bluuebunny/crossref_metadata_2025 huggingface dataset:
A physical model study of shear‐wave splitting and fracture intensity
Authors: Tatham Robert H. , Matthews Martin D. , Sekharan K. K. , Wade Christopher J. , Liro Louis M.
Published: October 2002

In a series of physical model experiments, fractured media are simulated by stacks of thin Plexiglas sheets clamped together tightly to form blocks. The plates are assembled underwater, and a very thin water layer between the sheets prevents formation of an effectively welded interface between them. Thus, the stacked material is not a series of welded plates but rather a truly fractured medium simulating a potential petroleum reservoir with only fracture porosity and permeability. Sheets of constant thickness are used, but the intensity of fracturing between the different models is simulated by using different thicknesses of Plexiglas for each model. Observation of direct shear‐wave arrivals through the stack, with propagation parallel to the sheets and polarization of particle motion allowed to be parallel to, normal to, or in any arbitrary angle to the sheets, definitively demonstrate the existence of shear‐wave splitting and hence anisotropy. For Plexiglas sheets 1/16 in thick (0.16 cm) representing a fracture intensity of about 16 fractures per wavelength, shear‐wave splitting and hence anisotropy are clearly observed. For greater fracture intensities (i.e., thinner plates) the degree of anisotropy is greater, and for less intense fracturing (i.e., thicker plates), the degree of anisotropy is less. These experimental data suggest that for fracture intensities of greater than about 10 fractures per wavelength there is a simple relation between fracture intensity and degree of anisotropy in two different polarizations of shear waves. For fracture intensities less than a threshold of about 10 per wavelength, there is no simple observed relation between them. Further, the faster of the split shear‐wave velocities is near the solid material velocity, and the observed variation in velocity for various fracture intensities is in the slower of the split shear‐wave velocities.
Another look at NMO stretch
Authors: Barnes Arthur E.
Published: October 2002

The normal moveout (NMO) correction is applied to seismic reflection data to transform traces recorded at non‐zero offset into traces that appear to have been recorded at zero offset; this introduces undesirable distortions called NMO stretch (Buchholtz, 1972). NMO stretch must be understood because it lengthens waveforms and thereby reduces resolution. Buchholtz (1972) gives a qualitative assessment of NMO stretch, Dunkin and Levin (1973) derive its effect on the amplitude spectra of narrow waveforms, while Yilmaz (1987, p. 160) considers its effect on dominant frequencies. These works are approximate and do not show how spectral distortions vary through time.
Modeling anelastic singular surface waves in the earth
Authors: Carcione José M.
Published: October 2002

The propagation of anelastic surface waves presents substantial differences compared to the elastic case. Therefore, a forward modeling scheme to study surface waves in an anelastic earth is of some relevance to the geophysical problem. When propagating anelastic waves, accuracy is very important; in particular, numerical dispersion should not be confused with physical velocity dispersion. One modeling algorithm, based on the velocity‐stress elastodynamic equations, uses a spectral method with a Chebychev expansion in the vertical direction. This approach allows the calculation of the spatial derivatives with high accuracy, and an effective incorporation of the free surface boundary conditions since the method is not periodic. However, a direct application of the traction‐free boundary conditions without regard to the other variables produces numerical instabilities. To solve this problem, a boundary treatment based on characteristics is implemented that results in a wave equation for the surface that automatically includes the boundary conditions. Two examples of wave propagation in an unconsolidated weathering zone are presented. The first model is homogeneous and the second structure contains a vertical interface separating an anelastic medium from an elastic region. The results indicate that the modeling correctly describes the anelastic properties of Rayleigh waves, even in the presence of a strong contrast in the material parameters.
Effects of heterogeneities and anisotropy on sonic and ultrasonic attenuation in rocks
Authors: Lucet Nathalie , Zinszner Bernard
Published: October 2002

