bluuebunny/crossref_metadata_2025 huggingface dataset:
Shear waves, multiple reflections, and converted waves found by a deep vertical wave test (vertical seismic profiling)
Authors: Lash C. C.
Published: October 2002

Evidence that shear (S) waves are much more important in seismic surveys than currently believed was found in each of two deep well tests conducted some time ago. Wave tests were recorded along vertical lines, following procedures which are now designated “vertical seismic profiling.” The results may be divided into (1) evidence that shear (S) waves are produced by in‐hole dynamite charges and by the resulting compressional (P) waves, and (2) evidence that the S‐waves subsequently produce P‐waves. The proof of S‐wave production is quite conclusive. Even if we say that only P‐waves are set up in the immediate vicinity of the shot, some S‐waves are then generated within a radius of 10 to 100 ft to form what we will call a direct or “source S wave.” Other S‐waves are set up by conversion of P‐wave energy to S‐wave energy at interfaces hundreds and thousands of feet from the dynamite charge. In contrast to the P to S conversion, the evidence for S to P conversion is less conclusive. The source S‐wave generated near the shot was found to have a long‐period character, with many cycles which are believed to be controlled by the layering near the shot. The PS converted waves, which appear later, resemble the P‐waves that produce them. The interference to primary reflections by multiple reflections and/or converted waves produces complex signals at points deep in the well which require directional discrimination to separate up‐traveling waves from down‐traveling waves.
Surface consistent corrections
Authors: Taner M. Turhan , Koehler Fulton
Published: October 2002

Amplitudes of seismic reflections have been of interest since the first days of exploration seismology. Any change of amplitude or anomalous behavior may be significant, so it is important that the zones of interest be free from outside disturbances, such as those caused by the near‐surface layers. Surface consistent factors may be divided into source, receiver, offset, and subsurface components, and these may be divided further into amplitude and phase (or time shift) factors. Correction of trace amplitudes using multiplication by a scale factor is similar to correction of phase distortions by a static shift, and both corrections enhance seismic data. Displays of surface consistent components for time and amplitude corrections provide an additional diagnostic for the geophysicist.
Dip limitations on migrated sections as a function of line length and recording time
Authors: Lynn Heloise Bloxsom , Deregowski Swavek
Published: October 2002

The length of a seismic profile and the recording time available as input to migration govern simple equations relating dip observable on migrated profiles to the spatial location of the reflector. This relationship is important to exploration geophysicists seeking critical seismic dip and to deep crustal geophysicists examining the nature of the continental crust. A certain amount of the observed decrease of dip with depth, and the dip biasing on the edges of migrated sections, can be related to the size of the input, as shown in a real data example. Any further decrease in dip with depth may have geologic significance. To portray (image) up to 45‐degree dips at the target depth, 50 percent more time must be recorded and input to the migration as the two‐way migrated time of the target. The lead‐in (or step‐in) required on both ends of the line is the depth to the target. For 0‐ to 30‐degree dips to be present at the target depth, one‐sixth more time must be recorded and input to the migration; the lead‐in must be 65 percent of the depth to target. Crooked profiles complicate the migration: either linear segments of the profile are migrated separately (which drastically decreases the dip resolution obtained on the section as a whole), or the line can be “straightened” (projected onto a dip line) and then migrated as a unit [which assumes the target horizon is two‐dimensional (2-D)].
Delineation of a low‐velocity body under the Roosevelt Hot Springs geothermal area, Utah, using teleseismic P‐wave data
Authors: Robinson Russell , Iyer H. M.
Published: October 2002

