Showing papers in "Geophysics in 1993"
TL;DR: In this article, the velocity dispersion and attenuation of seismic and acoustic waves in rocks with fluids are affected by the two most important modes of fluid/solid interaction: (1) the Biot mechanism where the fluid is forced to participate in the solid's motion by viscous friction and inertial coupling, and (2) the squirt-flow mechanism where fluid is squeezed out of thin pores deformed by a passing wave.
Abstract: The velocities and attenuation of seismic and acoustic waves in rocks with fluids are affected by the two most important modes of fluid/solid interaction: (1) the Biot mechanism where the fluid is forced to participate in the solid's motion by viscous friction and inertial coupling, and (2) the squirt-flow mechanism where the fluid is squeezed out of thin pores deformed by a passing wave. Traditionally, both modes have been modeled separately, with the Biot mechanism treated in a macroscopic framework, and the squirt flow examined at the individual pore level. We offer a model which treats both mechanisms as coupled processes and relates P-velocity and attenuation to macroscopic parameters: the Biot poroelastic constants, porosity, permeability, fluid com-pressibility and viscosity, and a newly introduced microscale parameter--a characteristic squirt-flow length. The latter is referred to as a fundamental rock property that can be determined experimentally. We show that the squirt-flow mechanism dominates the Biot mechanism and is responsible for measured large velocity dispersion and attenuation values. The model directly relates P-velocity and attenuation to measurable rock and fluid properties. Therefore, it allows one to realistically interpret velocity dispersion and/or attenuation in terms of fluid properties changes [e.g., viscosity during thermal enhanced oil recovery (EOR)], or to link seismic measurements to reservoir properties. As an example of the latter transformation, we relate permeability to attenuation and achieve good qualitative correlation with experimental data.
552 citations
TL;DR: In this article, a finite-difference solution for 3D transient electromagnetic problems is proposed, which uses a modified version of the Du Fort-Frankel method to solve first-order Maxwell's equations.
Abstract: We have developed a finite-difference solution for three-dimensional (3-D) transient electromagnetic problems. The solution steps Maxwell's equations in time using a staggered-grid technique. The time-stepping uses a modified version of the Du Fort-Frankel method which is explicit and always stable. Both conductivity and magnetic permeability can be functions of space, and the model geometry can be arbitrarily complicated. The solution provides both electric and magnetic field responses throughout the earth. Because it solves the coupled, first-order Maxwell's equations, the solution avoids approximating spatial derivatives of physical properties, and thus overcomes many related numerical difficulties. Moreover, since the divergence-free condition for the magnetic field is incorporated explicitly, the solution provides accurate results for the magnetic field at late times.An inhomogeneous Dirichlet boundary condition is imposed at the surface of the earth, while a homogeneous Dirichlet condition is employed along the subsurface boundaries. Numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth-order difference method at early times and a second-order method at other times. Numerical checks against analytical, integral-equation, and spectral differential-difference solutions show that the solution provides accurate results.Execution time for a typical model is about 3.5 hours on an IBM 3090/600S computer for computing the field to 10 ms. That model contains 100 X 100 X 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry, with the smallest grid spacing at 10 m and the highest resistivity at 100 Omega . m. The execution time indicates that the solution is computer intensive, but it is valuable in providing much-needed insight about TEM responses in complicated 3-D situations.
310 citations
TL;DR: In this article, a wavefront (WF) construction approach is proposed to estimate a new WF from the old one by using ray tracing, which is defined as a curve (in 2D) of constant traveltime from the source.
Abstract: We have developed and implemented a new method for estimating traveltimes and amplitudes in a general smooth two‐dimensional (2-D) model. The basic idea of this wavefront (WF) construction approach is to use ray tracing to estimate a new WF from the old one. The WF is defined as a curve (in 2-D) of constant traveltime from the source. The ray direction and amplitude will then be a function of s, the distance along the front. To maintain a sufficiently small sampling distance along the WF, it is scanned at every time step and new rays are interpolated whenever the distance between two rays becomes larger than a predefined limit. As the wavefronts are constructed, the data (i.e. traveltimes, amplitude coefficients, etc.) are transferred to the receivers by interpolation within the ray cells. Advantages of the WF construction method are its flexibility, robustness, and accuracy. First, second, and later arrivals may be found at any point in the model. Any shape of the initial wavefront is possible. The drawb...