We compare the attenuation obtained by the resonant bar technique in the sonic frequency range (3–10 kHz) with that obtained by the pulse transmission technique in the ultrasonic frequency range (500 kHz) on a set of 30 rocks, including sandstones and limestones. The sonic and ultrasonic measurements were performed under high effective pressure on adjacent water‐saturated samples from each rock block. Compressional ultrasonic attenuation was typically larger than extensional sonic attenuation, particularly in limestones. This is attributed to the presence of density heterogeneities, that can be seen on X‐ray scanner imagery. Heterogeneities at the scale of the ultrasonic wavelength produce diffraction of the waves, and as a consequence, high attenuation values. At ultrasonic frequencies, large apparent shear attenuation values, compared to compressional attenuation values, are explained by shear wave splitting.
3-D migration via McClellan transformations on hexagonal grids
Authors: Hedley Justin P.
Published: October 2002

Two‐dimensional (2-D) spatially varying convolutional filters for three‐dimensional (3-D) depth extrapolation are efficiently designed and implemented by using McClellan transformations. Although efficient, McClellan transformations only approximate circularly symmetric depth extrapolation filters. The accuracy of the extrapolation filters can be increased only at an increase in the computational cost of implementing those filters. By applying McClellan transformations on a hexagonal sampling grid, the accuracy of the extrapolation filters can be increased at a reduction in cost.
Geometrical spreading corrections of offset reflections in a laterally inhomogeneous earth
Authors: Tygel M. , Schleicher J. , Hubral P.
Published: October 2002

Compressional primary seismic nonzero offset reflections are the most essential wavefield attributes used in seismic parameter estimation and imaging. We show how the determination of angle‐dependent reflection coefficients can be addressed from identifying such events for arbitrarily curved three‐dimensional (3-D) subsurface reflectors below a laterally inhomogeneous layered overburden. More explicitly, we show how the geometrical‐spreading factor along a reflected primary ray with offset can be calculated from the identified (i.e., picked) traveltimes of offset primary reflections. Seismic traces in which all primary reflections are corrected with the geometrical‐spreading factor are, as is well‐known, referred to as true‐amplitude traces. They can be constructed without any knowledge of the velocity distribution in the earth model. Apart from possibly finding a direct application in an amplitude‐versus‐offset (AVO) analysis, the theory developed here can be of use to derive true‐amplitude time‐ and depth‐migration methods for various seismic data acquisition configurations, which pursue the aim of performing the wavefield migration (based upon the use of a macro‐velocity model) and the AVO analysis in one step.
Weathering structure of the east‐central Niger Delta, Nigeria
Authors: Uko Etim D. , Ekine Anthony S. , Ebeniro Joseph O. , Ofoegbu Charles O.
Published: October 2002

Refraction experiments were conducted over parts of the east‐central Niger Delta in an attempt to provide an interpretation of the region’s weathering structure. The velocity and depth of the weathered layer and the velocity of the refractor were calculated from critically refracted arrivals using flat‐layer models. An interpretation of the data, carried out using the time‐intercept method, shows that the thickness of the low velocity weathered layer in the region is highly variable, from between about 2.9 m and 45.5 m, with a regional average of about 20.0 m. The weathered layer and the refractor beneath it have an average compressional‐wave velocity of about 500.0 m/s and 1732.0 m/s, respectively. The knowledge of this weathering structure can be applied in oil and ground water exploration in the area of the study. It is also expected that this structure could be used by groups interested in civil engineering.
Modeling of water‐gun signatures
Authors: Landrø Martin , Zaalberg‐Metselaar Gitta , Owren Brynjulf , Vaage Svein
Published: October 2002

A method for calculating the acoustic signal generated by a water gun is presented. The equations describing the shuttle motion and the water jet formation are derived with the assumption that the water is incompressible. The motion of the shuttle is evaluated by assuming adiabatic expansion of the air initially contained in the air chamber of the gun. The formation and dynamics of the water jets emerging from the gun ports are closely connected to the shuttle motion. The combined effect of the water motion through the gun ports and the collapse of a cavity inside the gun nozzle can explain the first part of a water‐gun signature, often referred to as the precursor. The last part of the signature is mainly an impulsive shock wave caused by the collapse of external cavities. It is assumed that the external cavities are formed due to the pressure drop behind each water jet, and that the cavities collapse due to the hydrostatic pressure. The main effect of including interaction between the external cavities is to increase the bubble period (i.e., the collapse time). Comparison between modeled and measured near‐field signatures for an S80 SODERA water gun show a difference of less than 5 percent of the energy in the measurement.
Werner deconvolution for variable altitude aeromagnetic data
Authors: Ostrowski Julius S. , Pilkington Mark , Teskey Dennis J.
Published: October 2002