To assess the nature of the heat source associated with the Roosevelt Hot Springs geothermal area, we have investigated the P‐wave velocity structure of the crust and uppermost mantle in the vicinity of the Mineral Mountains, southwest Utah, a region of late Cenozoic rhyolitic and basaltic volcanic activity. A roughly square (30 × 30 km) array of 15 seismographs, centered on the mountains, was operated for a period of 46 days, during which 72 teleseismic events were recorded with sufficient quality for calculation of P‐wave traveltime residuals. Relative residuals, using the array average for each event as reference, show a clear pattern of azimuthal variation of up to 0.3 sec. This pattern implies the existence of a localized region of relatively low‐velocity material extending up from the upper mantle to depths of about 5 km under the Mineral Mountains. A three‐dimensional (3-D) inversion of the data confirms this conclusion and yields a model featuring a region of low velocity (5 to 7 percent less than the surrounding rock) centered under the geothermal area and extending from about 5-km depth down into the uppermost mantle. The near‐surface velocities obtained in the inversion clearly reveal the structure of the region, part of the Basin and Range province. An azimuthally changing pattern of wave‐form distortion, restricted to the central Mineral Mountains, indicates the presence of a small but intensely anomalous region of low velocity and high attenuation at depths of about 15 km. Although we cannot rule out an explanation for the low velocity purely in terms of compositional changes, in view of the geothermal and volcanic manifestations found in the region we prefer an explanation in terms of abnormally high temperature and a small fraction of partial melt. A partial melt model implies a much greater heat reservoir than does a model involving only circulation along deep fault zones.
A microearthquake survey at the Ngawha geothermal field, New Zealand
Authors: Robinson Russell
Published: October 2002

A twenty day microearthquake survey of the Ngawha geothermal field, New Zealand, was undertaken in order to establish the level of preproduction seismicity and to test the usefulness of such surveys in geothermal exploration. The Ngawha geothermal field, in the far northwest of the North Island (Northland) is associated with a region of Quaternary basaltic volcanism. It is not a part of the much more extensive Taupo volcanic zone in the central North Island, site of the well‐known Wairakei geothermal field, among others. Although surface thermal activity at Ngawha is limited to a few relatively small hot springs, resistivity surveys have outlined a [Formula: see text] area of hot water at the 1-km depth level (Macdonald et al. , 1977). Test bores to that depth have encountered temperatures of up to 250 °C within Mesozoic graywacke. Overlying the graywacke is about 500 m of Cenozoic claystone and siltstone which forms an impermeable cap.
Marine navigation with the LaCoste and Romberg inertial platform
Authors: Valliant H. D.
Published: October 2002

The LaCoste and Romberg gravimeter platform constitutes a complete inertial navigation system and can provide navigational information for marine gravity surveys. Potential applications include: (1) Inertial input to an integrated navigation system using Kalman filtering techniques to utilize all available navigation data; (2) provision of a relatively low cost back‐up system to provide navigation continuity in the event of a failure in the primary navigation; and (3) primary navigation in regions not served by long‐range systems such as Loran C and beyond the range of short‐range systems.
North American Gravity and Magnetic Anomaly Workshops
Authors: Hinze W. J. , O’Hara N. W. , Reford M. S. , Tanner J. G.
Published: October 2002

The North American Gravity and Magnetic Anomaly Map Workshops, realizing the importance of regional gravity and magnetic anomalies to investigating the structure and composition of the earth, enthusiastically support the preparation of North American gravity and magnetic anomaly maps. Sufficient magnetic and gravity anomaly data are available over the North American continent, the Caribbean, and adjacent marine areas to produce geologically meaningful maps. These maps will be published within the decade at a scale of 1:5 million on the same map base being used by a variety of organizations to produce other geologic/geochemical/geophysical maps in cooperation with the Geological Society of America’s Centennial Map Series. The anomaly maps will be published in color with transparent overlays also available. The gravity anomaly map will be contoured at a 10 mgal interval using Bouguer anomalies onshore corrected wherever possible and necessary for terrain effects and free‐air anomalies offshore. Existing or soon to be completed magnetic and gravity anomaly maps of Canada, the U.S., and Mexico will provide the nuclei for preparing the North American maps. Programs for producing these maps in a timely manner are organized based upon a series of committees and the cooperation of agencies of the involved North American nations.
The Vibroseis system: A high‐frequency tool
Authors: Chapman Wm. L. , Brown G. L. , Fair D. W.
Published: October 2002