301 citations
TL;DR: In this article, an algorithm for computing the magnetotelluric response of three-dimensional (3D) earth models is presented. But it does not require approximating derivatives of earth properties or electromagnetic fields, as happens when using the second order vector diffusion equation.
Abstract: We have developed an algorithm for computing the magnetotelluric response of three‐dimensional (3-D) earth models. It is a difference equation algorithm that is based on the integral forms of Maxwell’s equations rather than the differential forms. This formulation does not require approximating derivatives of earth properties or electromagnetic fields, as happens when using the second‐order vector diffusion equation. Rather, one must determine how averages are to be computed. Side boundary values for the H fields are obtained from putting two‐dimensional (2-D) slices of the model into a larger‐scale 2-D model and solving for the fields at the 3-D boundary positions. To solve the 3-D system of equations, we propagate an impedance matrix, which relates all the horizontal E fields in a layer to all the horizontal H fields in that same layer, up through the earth model. Applying a plane‐wave source condition and the side boundary H field values allows us to solve for the unknown fields within the model. The r...
286 citations
TL;DR: In this paper, Thompson et al. showed that the conversion of seismic to electromagnetic energy at the water table could be detected using surface antennas, and used them as geophones.
Abstract: In Volume 1 of Geophysics (1936), R.R. Thompson of Humble Oil and Refining Company proposed that the coupling of seismic and electrical energy can be used as an exploration tool. Subsequent efforts were directed toward using electric‐field antennas as geophones. Small‐scale studies concluded that antennas are not as sensitive as conventional geophones and their response is highly variable, depending on the local soil conditions. By 1959, Martner and Sparks of Pan American Petroleum reported in Geophysics a systematic study of seismoelectric coupling using explosives at various depths. Their results were the first to show that the conversion of seismic to electromagnetic energy at the water table could be detected using surface antennas. No studies have systematically explored the full potential of electroseismic methods using the same level of experimental sophistication used in seismic exploration.
232 citations
TL;DR: In this article, the authors measured velocities on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium and found that for wavelength much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters.
Abstract: Ultrasonic velocities were measured on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium. The measurements, normal, parallel, and oblique to the fractures, show that for wavelength much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters. This TI medium behavior is the same as that of an isotropic solid in which are embedded a set of parallel linear slip interfaces, specified by (1) the excess compliance tangential to the interfaces and (2) the excess compliance normal to the interfaces. At all static stress levels, the authors inverted the data for the background isotropic medium parameters and the excess compliances. The background parameters obtained were basically independent of stress level and agreed well with the bulk properties of the lucite. The excess compliances decreased with increasing static closing stress, implying that increasing static stress forces asperities on either side of a fracture into greater contact, gradually eliminating the excess compliance that gives rise to the anisotropy. A medium with such planes of excess compliance has been shown, theoretically, to describemore » the behavior of a medium with long parallel joints, as well as a medium with embedded parallel microcracks.« less
225 citations
TL;DR: In this paper, a method is proposed to study the possible contribution of remanent magnetization to a particular anomaly, by comparing two functions that are calculated directly from the observations: (1) the amplitude of the analytic signal, and (2) the horizontal gradient of pseudogravity.
Abstract: Remanent magnetization can have a significant influence on the shape of magnetic anomalies in areas that are generally characterized by induced magnetization. Since modeling of magnetic anomalies is nonunique, additional constraints on the direction of magnetization are useful. A method is proposed here to study the possible contribution of remanent magnetization to a particular anomaly, by comparing two functions that are calculated directly from the observations: (1) the amplitude of the analytic signal, and (2) the horizontal gradient of pseudogravity. From the amplitude and relative position of maxima in these derived quantities, we infer the deviation of the magnetization direction from that of the ambient field. The approach is applied to the magnetic anomaly in the center of the Manicouagan impact structure (Canada). Our results, based only on the magnetic anomaly observations, are in close agreement with constraints on the direction of remanent magnetization from rock samples.