The standard Werner deconvolution method is extended to include the effects of variable sensor altitude but this leads to a deconvolution algorithm that is unstable for slowly changing flight height. By expressing the sensor altitude as a linear function of horizontal position (within a specified window), we show that the numerical instability can be avoided. The subsequent selection and averaging of the raw solutions is controlled by three parameters that can be adjusted to specific survey data characteristics. Results for an aeromagnetic survey over Vancouver Island, British Columbia show that, in comparison with the variable altitude approach, the standard Werner method produces unacceptable errors when applied to variable altitude data.
Advantages of using the vertical gradient of gravity for 3-D interpretation
Authors: Marson I. , Klingele E. E.
Published: October 2002

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.
Sensitivity of reflected and transmitted seismic data
Authors: Mittet Rune , Houlder Tom
Published: October 2002

Seismic data have been reported to carry information on both small scale and large scale medium variations, but not for intermediate size objects. This is a paradox compared to many other experiments performed with probes of wave nature, where objects of size of the smallest wavelength or larger can be resolved. The sensitivity of reflected and transmitted seismic data to medium perturbations of varying sizes is investigated. The differences between data generated in a reference model and data generated in a perturbed model are measured. Both [Formula: see text] and [Formula: see text] type objective functions are used. The kernels of the objective functions consist of either stress or particle‐velocity field components. Several experimental configurations and the sensitivity to various ways of performing the medium perturbations are analyzed. For all perturbation types that change the impedances, we find a resonant behavior in the objective functions for perturbations of size of the typical wavelength of the source. For the experiments where impedances are kept fixed, we do not find this resonance, but there is a significant contribution to the objective function for all perturbation sizes larger then the shortest wavelength. That is, seismic data are sensitive to objects of size of the smallest wavelength or larger.
Singular value decomposition for cross‐well tomography
Authors: Michelena Reinaldo J.
Published: October 2002

I perform singular value decomposition (SVD) on the matrices that result in tomographic velocity estimation from cross‐well traveltimes in isotropic and anisotropic media. The slowness model is parameterized in four ways: One‐dimensional (1-D) isotropic, 1-D anisotropic, two‐dimensional (2-D) isotropic, and 2-D anisotropic. The singular value distribution is different for the different parameterizations. One‐dimensional isotropic models can be resolved well but the resolution of the data is poor. One‐dimensional anisotropic models can also be resolved well except for some variations in the vertical component of the slowness that are not sensitive to the data. In 2-D isotropic models, “pure” lateral variations are not sensitive to the data, and when anisotropy is introduced, the result is that the horizontal and vertical component of the slowness cannot be estimated with the same spatial resolution because the null space is mostly related to horizontal and high frequency variations in the vertical component of the slowness. Since the distribution of singular values varies depending on the parametrization used, the effect of conventional regularization procedures in the final solution may also vary. When the model is isotropic, regularization translates into smoothness, and when the model is anisotropic regularization not only smooths but may also alter the anisotropy in the solution.
Electromagnetic induction by a finite electric dipole source over a 2-D earth
Authors: Unsworth Martyn J. , Travis Bryan J. , Chave Alan D.
Published: October 2002

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.
Linear‐transform techniques for processing shear‐wave anisotropy in four‐component seismic data
Authors: Li Xiang‐Yang , Crampin Stuart
Published: October 2002