Exploration methods are extended to their limits as we continue the search for energy resources. Successful application of high‐frequency seismic method requires evaluating each element in the seismic acquisition system and ensuring that each part of the system contributes to the success of the method. This extends from seismic signal generation through data processing where good equipment performance and correct parameter selections are required. The Vibroseis® system depends upon the ability of vibrators to generate synchronous, repeatable sweeps over the frequency range of interest. To support our high‐frequency seismic efforts, Conoco, Inc., has developed and built a new high‐frequency vibrator. This paper includes some of the consideration used in building the vibrator, along with typical baseplate responses showing excellent drive levels to the design goal of 200 Hz. With an excellent source available, correct application is essential to assure retention of high‐frequency data. Recording offsets, array lengths, and array sampling must be selected for the sweep frequencies used. Also, approximate matching of the data acquisition system response to the spectral response of the earth reduces the dynamic range requirements for recording systems and subsequent data processing. Data are included showing the successful application of high‐frequency techniques to stratigraphic exploration problems.
The inverse problem of the direct current conductivity profile of a layered earth
Authors: Coen Shimon , Yu Michael Wang‐Ho
Published: October 2002

We present a direct (noniterative) inversion algorithm for the determination of the conductivity profile of a layered earth from the measurements of the apparent resistivity with the Schlumberger array. The necessary conditions for the existence of a one‐dimensional (1-D) continuous conductivity profile are determined, and the uniqueness of the solution is proved for complete and precise data. Examples are given in which the conductivity profile is determined from analytical data, incomplete and imprecise artificial data, and raw field data.
Dispersion patterns of the ground roll in eastern Saudi Arabia
Authors: Al‐Husseini Moujahed I. , Glover Jon B. , Barley Brian J.
Published: October 2002

Seismic surveys on land must be designed so that the source‐generated noise, such as ground roll, is preferentially attenuated before P‐wave signal amplification and recording. The correct specification of spatial and frequency filters requires prior knowledge of the noise properties in the area. We show that the strong Rayleigh wave component of source‐generated noise has a wavelength range which is predictable on a regional scale, using widespread P‐wave velocity measurements in shallow upholes. This predictive capability decreases the number of noise analyses required to map the boundaries between areas with different Rayleigh wave properties. The case history presented is for northeastern Saudi Arabia, an area of roughly [Formula: see text]. The data comprise 80 noise analyses and a data base of over 10,000 up‐hole measurements of P‐wave velocities, supplemented by maps of topography and geologic outcrops. Examples show that the frequency‐wavenumber transforms of time‐offset records can be interpreted in detail in terms of Rayleigh wave dispersion and air wave coupling, dictated by the elastic properties of the very shallow layers. P‐wave velocities, measured in shallow upholes at noise analysis sites, are used to form initial estimates of the corresponding shear‐wave velocities and subsequently refined by matching the observed and predicted dispersion curves. Even without this refinement process, the initial S‐wave velocities can be used to estimate Rayleigh wave velocities at frequencies which typify the top and bottom of current vibrator sweeps (10 and 80 Hz). These velocities are mapped for the area and used to determine the wavelength range of Rayleigh waves. An effort is also made to map regions where Rayleigh wave scattering from surface topography is likely to occur.
Linear inversion of body wave data—Part I: Velocity structure from traveltimes and ranges
Authors: Dorman LeRoy M. , Jacobson R. S.
Published: October 2002

In a laterally homogeneous medium, the traveltime (T) and distance (X) for a ray with horizontal slowness p are linearly related to the depth Z(v) at which the velocity v = 1/p occurs. In order to exploit this linearity, we must infer the inverse velocity p from the observations of X, T pairs. Uncertainty in the determination of p causes correlation between the X and T observations. This correlation can be eliminated by rotation of the data into a coordinate system in which the covariance matrix is diagonal. These independent coordinates are, except for a scaling factor, the well‐known intercept time [Formula: see text] and a new variable [Formula: see text] The derivatives of T and X with respect to a depth‐velocity model contain singularities and so do those for ζ. These singularities can be quelled by representing the model as a stack of layers, each of which has a constant velocity gradient. Depth is then obtained by integration of the gradients. The sharpness of the partial derivatives of ζ w.r.t. the layer gradients indicates that ζ contains information in a more concentrated form than does τ. This manifests itself in smaller error bounds on the solution when ζ observations are used to supplement τ data. In the determination of ζ(p) from X,T data, an uncertainty principle or tradeoff applies. The delta‐like nature of the zeta partial derivatives means that the uncertainty in ζ will be closely related to the solution uncertainty and that we should choose in the parameterization the ζ, p pair which minimizes the uncertainty in ζ. This will avoid degrading the ultimate depth resolution achievable while still in the parameterization stage. We have applied these methods to sea floor hydrophone and surface buoy data from the Bengal Fan, and, we derive a model whose gradient is [Formula: see text] at the surface reaching [Formula: see text] at 500 m and remaining constant to at least 5.5 km.
A composite model for the anisotropic elastic moduli of lean oil shale
Authors: Rundle John B. , Schuler Karl W.
Published: October 2002

