ 3 tensor whose elements can vary arbitrarily with position throughout the formation.
Abstract: The bulk electrical anisotropy of sedimentary formations is a macroscopic phenomenon which can result from the presence of porosity variations, laminated shaly sands, and water saturation. Accounting for its effect on induction log responses is an ongoing research problem for the well-logging community since these types of sedimentary structures have long been correlated with productive hydrocarbon reservoirs such as the Jurassic Norphlet Sandstone and Permian Rotliegendes Sandstone. Presented here is a staggered-grid finite-difference method for simulating electromagnetic (EM) induction in a fully 3-D anisotropic medium. The electrical conductivity of the formation is represented as a full 3£ 3 tensor whose elements can vary arbitrarily with position throughout the formation. To demonstrate the validity of this approach, finite-difference results are compared against analytic and quasi-analytic solutions for tractable 1-D and 3-D model geometries. As a final example, we simulate 2C‐40 induction tool responses in a crossbedded aeolian sandstone to illustrate the magnitude of the challenge faced by interpreters when electrical anisotropy is neglected.

Journal ArticleDOI
TL;DR: In this article, the authors describe an algorithm that allows georadar data to be migrated directly from gently to highly irregular acquisition surfaces, where the depths to target structures are comparable to undulations in the surface topography.
Abstract: Application of conventional elevation static corrections and migration to wavefield data recorded on irregular surfaces may result in poor reconstructions of complex subsurface features. Particulary poor images may be obtained at locations where the depths to target structures are comparable to undulations in the surface topography. For example, topographic relief of only 1-2 m may be important for the processing of georadar data. We describe an algorithm that allows georadar data to be migrated directly from gently to highly irregular acquisition surfaces. When applied to a variety of complicated synthetic data sets, topographically migrated images are observed to be markedly superior to those produced by two standard processing schemes. Extensive tests demonstrate that topographic migration should be considered in regions characterized by surface gradients ≫10% (i.e., dips ≫6°). For effective topographic migration, lateral and vertical coordinates of the georadar antennas should be determined to better ...

Journal ArticleDOI
TL;DR: In this article, a gravity inversion method for determining the volumes of bodies with pre-established density contrasts is presented, which works step-by-step on a prismatic partition of the subsurface volume, expanding the anomalous bodies to fit the observed gravity values in a systematic exploration of model possibilities.
Abstract: This paper presents a gravity inversion method for determining the volumes of bodies with pre‐established density contrasts. The method works step‐by‐step on a prismatic partition of the subsurface volume, expanding the anomalous bodies to fit the observed gravity values in a systematic exploration of model possibilities. The process is treated in a 3-D context; at the same time, it can determine a simple regional trend. Moreover, positive and negative density contrasts are simultaneously accepted. The solution is obtained by a double condition: (1) the 𝓁2-fitness to the observed gravity data (model fitness) and (2) the minimization of the total (weighted) anomalous mass (model smoothness). A positive parameter is used to balance the two minimization terms. The method is applied to a simulated example and also to a real example: the volcanic island of Gran Canaria (Canary Islands, Spain). In both cases, the results obtained show the possibilities of the method.

Journal ArticleDOI
TL;DR: In this article, the authors measured Stoneley wave induced electrical fields in an uncased water well drilled in fractured granite and diorite near Hamilton, Massachusetts, and confirmed that they were induced by fluid flow in the fractured formation.
Abstract: In 1996, we measured Stoneley‐wave‐induced electrical fields in an uncased water well drilled in fractured granite and diorite near Hamilton, Massachusetts. Stoneley waves generated by sledgehammer blows to the surface casing produced a flow of pore fluid in permeable zones intersected by the borehole. In turn, this flow induced a streaming electrical field. Even though these electrical signals were very small (tens of microvolts), we were able to detect them using electrodes placed in the borehole, after power line and telluric signals were canceled by remote referencing and notch‐filtering. Amplitude analysis of the electrical fields confirmed that they were induced by fluid flow in the fractured formation. The normalized amplitudes of these electrical fields correlate with the fracture density log and agree with the theoretical model for this electroseismic phenomenon. Our Biot‐theory‐based model predicts that borehole electroseismic measurements can be used to characterize permeable zones. According t...