Most published techniques for analyzing shear‐wave splitting tend to be computing intensive, and make assumptions, such as the orthogonality of the two split shear waves, which are not necessarily correct. We present a fast linear‐transform technique for analyzing shear‐wave splitting in four‐component (two sources/ two receivers) seismic data, which is flexible and widely applicable. We transform the four‐component data by simple linear transforms so that the complicated shear‐wave motion is linearized in a wide variety of circumstances. This allows various attributes to be measured, including the polarizations of faster split shear waves and the time delays between faster and slower split shear waves, as well as allowing the time series of the faster and slower split shear waves to be separated deterministically. In addition, with minimal assumptions, the geophone orientations can be estimated for zero‐offset verticle seismic profiles (VSPs), and the polarizations of the slower split shear waves can be measured for offset VSPs. The time series of the split shear‐waves can be separated before stack for reflection surveys. The technique has been successfully applied to a number of field VSPs and reflection data sets. Applications to a zero‐offset VSP, an offset VSP, and a reflection data set will be presented to illustrate the technique.
Instantaneous spectral bandwidth and dominant frequency with applications to seismic reflection data
Authors: Barnes Arthur E.
Published: October 2002

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 the instantaneous amplitude. Instantaneous dominant frequency is the square root of the sum of the squares of the instantaneous frequency and instantaneous bandwidth. Instantaneous bandwidth and dominant frequency find employment as additional complex seismic trace attributes in the detailed study of seismic data. Instantaneous bandwidth is observed to be nearly always less than instantaneous frequency; the points where it is larger may mark the onset of distinct wavelets. These attributes, together with instantaneous frequency, are perhaps, of greater use in revealing the time‐varying spectral properties of seismic data. They can help in the search for low frequency shadows or in the analysis of frequency change due to effects of data processing. Instantaneous bandwidth and dominant frequency complement instantaneous frequency and should find wide application in the analysis of seismic reflection data.
Two‐dimensional induction log modeling using a coupled‐mode, multiple‐reflection series method
Authors: Pai David M. , Ahmad J. , Kennedy W. David
Published: October 2002

In induction logging, both vertical and radial conductivity variations exist in the logged medium; elementary separation of variables cannot be applied directly to the partial differential equation describing the electromagnetic field in such a medium. A modal expansion method of solution can be designed using modes defined with respect to the vertical coordinate. This method breaks the original two‐dimensional (2-D) problem into a set of independent one‐dimensional (1-D) problems. The receiver signal is decomposed into a direct signal traveling within the borehole and a reflection signal bearing information about the conductivity distribution outside the borehole. The solution is obtained as a coupled‐mode, multiple‐reflection series accounting for repeated mode reflections at the vertical boundaries in the medium. Each term in the series represents the next higher order reflection in a sequence of multiple reflections; results show two terms are sufficient to reach accuracy acceptable for log modeling.
A numerical simulation of the acoustic and elastic wavefields radiated by a source on a fluid‐filled borehole embedded in a layered medium
Authors: Bouchon Michel
Published: October 2002

We present a method of calculation to simulate the propagation of acoustic and elastic waves generated by a borehole source embedded in a layered medium. The method is formulated as a boundary element technique where the Green’s functions are calculated by the discrete wavenumber method. The restrictive assumptions are that the borehole is cylindrical and that its axis runs normal to the layer interfaces. The physics of the method rely on Huygens’s principle that states that a diffracting boundary—the borehole wall in the present case—can be represented as a distribution of secondary sources. The borehole is discretized into small cylindrical elements and each element is represented by three sources: a volume source representing the wavefield diffracted in the fluid and two surface forces that give rise to the elastic wavefield radiated outside the borehole. The strength of each source is obtained by solving the linear system of equations that describes the boundary conditions at the borehole wall. The method is used to generate synthetic acoustic logs and to investigate the wavefield radiated into the formation. The simulations considered display the Stoneley wave reflections at the bed boundaries and show the importance of the diffraction that takes place where the borehole wall intersects the layer interfaces.
A review of gravity gradiometer survey system data analyses
Authors: Jekeli Christopher
Published: October 2002