A model to predict the anisotropic elastic moduli of lean oil shale is formulated. Deformation of a homogeneous ellipsoidal inclusion in a host matrix is used as the basis for computing the deformation of the composite. Both inclusions and the host rock are presumed to be separately isotropic. Anisotropy of the composite arises from the nonspherical shape of the kerogen inclusions. Six parameters are needed to quantify the model fully: two elastic moduli for the host rock, two for the inclusions, the kerogen content, and the inclusion aspect ratio. The model is compared to a set of statically measured elastic moduli. Good agreement with lean oil shale data was found. However, some systematic differences appear in comparison with moduli measured ultrasonically.
On: “Long‐wave elastic anisotropy in transversely isotropic media” by J. G. Berryman, and “Seismic velocities in transversely isotropic media” by F. K. Levin (GEOPHYSICS, v. 44, May 1979, p. 896–917 and p. 918–936, respectively).
Authors: Lyakhovitskiy Felix M.
Published: October 2002

Berryman and Levin made an assumption about constancy or limited variations of Poisson’s ratio in the thin layers, in their analyses of elastic anisotropy in thin‐layered media. Berryman states (p. 913): “Rare cases can occur with large variations in Poisson’s ratio.” However, on p. 911 Berryman does point out (with reference to Benzing) that range of variations of the parameter γ = VS/VP from 0.45 to 0.65 is typical of rocks. That corresponds to a range of variations of Poisson’s ratio of 0.373 to 0.134 (i.e., almost three times as much).
Analysis of electrical conductivity imaging
Authors: Dines K. A. , Lytle R. J.
Published: October 2002

We investigate the feasibility of imaging the electrical conductivity in a cross‐section of an object (such as a core sample) by numerical inversion of low‐frequency, electromagnetic (EM) boundary data. Current flow is assumed to be confined to the cross‐section, which is modeled as a network of resistors. The network serves as a discrete approximation of the distributed‐parameter system that is described mathematically by Maxwell’s equations for steady current flow in a nonhomogeneous medium. A complete set of linearly independent voltage vectors is applied to the peripheral nodes, and the resulting node currents serve as the measured data for estimating the internal conductivity pattern (image). We generate estimates of this conductivity image by using an iterative process on network equations that are linearized in the unknown conductance variables. The mathematical feasibility of this approach is demonstrated by computer simulation studies using data generated from the network model. Reconstructed images are presented for sample conductance patterns under both ideal and noisy data conditions. An error analysis is performed to relate data noise to image‐estimation error.
Transient electromagnetic response of a polarizable ground
Authors: Lee T.
Published: October 2002

When a uniform ground has a conductivity which may be described by a Cole‐Cole relaxation model with a positive time constant, then the transient response of such a ground will show evidence of induced polarization (IP) effects. The IP effects cause the transient initially to decay quite rapidly and to reverse polarity. After this reversal the transient decays much more slowly, the decay at this stage being about the same rate as a nonpolarizable ground.
Maximum entropy spectral decomposition of a seismogram into its minimum entropy component plus noise
Authors: Treitel Sven , Robinson Enders A.
Published: October 2002

We consider an N‐layered elastic medium which is perfectly insulated from its embedding space. Each layer has unit two‐way vertical traveltime, and a coincident source‐receiver pair is located just below the top interface. If the insulated medium is excited in the remote past, the power spectrum of the resulting impulsive normal‐incidence synthetic seismogram is a pure line spectrum; because no random elements exist in the system at the time of measurement, this spectrum is a minimum entropy spectrum. If we add white noise to the seismogram, the power spectrum becomes a maximum entropy spectrum. The maximum entropy spectrum can thus be decomposed into the sum of a minimum entropy spectrum plus white noise; this spectral decomposition is due to Pisarenko (1973). If the insulated medium is excited at time t = 0, the resulting synthetic seismogram differs rather remarkably from the seismogram obtained for excitation in the remote past.
On: “Frequency‐independent background internal friction in heterogeneous solids” by Baxter H. Armstrong (GEOPHYSICS, June 1980, p. 1042–1054).
Authors: Korvin Gábor
Published: October 2002