173 citations
TL;DR: In this article, the authors investigate the effect of the ray approximation itself; scattering is ignored and the information contained in a seismic trace is reduced to one traveltime pick, finding that the minimum feature size resolvable by ray tomography is of the order of the width of the first Fresnel zone.
Abstract: Several factors limit the resolution obtained in ray tomography. Of these the least thoroughly discussed in the geophysical literature is the effect of the ray approximation itself; scattering is ignored and the information contained in a seismic trace is reduced to one traveltime pick. Frequency domain comparisons of ray tomography with diffraction tomography have suggested that the minimum feature size resolvable by ray tomography is of the order of the width of the first Fresnel zone. We investigate resolution in the spacetime domain with a numerical experiment. Four synthetic data sets were generated with a finite‐difference program corresponding to crosshole tomographic surveys at two hole separations and two frequencies. The scale of resolution achieved in tomograms derived from these is then assessed by calculating their semblance to filtered versions of the original model and reconstructions from data sets obtained by tracing rays through the original models. The results broadly confirm the relati...
171 citations
ARCO1
TL;DR: A backpropagation neural network (BNN) paradigm modified to improve the convergence rate of the BNN is employed and automated trace editing and first‐break picking based on the modified BNN paradigm achieve 90 to 98 percent agreement with each other.
Abstract: Interactive seismic processing systems for editing noisy seismic traces and picking first‐break refraction events have been developed using a neural network learning algorithm. We employ a backpropagation neural network (BNN) paradigm modified to improve the convergence rate of the BNN. The BNN is interactively “trained” to edit seismic data or pick first breaks by a human processor who judiciously selects and presents to the network examples of trace edits or refraction picks. The network then iteratively adjusts a set of internal weights until it can accurately duplicate the examples provided by the user. After the training session is completed, the BNN system can then process new data sets in a manner that mimics the human processor. Synthetic modeling studies indicate that the BNN uses many of the same subjective criteria that humans employ in editing and picking seismic data sets. Automated trace editing and first‐break picking based on the modified BNN paradigm achieve 90 to 98 percent agreement wit...
168 citations
TL;DR: In this paper, a general formula for the back projection of traveltime residuals in traveltime tomography is presented, which is based on the Woodward-Rocca method and wavepath eikonal traveltime inversion (WET).
Abstract: We present a general formula for the back projection of traveltime residuals in traveltime tomography. For special choices of an arbitrary weighting factor this formula reduces to the asymptotic back‐projection term in ray‐tracing tomography (RT), the Woodward‐Rocca method, wavepath eikonal traveltime inversion (WET), and wave‐equation traveltime inversion (WT). This unification provides for an understanding of the differences and similarities among these traveltime tomography methods. The special case of the WET formula leads to a computationally efficient inversion scheme in the space‐time domain that is, in principle, almost as effective as WT inversion yet is an order of magnitude faster. It also leads to an analytic formula for the fast computation of wavepaths. Unlike ray‐tracing tomography, WET partially accounts for band‐limited source and shadow effects in the data. Several numerical tests of the WET method are used to illustrate its properties.
167 citations
TL;DR: In this article, the authors decompose the velocities into moduli that are intrinsic measures of the rock frame and pore fluid compressibilities, and compare them to the porosity of pure quartz sandstones.
Abstract: The advent of borehole shear slowness measurements in sonically slow formations has lead to breakthroughs in the subsurface profiling of geological bodies. In sand bodies, compressional and shear velocities depend predictably on porosity, mineralogy, grain contacts, and fluid saturation. An interpretation is best performed by decomposing the velocities into moduli that are intrinsic measures of the rock frame and pore fluid compressibilities. Careful experiments on pure materials (i.e., pure quartz sandstones) demonstrate two simplifying constitutive relationships. First, the bulk and shear frame moduli are simple functions of the porosity. A comparison of the measured shear frame modulus to the prediction for the pure material distinguishes sand from shale. Second, the ratio of the bulk and shear frame moduli is a constant 0.9 independent of the porosity. The measured velocities are directly inverted to yield the bulk modulus of the pore fluid. The fluid saturation effects are so dramatic at high porosity that not only gas but oil may also be distinguished from water. The relationships are tested in several case studies where the results are encouraging. Finite-frequency effects may complicate the interpretation where filtrate invasion is significant. Attenuation provides further information because compressional absorption is particularly sensitive to gas saturation. A potential application of the modulus decomposition may be to quantify, in amplitude versus offset seismics proximal to the wellbore, the fractional change in shear frame modulus from the fractional change in pore fluid modulus.