The Gravity Gradiometer Survey System (GGSS) was designed to measure the local and regional gravity field from a ground or airborne moving platform. With the first and only airborne field test, the GGSS was able to recover five‐arcminute by five‐arcminute mean gravity anomalies to an accuracy of a few mGal. These results were obtained by flying the system, with an operational precision of about 10 Eötvös (ten‐second average), on a grid of orthogonal tracks spaced 5 km apart at an altitude of about 700 m above the terrain. Despite perpetual navigation problems with the Global Positioning System and several periods of excessive system noise, the results of a performance analysis on 19 out of 128 tracks demonstrated the potential accuracy and efficiency of the GGSS as an airborne gravity mapping system. The ground tests (both road and railway), suffering from undue vehicle vibrations and from a lack of ground truth data, were correspondingly less successful, but they also showed no surprises in the system corrupted by these adverse conditions. Unfortunately, the GGSS program has terminated; and it is appropriate to reflect on its accomplishments. Without going into technical details, this somewhat historical review summarizes the field tests, the data reduction algorithms, and the test results, which together portray the breadth of expertise the program engendered in the area of gravity gradiometry.
A simple approximation to the P‐wave reflection coefficient and its implication in the inversion of amplitude variation with offset data
Authors: Mallick Subhashis
Published: October 2002

I derive an approximate formula for the plane P‐wave reflection coefficient as a function of ray‐parameter. The approximation shows that the behavior of the P‐wave reflection coefficient at nonnormal angles of incidence is mainly controlled by two parameters: (1) [Formula: see text], the fluid‐fluid reflection coefficient (i.e., the reflection coefficient when the S‐wave velocities in both media are set to zero) and (2) Δμ/ρ, the ratio of the contrast in shear moduli to the average bulk density. I also show that the other formulas for the P‐wave reflection coefficient given by R. Bortfeld and R. Shuey can be approximately derived from my formula. I give numerical examples to demonstrate the accuracy of the formula. Using a least‐squares inversion of theoretical values for the reflection coefficients, I demonstrate that, in a linear inversion of amplitude versus offset data, Δμ/ρ is better estimated than the contrast in Poisson’s ratio, Δσ. Finally, comparing the exact reflection coefficient with Shuey’s approximation for typical shale and Class 1 gas‐sand models, I show that Shuey’s approximation under‐estimates the value of |Δσ| for such reflections.
Inversion of aeromagnetic data using digital terrain models
Authors: Woodward Derek J.
Published: October 2002

Although draped magnetic surveys contain more information about the magnetization of the rocks near the surface of the earth than surveys at constant elevation, allowance for the effects of the terrain is critical for their correct interpretation. A new method for calculating the magnetic effect of the topography from a digital terrain model by integrating analytically in the vertical direction and then numerically in the horizontal plane is presented. This method lends itself to the calculation of anomalies when the magnetization of the rocks varies with position and thus is well suited to the inversion of draped aeromagnetic surveys to obtain the apparent magnetization of the surficial rocks. This inversion is achieved by repeated use of an approximate inverse function in the form of a two‐dimensional (2-D) filter that is applied to gridded data. An example, using draped magnetic data collected over White Island, an active volcanic island of high relief, shows that although the anomaly pattern is dominated by topographic effects, the distribution of near‐surface magnetic bodies can be determined by a joint inversion of the data and the topography. One of the highly magnetized areas of White Island is interestingly in the vicinity of the active crater, with another near the inner wall of the caldera where there are numerous fumaroles. It may be expected that the higher temperatures in these areas would reduce the magnetization. However, it appears that an explanation for the higher magnetization can be found in the stability field of the mineral magnetite.
Identifying remanent magnetization effects in magnetic data
Authors: Roest Walter R. , Pilkington Mark
Published: October 2002

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.
Resolution limits in ray tomography due to wave behavior: Numerical experiments
Authors: Williamson Paul R. , Worthington M. H.
Published: October 2002

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 relation of resolution to Fresnel zones. It is therefore possible that such limits on resolution may be at least as significant as those due to other factors such as experimental geometry.
High‐resolution seismic reflections in a potash mine
Authors: Gendzwill D. J. , Brehm Randy
Published: October 2002