Journal ArticleDOI
TL;DR: In this article, the authors investigated whether accounting for multiple arrivals in ray-based preserved amplitude prestack depth migration allows one to improve quantitative imaging of complex media, and they demonstrated that ray-Born inversion can provide a reliable quantitative estimation of the relative impedance perturbation even in the complex deep part of the model, for which the amplitudes were underestimated drastically when only a single arrival was considered.
Abstract: Ray‐based prestack depth migration fails to image quantitatively complex structures when a single arrival—for example, the first or the strongest one—is taken into account. In this paper, we investigate whether accounting for multiple arrivals in ray‐based preserved amplitude prestack depth migration allows one to improve quantitative imaging of complex media. The asymptotic ray‐Born migration/inversion, originally designed to process one single arrival, is extended to the case of multiple arrivals by accounting for the cross‐contributions of all the source and receiver raypaths. Multiple arrivals in the folded ray fields are computed by a dynamic ray tracing based on a wavefront construction technique. With an application to the complex Marmousi model, we demonstrate that ray‐Born inversion can provide a reliable quantitative estimation of the relative impedance perturbation even in the complex deep part of the model, for which the amplitudes were underestimated drastically when only a single arrival was...

Journal ArticleDOI
TL;DR: In this article, resistivity increases in the near surface and at depth, upbeach of the high-tide mark, accompanied by tidal transgression, and the authors attribute this to desaturation and decreasing salinity in the far surface and decreasing at depth.
Abstract: We demonstrate the use of resistivity/induced polarization (IP) monitoring of salt transport under natural hydraulic loads. Electrical monitoring of saline tracer transport during forced injection has been demonstrated previously. Detection of tracer transport under natural hydraulic loading is difficult because neither the hydraulic load nor the tracer resistivity can be controlled. In one study, we identify the electrical response to salt transport in a dynamic beach environment. Resistivity/IP imaging resolved the structure of the saltwater‐freshwater interface and evidence for tide‐induced groundwater transport. Resistivity increases in the near surface and at depth, upbeach of the high‐tide mark, accompanied by tidal transgression. We attribute this to desaturation and decreasing salinity in the near surface and to decreasing salinity at depth, despite tidal transgression. Monitoring of groundwater levels indicates a phase lag between the tide level and groundwater level, supporting the electrical da...

Journal ArticleDOI
TL;DR: In this paper, an algorithm for inverting induced polarization (IP) data acquired in a 3D environment is presented 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.
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.

Journal ArticleDOI
TL;DR: A new finite‐difference method is presented that circumvents the need to resimulate the complete model for local changes by requiring only calculations in the subvolume and its neighborhood, which makes possible significant reductions in computational cost and memory requirements.
Abstract: Seismic modeling, processing, and inversion often require the calculation of the seismic response resulting from a suite of closely related seismic models. Even though changes to the model may be restricted to a small subvolume, we need to perform simulations for the full model. We present a new finite‐difference method that circumvents the need to resimulate the complete model for local changes. By requiring only calculations in the subvolume and its neighborhood, our method makes possible significant reductions in computational cost and memory requirements. In general, each source/receiver location requires one full simulation on the complete model. Following these pre‐computations, recalculation of the altered wavefield can be limited to the region around the subvolume and its neighborhood. We apply our method to a 2-D time‐lapse seismic problem, thereby achieving a factor of 15 reduction in computational cost. Potential savings for 3-D are far greater.

Journal ArticleDOI
TL;DR: The use of airborne and ground gamma-ray spectrometers to detect and map potassium alteration associated with different styles of mineralization is documented in case histories of Canadian case histories as discussed by the authors, which can be distinguished from normal lithologic potassium variations by characteristic lows in eTh/K ratios.
Abstract: Canadian case histories document the use of airborne and ground gamma‐ray spectrometry to detect and map potassium alteration associated with different styles of mineralization. These include: volcanic‐hosted massive sulfides (Cu‐Pb‐Zn), Pilley’s Island, Newfoundland; polymetallic, magmatic‐hydrothermal deposits (Au‐Co‐Cu‐Bi‐W‐As), Lou Lake, Northwest Territories; and porphyry Cu‐Au‐(Mo) deposits at Mt. Milligan, British Columbia and Casino, Yukon Territory. Mineralization in two of these areas was discovered using airborne gamma‐ray spectrometry. In each case history, alteration produces potassium anomalies that can be distinguished from normal lithologic potassium variations by characteristic lows in eTh/K ratios. Interpretations incorporating airborne and ground spectrometry, surficial and bedrock geochemistry and petrology show that gamma‐ray spectrometric patterns provide powerful guides to mineralization. This information complements magnetic, electromagnetic, geological, and conventional geochemica...