TL;DR: In this article, the authors defined instantaneous power spectra in place of Fourier power spectras, so that they are instantaneous in time though they represent averages in frequency, and defined the instantaneous bandwidth as the absolute value of the derivative of the instantaneous amplitude divided by t.
Abstract: Fourier power spectra are often usefully characterized by average measures. In reflection seismology, the important average measures are center frequency, spectral bandwidth, and dominant frequency. These quantities have definitions familiar from probability theory: center frequency is the spectral mean, spectral bandwidth is the standard deviation about that mean, and dominant frequency is the square root of the second moment, which serves as an estimate of the zero‐crossing frequency. These measures suggest counterparts defined with instantaneous power spectra in place of Fourier power spectra, so that they are instantaneous in time though they represent averages in frequency. Intuitively reasonable requirements yield specific forms for these instantaneous quantities that can be computed with familiar complex seismic trace attributes. Instantaneous center frequency is just instantaneous frequency. Instantaneous bandwidth is the absolute value of the derivative of the instantaneous amplitude divided by t...
TL;DR: In this article, the authors performed model studies with the combined use of maxima of analytic signal and of horizontal gradient and the Euler deconvolution techniques on the gravity field and its vertical gradient, demonstrating the superiority of the latter in locating density contrasts.
Abstract: Gravity gradiometric data or gravity data transformed into vertical gradient can be efficiently processed in three dimensions for delineating density discontinuities. Model studies, performed with the combined use of maxima of analytic signal and of horizontal gradient and the Euler deconvolution techniques on the gravity field and its vertical gradient, demonstrate the superiority of the latter in locating density contrasts. Particularly in the case of interfering anomalies, where the use of gravity alone fails, the gravity gradient is able to provide useful information with satisfactory accuracy.
TL;DR: In this paper, the authors compare analytical expressions for the decomposed wavefields, and present several processing algorithms of interest for the geophysicist, which may be applied to marine point-source data acquired over a horizontally layered viscoelastic and anisotropic medium.
Abstract: In seismic processing, plane‐wave decomposition has played a fundamental role, serving as a basis for developing sophisticated processing techniques valid for depth‐dependent models. By comparing analytical expressions for the decomposed wavefields, we review several processing algorithms of interest for the geophysicist. The algorithms may be applied to marine point‐source data acquired over a horizontally layered viscoelastic and anisotropic medium. The plane‐wave decomposition is based on the Fourier transform integral for line‐source data and the Hankel transform integral for point‐source data. The involved wavenumber integrals of the cosine or Bessel‐function type are difficult to evaluate accurately and efficiently. However, a number of the processing techniques can easily be run as a filtering operation in the spatial domain without transforming to the wavenumber domain. The mathematical expressions for the spatial filters are derived using plane wave analysis. With numerical examples, we demonstra...
TL;DR: In this paper, the authors showed that the first arrival is most often associated with a marginally energetic event whenever subsequent arrivals exist and recommended that first-arrival traveltime fields, such as those computed by finite-differencing the eikonal equation, be used in Kirchhoff migration only with great care when the velocity field hosts multiple transmitted arrivals.
Abstract: The authors experienced difficulties when attempting to perform seismic imaging in complex velocity fields using prestack Kirchhoff depth migration in conjunction with traveltimes computed by finite-differencing the eikonal equation. The problem arose not because of intrinsic limitations of kirchhoff migration, but rather from the failure of finite-differencing to compute traveltimes representative of the energetic part of the wavefield. Further analysis showed that the first arrival is most often associated with a marginally energetic event wherever subsequent arrivals exist. The consequence is that energetic seismic events are imaged with a kinematically incorrect operator and turn out mispositioned at depth. They therefore recommend that first-arrival traveltime fields, such as those computed by finite-differencing the eikonal equation, be used in Kirchhoff migration only with great care when the velocity field hosts multiple transmitted arrivals; such a situation is typically met where geological structure creates strong and localized velocity hetero-geneities, which partition the incident and reflected wavefields into multiple arrivals; in such an instance, imaging cannot be strictly considered a kinematic process, as it must be performed with explicit reference to the relative amplitudes of multiple arrivals.