High‐resolution seismic reflections underground in a deep potash mine in Canada have been collected using a hammer for a seismic source, 50 Hz geophones, and a digital, stacking seismograph with 0.1 ms sampling rate. Data were obtained with 12‐fold redundancy in both downward and upward directions from the mine openings. Reflections with dominant frequency up to 1100 Hz were observed between 20 and 80 ms time. Both single geophones and arrays of geophones were tested. For the roof profiles, geophones were bolted to the rock with specially designed base plates. Computer processing used deconvolution filters to remove spurious high‐frequency resonance of the geophones. Constant velocity for salt was used for all static corrections and normal moveout corrections. An unexpected result was the appearance of near‐vertical reflected waves that traveled both ways at the shear‐wave speed. These are thought to have been caused by near‐surface fractures or near‐surface anisotropy of the rock. Synthetic seismograms calculated from logs of a nearby well agree with the seismic reflection data. Normal stratification of the flat‐bedded sedimentary rocks and a small structure were mapped by the seismic data, confirming the vertical extent of geological anomalies observed at the mine level.
A finite‐difference, time‐domain solution for three‐dimensional electromagnetic modeling
Authors: Wang Tsili , Hohmann Gerald W.
Published: October 2002

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 [Formula: see text] 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 Ω ⋅ 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.
Temperature‐dependent propagation of P‐ and S‐waves in Cold Lake oil sands: Comparison of theory and experiment
Authors: Eastwood John
Published: October 2002

The measured dependence of ultrasonic velocity in Cold Lake oil sands on temperature is compared to theoretical model predictions for seismic wave propagation in porous media. The experiments indicated that change in fluid properties with temperature most greatly affect observed velocities. The theoretical model was constructed to account for temperature dependent fluid properties using correlations independent of the ultrasonic experiments. Theoretical and experimental P‐wave velocities agree within 5 percent for temperatures between 22°C to 125°C and effective stresses of 1 MPa and 8 MPa. The modeling indicates that the change in fluid bulk modulus with temperature dominates the observed 15 percent P‐wave velocity decrease between 22°C to 125°C. Over the same temperature range the model predicts the S‐wave velocity remains almost constant (<1 percent increase).
Subtraction of powerline harmonics from geophysical records
Authors: Butler Karl E. , Russell R. Don
Published: October 2002

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.
Noniterative nonlinear gravity inversion
Authors: Guspí Fernando
Published: October 2002

To obtain the shape of a homogeneous body from its gravity anomalies, the inverse of Parker’s formula is expressed here by means of a power series expansion in the reciprocal of the density contrast. The calculation of the nth coefficient of the series needs the evaluation of [Formula: see text] Fourier transforms of products and sums of the preceding coefficients and a sufficient storage to contain all of them. Computer time is modest for the first several terms, but grows rapidly as the number of terms increases. Fortunately, most inversions require a small number of terms. The method reproduces Oldenburg’s iteration results exactly and faster whenever it converges, and it can also converge in other cases. Nevertheless, its main advantage comes from the fact that once the series coefficients have been computed, the inversion can be performed immediately for a variety of density contrasts, allowing the choice of best values to match constraints such as seismic or borehole data.
Traveltime and amplitude estimation using wavefront construction
Authors: Vinje Vetle , Iversen Einar , Gjøystdal Håvar
Published: October 2002

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 drawbacks of the method are the same as for conventional ray tracing: large velocity contrasts, caustics and near‐critical incidence angle of rays onto interfaces will give less accurate solutions.
Relationship between Deregowski‐Rocca and Hale operators
Authors: Sincer Ismet , Kayiran Turan
Published: October 2002

The relationship between two commonly used approaches, namely that of Deregowski and Rocca (1981) and Hale (1984), has not been specified explicitly. In this short note, we show an analytical interrelation between the two methods in terms of their kinematic behavior.
An overview of some of the large scale mechanisms of salt dissolution in western Canada
Authors: Anderson Neil L. , Knapp Ralph
Published: October 2002