In his recent paper Dr. Armstrong proposes a novel approach based on considerations of thermal conduction and thermoelastic dissipation to explain the observed nearly constant Q behavior toward low frequencies in randomly heterogeneous solids. I feel, however, the fluctuation coefficient R defined by his equation (22) does have an inherent frequency dependence introduced through the [Formula: see text] factors so that the attenuation coefficient A might be a more complicated function of frequency than suggested by equation (24).
Inversion of gamma‐ray data for element abundances
Authors: Crossley D. J. , Reid A. B.
Published: October 2002

The conversion of airborne spectrometer data to abundances of K, U, and Th on the ground poses several problems concerning gamma‐ray interpretation. We show that the solution of the associated matrix equation Ax = c for x (the unknown abundances), where the elements of A form the empirical spectra (or calibration constants), is very dependent upon the selection of spectrometer channels or windows included in the count vector c. Assuming the matrix A is known for a particular source and detector system (here provided by the South African Geological Survey), the matrix inversion shows (1) cosmic background abundance apparently can vary within the time of a few seconds along a flight line, (2) a full‐spectrum multichannel solution is necessary to solve accurately for x, and (3) some hitherto largely ignored low energy peaks (0.94 MeV for Th and 1.12 MeV for U) should be seriously considered for the most accurate abundance estimation with a small number of channels.
Asymptotic expansions for transient electromagnetic fields
Authors: Lee T.
Published: October 2002

Asymptotic expansions may be derived for transient electromagnetic (EM) fields. The expansions are valid when [Formula: see text] is less than about 0.1. Here l, σ, [Formula: see text], and t are the respective lengths, conductivities, permeabilities of free space and time. Cases for which asymptotic expansions are presented include (1) layered grounds, (2) axisymmetric structure, and (3) two‐dimensional (2-D) structures. In all cases the transient voltage eventually approaches that of the host medium alone, the ratio of anomalous response to the half‐space response being proportional to [Formula: see text]. Here v is equal to 0.5 for layered structures and 1.0 for 2-D or 3-D structures.
The response of perturbation and induction arrows to a three‐dimensional buried anomaly
Authors: Lam H. L. , Jones F. W. , Hibbs R. D.
Published: October 2002

A numerical model is employed to calculate theoretical perturbation and induction arrows for a spatially confined three‐dimensional (3-D) conductivity anomaly located at various depths below the surface of the earth for two source periods. The results indicate that the magnitudes of the induction arrow decrease as the anomaly depth increases and the arrows point toward the conductive anomaly even at great depth below the surface. It is found that the extent of the anomalous induced currents depends upon the depth of the inhomogeneity and on the source field period. The ([Formula: see text]) perturbation arrow can be used to outline the spatial extent of the anomaly, and the ([Formula: see text]) quadrature‐phase arrows better indicate the spatial extent than the in‐phase arrows if the source period is not an optimum one.
COCORP: Oklahoma Area, Part II
Authors: Kaufman S.
Published: October 2002

The Consortium for Continental Reflection Profiling (COCORP) announces the availability of the data package and tapes for the Oklahoma area, part II, for the cost of reproduction and shipping. These data were obtained and processed by COCORP whose operation is part of the U.S. Geodynamics Project sponsored by the National Academy of Sciences and funded by the National Science Foundation. The executive group of the consortium consists of members from Cornell University, Dartmouth College, Princeton University, Rice University, and the University of Wisconsin. Cornell University is the operating institution.
The velocity inversion problem—Present status, new directions
Authors: Bleistein Norman , Cohen Jack K.
Published: October 2002

The research program in seismic exploration in progress in the Mathematics Dept. of the Univ. of Denver is described. The mathematical formulations employed by this group are outlined and results of computer implementation are depicted. Ongoing research is also presented. The main method we have developed is identified here by the term “velocity inversion.” This is a method based upon perturbation theory, leading to a linear integral equation for the variation in velocity from a fixed reference value. Applied to high‐frequency data, the method yields a map of the interfaces in the interior of the earth, as well as estimates of reflection strength at those interfaces. A new non‐perturbation approach to the velocity inversion problem is also presented. This is a high‐frequency method which accounts for two major nonlinear effects, namely, transmission losses and refraction. The method also has some similarity to wave‐equation migration in that a wave equation is derived for the ensemble of backscattered signals, scaled by time, and with initial data having their support on the reflecting surfaces and in known proportion to the reflection strength.
An implicit finite‐difference formulation of the elastic wave equation
Authors: Emerman Steven H. , Schmidt W. , Stephen R. A.
Published: October 2002