TL;DR: In this article, the authors present two-dimensional and three-dimensional forward modeling in linear viscoelastic media, which implements Boltzmann's superposition principle based on a spectrum of relaxation mechanisms.
Abstract: Anelasticity is usually caused by a large number of physical mechanisms which can be modeled by different microstructural theories. A general way to take all these mechanisms into account is to use a phenomenologic model. Such a model which is consistent with the properties of anelastic media can be represented mechanically by a combination of springs and dash‐pots. A suitable system can be constructed by the parallel connection of several standard linear elements and is referred to as the general standard linear solid rheology. Two relaxation functions that describe the dilatational and shear dissipation mechanisms of the medium are needed. This model properly describes the short and long term behaviors of materials with memory and is the basis for describing viscoelastic wave propagation. This work presents two‐dimensional (2-D) and three‐dimensional (3-D) forward modeling in linear viscoelastic media. The theory implements Boltzmann’s superposition principle based on a spectrum of relaxation mechanisms...
TL;DR: In this paper, it is shown that the sensitivity of the prestack depth migration result to the velocity model is examined using a complex synthetic data set (the Marmousi data set) for which the exact model is known.
Abstract: To get a correct earth image from seismic data acquired over complex structures it is essential to use prestack depth migration. A necessary condition for obtaining a correct image is that the prestack depth migration is done with an accurate velocity model. In cases where we need to use prestack depth migration determination of such a model using conventional methods does not give satisfactory results.Thus, new iterative methods for velocity model determination have been developed. The convergence of these methods can be accelerated by defining constraints on the model in such a way that the method only looks for those components of the true earth velocity field that influence the migrated image. In order to determine these components, the sensitivity of the prestack depth migration result to the velocity model is examined using a complex synthetic data set (the Marmousi data set) for which the exact model is known. The images obtained with increasingly smoothed versions of the true model are compared, and it is shown that the minimal spatial wavelength that needs to be in the model to obtain an accurate depth image from the data set is of the order of 200 m. The model space that has to be examined to find an accurate velocity model from complex seismic data can thus be constrained. This will increase the speed and probability of convergence of iterative velocity model determination methods.
TL;DR: In this article, a numerical solution for the frequency domain electromagnetic response of a two-dimensional conductivity structure to excitation by a three-dimensional (3-D) current source has been developed.
Abstract: A numerical solution for the frequency domain electromagnetic response of a two-dimensional (2-D) conductivity structure to excitation by a three-dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite-element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far-field. In combination with an iterative solution for the along-strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air-earth interface are presented to illustrate the usefulness of the code.
TL;DR: In this article, the authors consider a two-dimensional (2-D) model where the large scale inhomogeneities are represented by a homogeneous medium and small scale inhomalogeneities were randomly distributed inside the homogenous medium, characterized by an ellipsoidal autocorrelation function in the medium properties.
Abstract: The integration of surface seismic data with borehole seismic data and well‐log data requires a model of the earth which can explain all these measurements. We have chosen a model that consists of large and small scale inhomogeneities: the large scale inhomogeneities are the mean characteristics of the earth while the small scale inhomogeneities are fluctuations from these mean values. In this paper, we consider a two‐dimensional (2-D) model where the large scale inhomogeneities are represented by a homogeneous medium and small scale inhomogeneities are randomly distributed inside the homogeneous medium. The random distribution is characterized by an ellipsoidal autocorrelation function in the medium properties. The ellipsoidal autocorrelation function allows the parameterization of small scale inhomogeneities by two independent autocorrelation lengths a and b in the horizontal and the vertical Cartesian directions, respectively. Thus we can describe media in which the inhomogeneities are isotropic (a = b...
TL;DR: In this paper, the authors investigate the effect of electric and magnetic fields at the fundamental frequency of power transmission (typically 60 Hz in North America) and its harmonics on geophysicists.
Abstract: Harmonic noise generated by power lines and electric railways has plagued geophysicists for decades. The noise occurs as electric and magnetic fields at the fundamental frequency of power transmission (typically 60 Hz in North America) and its harmonics. It may be recorded directly during time‐domain measurements of electric and magnetic felds, or indirectly, by geophone cables during the acquisition of seismic data.