Well log and seismic data indicate that the bedded rock salts (salts) of the Devonian Age Prairie Formation were widely distributed and uniformly deposited in the Lloydminster area, Western Canada (T45-65, R20W3M-R5W4M); however, as a result of extensive leaching, the distribution of these salts is not now what it once was. The Lloydminster area is now bisected by the north‐south trending main dissolutional edge of the Prairie salt. Thick salt (up to 150 m) is preserved to the west of this edge; to the east the salt is mostly absent. Analyses of remnant salt and patterns of subsurface structural relief suggests that the dissolution of the Prairie salt in the Lloydminster area was triggered and/or accentuated in part by several different large scale mechanisms including: near‐surface exposure, centripetal flow of unsaturated waters, regional faulting/fracturing, glacial loading and/or unloading, dissolution of the underlying salt, and salt creep. These mechanisms are supported by the incorporated seismic and well log control that indicate a direct relationship between the thicknesses of remnant salt and post‐salt strata. Well log and seismic data also indicate that the bedded salts of the Devonian Age Black Creek Member were uniformly deposited within the Black Creek sub‐basin, Rainbow Lake area, western Canada (T105-112, R5-R10W6M); however, as a result of extensive leaching, distribution of these salts is not now what it once was. The Black Creek salts are now preserved only as discontinuous remnants with maximum gross thicknesses on the order of 80 m. Seismic and well log control suggests that the dissolution of the Black Creek salt in the Rainbow Lake study area was triggered and/or accentuated in part by several different large scale mechanisms including: centrifugal flow of unsaturated waters, regional faulting/fracturing and salt creep. Bedded salt is preserved within five other Devonian Age evaporitic units in Alberta, Canada: the Lotsberg Formation, Cold Lake Formation, Beaverhill Lake Group, Leduc Formation, and Wabamun Group. Each of these salts has also been extensively leached in places. In the literature, dissolution is generally attributed to one or more of the previously noted large scale mechanisms. Herein we present an overview of the envisioned principal mechanisms of salt dissolution. In support of these hypothesized mechanisms, we present seismic and geologic control from both the Lloydminster and Rainbow Lake areas of western Canada, which illustrate that the dissolution of subsurface salts is accompanied by the subsidence of post‐salt strata and that the analyses of this information can be used to elucidate the timing and large scale mechanisms of salt dissolution.
Separation and enhancement of split S‐waves on multicomponent shot records from the BIRPS WISPA experiment
Authors: Boulfoul M. , Watts D. R.
Published: October 2002

Instantaneous rotations are combined with f-k filtering to extract coherent S‐wave events from multicomponent shot records recorded by British Institutions Reflection Profiling Syndicate (BIRPS) Weardale Integrated S‐wave and P‐wave analysis (WISPA) experiment. This experiment was an attempt to measure the Poisson’s ratio of the lower crest by measuring P‐wave and S‐wave velocities. The multihole explosive source technique did generate S‐waves although not of opposite polarization. Attempts to produce stacks of the S‐wave data are unsuccessful because S‐wave splitting in the near surface produced random polarizations from receiver group to receiver group. The delay between the split wavelets varies but is commonly between 20 to 40 ms for 10 Hz wavelets. Dix hyperbola are produced on shot records after instantaneous rotations are followed by f-k filtering. To extract the instantaneous polarization, the traces are shifted back by the length of a moving window over which the calculation is performed. The instantaneous polarization direction is computed from the shifted data using the maximum eigenvector of the covariance matrix over the computation window. Split S‐waves are separated by the instantaneous rotation of the unshifted traces to the directions of the maximum eigenvectors determined for each position of the moving window. F-K filtering is required because of the presence of mode converted S‐waves and S‐waves produced by the explosive source near the time of detonation. Examples from synthetic data show that the method of instantaneous rotations will completely separate split S‐waves if the length of the moving window over which the calculation is performed is the length of the combined split wavelets. Separation may be achieved on synthetic data for wavelet delays as small as two sample intervals.
3-D transmission tomography using wide aperture data for velocity estimation for irregular salt bodies
Authors: Zhang Jie , McMechan George A.
Published: October 2002

Reliable 3-D velocity estimation is a prerequisite to 3-D migration in laterally varying environments, but is difficult with data from conventional seismic surveys because of limited aperture, especially in the crossline direction. A possible solution to this problem is tomographic estimation of the 3-D velocity distribution using transmitted (turned) rays recorded in wide areal apertures. Using this approach, the shape and position of salt structures, including overhangs, subsalt features, and deformation of surrounding sediments, are accurately estimated from synthetic test data. Model enhancement based on a priori geologic constraints gives 3-D macro velocity distributions for models of three actual salt structures: a salt tongue in the Gulf Coast, and the Hainesville and Mount Sylvan domes in the East Texas Basin. The geometries required are feasible with current land acquisition systems. The main practical limitations are the requirements for nonstandard (wide aperture) recording arrays and for accurate time picking of the transmitted arrivals.
Characterization of resolution and uniqueness in crosswell direct‐arrival traveltime tomography using the Fourier projection slice theorem
Authors: Rector James W. , Washbourne John K.
Published: October 2002