The problem with existing finite‐difference formulations of the elastic wave equation is that they have a limited stability range, and the necessity of taking small time steps can result in excessively high computation costs. It is possible to formulate a finite‐difference scheme which is stable for arbitrarily large time steps. However, the solutions obtained by the unconditionally stable scheme are unacceptably inaccurate for time steps outside the stability range of finite‐difference schemes currently in use.
Sign‐bit amplitude recovery with applications to seismic data
Authors: O’Brien J. T. , Kamp W. P. , Hoover G. M.
Published: October 2002

Sign‐bit digital recording means that only the sign of the analog signal is recorded with one bit. In conventional seismic recording, 16 to 20 binary bits are acquired per sample point. The economic advantages of sign‐bit acquisition are immediately obvious. Complete amplitude recovery, comparable to full‐gain recording, can be achieved by correct application of sign‐bit techniques. We describe the amplitude recovery process in a semiintuitive manner to promote the understanding necessary for proper application of the technique. The dynamic range requirements in seismic applications are discussed. Sign‐bit digitization is a completely viable technique for recording seismic data, provided that two conditions are fulfilled. First, in real time, the coherent‐signal‐to‐randomnoise‐ratio must be ⩽1.0. Second, the data must be recorded with sufficient redundancy. Redundancy is achieved by source repetition, sweep correlation, and high‐fold common‐depth‐point stacking, usually in combination. Failure to abide by these two restrictions results in (1) incomplete amplitude recovery, i.e., clipped data, and (2) insufficient dynamic range in the recovered signal. We derive the requirement that the signal‐to‐noise ratio be less than one; we also discuss the consequences of violating that requirement, namely clipping, at various points in the processing sequence. The amount of information lost is proportional to the degree of clipping; a small amount can be tolerated. Calculated expectation values show that (subject to the requirement that the signal‐to‐noise ratio be less than 1.0) an unbiased estimator can be chosen. The variance of these estimators is approximately the same as that for full‐gain seismic techniques. With sufficient redundancy, the variance can be made as small as necessary to achieve the required dynamic range. With proper attention to these findings, sign‐bit digitized data are found to be a totally viable tool.
Estimation of formation temperature and thermal property from dissipation of heat generated by drilling
Authors: Lee Tien‐Chang
Published: October 2002

Dissipation of heat generated in the process of drilling depends upon the physical properties and condition of the rock and drilling mud, drilling rate and duration, mud circulation rate, casing, and depth of penetration. By treating the initial condition as an instantaneous temperature drop near the bottom of a drill hole, an analytical solution is obtained to show drilling‐induced heat dissipation. Two graphical methods are presented and illustrated with examples to determine, from transient temperature measurements, the equilibrium formation temperature as well as insitu thermal conductivity ratio and diffusivity of rock and drilling mud. One method requires the measurement of initial mud temperature [Formula: see text], while the other method requires knowing the thermal diffusivity of drilling mud [Formula: see text]. Either [Formula: see text] or [Formula: see text] can also be estimated with the trial‐and‐error procedure. A finite‐element analysis is further developed to handle thermal disturbance for the case where the temperature drop is not necessarily instantaneous; hence the solution is applicable at any depth in a drill hole.
Seismic parameters for media with elliptical velocity dependencies
Authors: Byun Bok S.
Published: October 2002