TL;DR: In this paper, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis.
Abstract: Tube‐wave speed in the presence of a weakly anisotropic formation can be expressed in terms of an effective shear modulus for an equivalent isotropic formation. When combined with expressions for the speeds of the SH‐ and quasi‐SV‐waves along the borehole axis, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis. Subsequently, a fourth combination of elastic moduli can be estimated from the expression for the qP‐wave speed along the borehole axis. The possibility of determining all five elasticities of a TI formation based on an assumed correlation between two anisotropy parameters is discussed.
TL;DR: In this paper, anisotropic response related to a very fine, bedding-parallel lamination of organic matter and preferred orientation of clay particles in the rock matrix is investigated.
Abstract: Recent experimental studies of ultrasonic velocity anisotropy in kerogen‐rich shales indicate that these rocks are characterized by a very strong anisotropic response related to a very fine, bedding‐parallel lamination of organic matter and preferred orientation of clay particles in the rock matrix (Vernik and Nur, 1992). This intrinsic anisotropy is further enhanced in thermally mature shales by bedding‐parallel microcracks caused by the processes of hydrocarbon generation (Vernik, paper in preparation). However, the potential of recognizing mature source‐rocks in situ using downhole sonic, crosshole seismic, or VSP data clearly depends on our ability to discriminate between these two major causes of elastic anisotropy, remove the effect of the intrinsic anisotropy, and estimate crack density and crack porosity from velocity measurements.
TL;DR: In this paper, the authors used the fourth-order cumulant of the data, and a moving-average, non-causal parametric model for the wavelet, to estimate mixed-phase wavelets.
Abstract: In recent years methods have been developed in the field of high‐order statistics that can reliably estimate a mixed‐phase wavelet from the noisy output of a convolutional process. These methods use high‐order covariance functions of the data called cumulants, which retain phase information and allow recovery of the wavelet. The assumption is that the reflection coefficient series is a non‐Gaussian, stationary, and statistically independent random process. The method described in this paper uses the fourth‐order cumulant of the data, and a moving‐average, noncausal parametric model for the wavelet. The fourth‐order moment function of this wavelet matches the fourth‐order cumulant of the data in a minimum mean‐squared error sense. Numerical simulations demonstrate that the method can accurately estimate mixed‐phase wavelets, even when the reflectivity has a distribution close to Gaussian. Three seismic data examples demonstrate possible uses of the method. In the first two, an average source wavelet is est...
TL;DR: In this article, the authors report the results from the application of a nonlinear global optimization method known as simulated annealing (SA) in the direct interpretation of resistivity sounding data.
Abstract: The resistivity interpretation problem involves the estimation of resistivity as a function of depth from the apparent resistivity values measured in the field as a function of electrode separation. This is commonly done either by curve matching using master curves or by more formal linearized inversion methods. The problems with linearized inversion schemes are fairly well known; they require that the starting model be close to the true solution. In this paper, we report the results from the application of a nonlinear global optimization method known as simulated annealing (SA) in the direct interpretation of resistivity sounding data. This method does not require a good starting model but is computationally more expensive. We used the heat bath algorithm of simulated annealing in which the mean square error (difference between observed and synthetic data) is used as the energy function that we attempt to minimize. Samples are drawn from the Gibbs probability distribution while the control parameter the ...
TL;DR: In this article, the authors show that the application of elevation statics or field statics, or fieldstatics followed by refraction statics never leaves the seismic data completely free of static anomalies.
Abstract: Residual statics. The application of elevation statics, or field statics, or field statics followed by refraction statics never leaves the seismic data completely free of static anomalies. These “residual” static anomalies are due to unaccounted for variations in the low velocity layer. No matter how well the deterministic technique may derive velocities and thicknesses of the near surface, it leaves something to be desired.
TL;DR: Improvements include perturbing the ray at interfaces according to Snell’s Law, and a method to find correct rays efficiently in regions of low velocity contrast, which makes SPR more attractive for tomographic applications in three dimensions.