The process of acquiring a crosswell seismic direct‐arrival traveltime data set can be approximated by a series of truncated plane‐wave projections through an interwell slowness field. Using this approximation, the resolution and uniqueness of crosswell direct‐arrival traveltime tomograms can be characterized by invoking the Fourier projection slice theorem, which states that a plane‐wave projection through an object constitutes a slice of the object’s spatial spectrum. The limited vertical aperture of a crosswell survey introduces a small amount of nonuniqueness into the reconstructed tomogram by truncating the plane‐wave projection. By contrast, the limitations on angular aperture have a significant effect on resolution. The reconstructed tomogram is smeared primarily along the limiting projection angles, with the amount of smearing dependent upon the well spacing and the angular aperture. The amount of smearing was found to be inversely proportional to tan Δϕ, where Δϕ is the angular aperture illuminating a sector of the interwell plane. Consequently, the amount of smearing can be large where the angular aperture becomes small, such as at the top and bottom of the tomogram. For interwell sectors illuminated by large angular apertures, Fresnel zone effects will generally be the limiting factor in crosswell tomogram resolution. However, in some circumstances, angular aperture effects may control the tomogram resolution. The effects of angular aperture and direct‐arrival Fresnel zones produce tomograms with spatial resolution that is dependent upon the well spacing. This study indicates that direct‐arrival traveltime tomography will not usually produce tomograms with substantially greater resolution than surface seismic techniques for normal oil and gas well spacings.
Understanding air‐gun bubble behavior
Authors: Johnson Daniel T.
Published: October 2002

An air‐gun bubble behaves approximately as a spherical bubble of an ideal gas in an infinite volume of practically incompressible water. With this simplification, the equation of bubble motion and its far‐field signature is more understandable than with the more exact theory commonly cited in the literature. The terms of the equation of bubble motion are explained using elementary physics and mathematics, computation of numerical results is outlined, and an example signature is shown. An air‐gun bubble is analogous to a simple harmonic oscillator consisting of a mass on a spring, with an equivalent mass equal three times that of the water displaced by the bubble, and air pressure following an ideal gas law corresponding to a spring. With this understanding, one is prepared to deal with the effects of interactions among air guns and with the higher‐order terms and other features that must be included to model the air‐gun signature of actual seismic source arrays.
A generalized O’Doherty‐Anstey formula for waves in finely layered media
Authors: Shapiro Serge A. , Zien Holger , Hubral Peter
Published: October 2002

We investigate the angle‐dependent plane wave transmissivity of a pressure wave in a random, multilayered, acoustic, variable velocity and variable density medium. The main result of our consideration is a simple, explicit analytic description of the influence of such a medium on the transmissivity kinematics and dynamics for the whole frequency range. We assume that the velocity and density dependencies on depth are typical realizations of random stationary processes. Moreover, the fluctuations in both values must be relatively small compared to their constant mean values (of the order of 30 percent or smaller). In our derivation, we combine the small perturbation technique with the localization and self‐averaging theory. We obtain the attenuation and the phase of the time‐harmonic transmissivity, as well as the pulse form of the transient transmissivity from an angle‐dependent combination of the auto‐ and crosscorrelation functions of both the sonic and density logs. Our results for the kinematics of the transmissivity yield the wellknown “Backus averaging” in the low‐frequency limit. Likewise, they provide the ray theory result as the high‐frequency asymptotic value. The analytic expression for the transmissivity can be viewed as a generalization of the O’Doherty‐Anstey formula. Numerical computations of the actual transmissivity show fluctuations around the theoretical prediction given by our formula, which is strictly valid only in the case of infinitely thick media. The larger the layered medium, the smaller are these fluctuations. They can be well estimated with a formula which we derive to describe the deviations between the analytic and the exact transmissivity obtained for a layered medium of finite thickness.