The concept of wavefront curvature has been discussed extensively in the literature to relate surface seismic reflection data to subsurface geologic parameters. Developed initially for the case of homogeneous, isotropic, but arbitrarily dipping layered media, this technique has been extended to the inhomogeneous case. Now with the advent of new seismic techniques, such as vertical seismic profiling, three‐dimensional seismic methods, and shear‐wave techniques, the problem of velocity anisotropy is of growing concern to exploration seismologists. The essence of this paper is to extend the method of wavefront curvature to the “elliptically anisotropic” case in which the ray velocity varies elliptically with the direction of propagation. A fundamental feature of wave propagation in the anisotropic medium is that the direction of propagation of the disturbance (or the ray velocity direction) generally differs from that of the wavefront (or the phase velocity direction). Based on the assumption of two‐dimensional dipping layers in which velocity is “elliptically dependent” on the angle of propagation, relationships are developed between important seismic properties and model parameters. First, a relationship between the incident and refracted rays across the interface is expressed through the ray parameter. A geometrical divergence law is then developed relating the radii of the elliptical wave surfaces of the incident and refracted rays. A Dix‐type formula is finally derived which relates the normal moveout (NMO) velocity to the subsurface parameters. An example is shown to compare the radius of the wave surface and the NMO velocity for the elliptically anisotropic case with those for the equivalent isotropic case.
Common mode interference reduction in seismic recording
Authors: Smither Miles A. , Pater Arnold
Published: October 2002

In spite of the prevalence of high common mode rejection ratio (CMRR) input amplifiers, notch filters are routinely used in seismic recording operations to reduce common mode induced interference. An electrical model of the recording environment which predicts the degradation in system CMRR caused by cable imperfections such as imbalance and leakage is described in this paper. System CMRRs as low as 20 dB can be caused by poor quality cables. A new method of controlling common mode interference has been developed which has none of the disadvantages of notch filters. The method minimizes the correlation between the common mode and differential mode signals at the recording instrument. This process has no effect on the desired seismic signals, has minimal effect on the system noise, and typically results in a system CMRR in excess of 100 dB.
Regional thermal‐inertia mapping from an experimental satellite
Authors: Watson Kenneth
Published: October 2002

A new experimental satellite has provided, for the first time, thermal data that should be useful in reconnaissance geologic exploration. Thermal inertia, a property of geologic materials, can be mapped from these data by applying an algorithm that has been developed using a new thermal model. A simple registration procedure was used on a pair of day and night images of the Powder River basin, Wyoming, to illustrate the method. Preliminary assessment of these satellite data suggests that they will be of significant use for resource exploration when used in conjunction with other geologic, geophysical, and geochemical data.
Optimum second vertical derivatives in geologic mapping and mineral exploration
Authors: Gupta V. K. , Ramani N.
Published: October 2002

The second vertical derivative is often used in gravity interpretation to enhance localized near‐surface features. Since high‐frequency noise is amplified considerably in a true second derivative map, some smoothing is always necessary. One of the methods available to the interpreter is the optimum second derivative technique which utilizes Wiener theory to design filters from an analysis of the power spectrum to suit the degree of noise in the data. The power spectrum of the Bouguer gravity field obtained from over 5100 gravity stations covering an area of approximately [Formula: see text] in Archean greenstone belts of northern Ontario was computed. The radially averaged spectrum decreased monotonically with frequency and flattened at the high‐frequency end. The spectrum, separated into its signal and noise components, was used to design an optimum second vertical derivative filter which has a peak at 0.35 cycles/grid interval with low‐ and high‐frequency cut‐off at 0.12 and 0.44 cycles/grid intervals, respectively. The resultant second derivative map corresponds remarkably well with the known surface geology. In most of the mapped regions the zero contours coincide with the lithological boundaries; positive and negative anomalies match surface exposures of the mafic and felsic rock units, respectively. In the central part of the area which covers the Birch‐Uchi greenstone belt, where the geology has been well mapped, the second derivative map is quite successful in delineating the successive groups of mafic to felsic metavolcanic rocks that represent the product of cyclic volcanism. The distribution of the mineral deposits in the study area can be related to the positive or negative second derivative anomalies. For example, most of the known gold and silver mineralization occurring in mafic metavolcanics is associated with positive second derivative anomalies. Similarly, the polymetallic Zn‐Cu‐Ag deposits are mainly located in the negative second derivative anomalies caused by felsic metavolcanics. A properly designed second derivative map can thus be an important supplement to geologic mapping in the identification of lithological units, in the study of structure, and as an indirect tool in regional mineral exploration.
Interpretation of synthetic common‐depth‐point gathers for a single anisotropic layer
Authors: Crampin Stuart , Radovich Barbara J.
Published: October 2002