Abstract: A technique for improving the efficiency of shortest path ray tracing (SPR) is presented. We analyze situations where SPR fails and provide quantitative measures to assess the performance of SPR ray tracing with varying numbers of nodes. Our improvements include perturbing the ray at interfaces according to Snell’s Law, and a method to find correct rays efficiently in regions of low velocity contrast. This approach allows the investigator to use fewer nodes in the calculation, thereby increasing the computational efficiency. In two‐dimensional (2-D) cross‐borehole experiments we find that with our improvements, we need only use 2/3 as many nodes, saving up to 60 percent in time. Savings should be even greater in three dimensions. These improvements make SPR more attractive for tomographic applications in three dimensions.
TL;DR: This method uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections that are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction.
Abstract: Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approa...
TL;DR: In this paper, a method of seismic pulse generation that preferentially concentrates the air gun's energy in the low range of the seismic frequency band by centering the output on the first bubble pulse instead of the initial (primary) pulse is presented.
Abstract: Large tuned air‐gun arrays operated in off‐shore petroleum exploration are also used for deep penetration marine seismic reflection surveys conducted to define structures in the earth’s crust. Because of the attenuation of higher frequencies, the useful upper frequency limit of these records is usually about 50–60 Hz. The aim of this paper is to report on a method of seismic pulse generation that preferentially concentrates the air gun’s energy in the low range of the seismic frequency band by centering the output on the first “bubble pulse” instead of the initial (primary) pulse. Experimental results show that, due to the increased low‐frequency energy content of this “single bubble” pulse, air‐gun arrays considerably reduced both in size and volume can generate the necessary acoustic energy for deep seismic exploration.
TL;DR: In this paper, the authors presented a new method for interpreting electromagnetic (EM) data using ray tomography, which is difficult to apply directly to low-frequency EM data because of the diffusive nature of the field.
Abstract: The authors present a new method for interpreting electromagnetic (EM) data using ray tomography. Direct application of ray tomography to low-frequency EM data is difficult because of the diffusive nature of the field. Diffusive EM fields can, however, be mathematically transformed to wavefields defined in a time-like variable. The transform uniquely relates a field satisfying a diffusion equation in time, or in frequency, to an integral of the corresponding wavefield. If the corresponding wavefields can be computed from low-frequency EM data, one should be able to interpret these data using techniques developed for the wavefields. To test the idea, numerically calculated transient magnetic fields were first transformed to wavefields. The typical window of the time-domain data required for the transform is 1.5 decades. Traveltimes from a source to the receivers were estimated from the reconstructed wavefields. Time-domain data with a Gaussian noise of 3 percent gave a traveltime resolution of better than one percent. For the tomographic inversion, the cross-section between the transmitter and receiver boreholes is divided into a number of rectangular elements, and a continuous slowness is assigned to each of these elements. A functional is formulated by invoking Fermat's principle for the traveltime data. Imposing a stationarymore » condition on the functional gives an iterative procedure for the slowness model. Rays are allowed to bend smoothly within each cell. Incorporating smoothly bending rays is extremely important when the velocity contrast is large. A model with a conductivity contrast of ten (10) has been successfully imaged in 120 iterations with 5 CPU hours on a SUN SPARCstation 2.« less
TL;DR: In this paper, the amplitude-preserving dip-moveout (DMO) filter was proposed to preserve the amplitude of an arbitrary 3-D dipping reflector in seismic imaging.
Abstract: True‐amplitude seismic imaging produces a three dimensional (3-D) migrated section in which the peak amplitude of each migrated event is proportional to the reflectivity. For a constant‐velocity medium, the standard imaging sequence consisting of spherical‐divergence correction, normal moveout (NMO), dip moveout (DMO), and zero‐offset migration produces a true‐amplitude image if the DMO step is done correctly. There are two equivalent ways to derive the correct amplitude‐preserving DMO. The first is to improve upon Hale’s derivation of F-K DMO by taking the reflection‐point smear properly into account. This yields a new Jacobian that simply replaces the Jacobian in Hale’s method. The second way is to calibrate the filter that appears in integral DMO so as to preserve the amplitude of an arbitrary 3-D dipping reflector. This latter method is based upon the 3-D acoustic wave equation with constant velocity. The resulting filter amounts to a simple modification of existing integral algorithms. The new F-K an...