Analysis of synthetic traveltime gathers shows that anisotropy may have a large enough effect on P, SH, and SV propagation to alter significantly the interpretation of the subsurface below the anisotropic layers. Consequently, if anisotropy exists below a seismic line, it is important to estimate the anisotropic parameters correctly. We discuss the effects of anisotropy on seismic waves and present a method for estimating the elastic constants of a transversely isotropic layer from P and SH arrival‐time gathers. The technique may be extended to more general anisotropic symmetries by analyzing gathers from several azimuths. To illustrate the possible effect of anisotropy on exploration surveys, P, SH, and SV velocity variations are calculated for several types of anisotropic sedimentary fabrics. Alignments due to bedding, shale lithology, and dry parallel cracks may have similar velocity variations. Fabrics with other configurations of cracks may still possess overall transversely isotropic symmetry, but they have a wide range of angular velocity variations with different polarities and periodicities. Synthetic gather curves are generated for a range of models with an anisotropic layer over an isotropic substrate. They show departures from hyperbolas, and erroneous depth determinations, that depend upon the elastic constants of the anisotropic layer. The elastic constants of the anisotropic layers are estimated from the synthetic gather curves by means of approximate equations for the angular velocity variations, which are linear in the elastic constants. Formulas are developed which relate tangents to the gather curves directly in terms of the elastic constants. These are tested for single‐layer transversely isotropic models and allow the five elastic constants to be estimated by drawing three tangents to P and SH synthetic arrival‐time gathers in [Formula: see text] space. Comparisons of estimated with original elastic constants are good for a number of different types of transversely isotropic fabrics. Gathers are also calculated at two azimuths in an anisotropic layer with orthorhombic symmetry and are analyzed with some success.
Inversion of normal incidence seismograms
Authors: Bamberger A. , Chavent G. , Hemon Ch. , Lailly P.
Published: October 2002

The well‐known instability of Kunetz’s (1963) inversion algorithm can be explained by the progressive manner in which the calculations are done (descending from the surface) and by the fact that completely different impedances can yield indistinguishable synthetic seismograms. Those difficulties can be overcome by using an iterative algorithm for the inversion of the one‐dimensional (1-D) wave equation, together with a stabilizing constraint on the sums of the jumps of the desired impedance. For computational efficiency, the synthetic seismogram is computed by the method of characteristics, and the gradient of the error criterion is computed by optimal control techniques (adjoint state equation). The numerical results on simulated data confirm the expected stability of the algorithm in the presence of measurement noise (tests include noise levels of 50 percent). The inversion of two field sections demonstrates the practical feasibility of the method and the importance of taking into account all internal as well as external multiple reflections. Reflection coefficients obtained by this method show an excellent agreement with well‐log data in a case where standard estimation techniques [deconvolution of common‐depth‐point (CDP) stacked and normal‐moveout (NMO) correction section] failed.
Interpretative lessons from three‐dimensional modeling
Authors: Hilterman Fred J.
Published: October 2002

Three‐dimensional (3-D) seismic modeling has been accomplished by describing geologic surfaces with triangular plates and then computing the seismic response by Kirchhoff wave theory. The resulting time sections illustrate many interesting 3-D phenomena which are useful in interpreting geologic structures. Three‐dimensional resolution studies relate the concept of Fresnel zone reflection to seismic resolution. If high resolution is desired both horizontally and vertically, then not only is a dense field survey required, but also a detailed amplitude study. The dense seismic coverage is required to map the focal line of concave boundary edges, which are difficult to delineate with conventional seismic data. Additional studies on complex models, such as grabens and 3-D permeability traps, associate interpretational pitfalls to a wandering specular reflection path, that is, “side‐swipe.” In each geologic model, maximum resolution is obtained on a principal plane line (dip line). If a seismic dip line is not available, the necessity of doing 3-D migration is emphasized, even if it is a migration of the time map.
The encoded sweep technique for Vibroseis
Authors: Edelmann H. A. K. , Werner H.
Published: October 2002

In many areas correlation noise has become a serious problem because of the high dynamic range of more than 60 dB between the strong first arrivals and the weak reflection events arriving several seconds later. Several efforts have been made to reduce correlation noise either by tapering the sweep signals or by deconvolution. The effect of tapering is limited by the strong amplitude distortion of the reflected signals; deconvolution cannot cope with such a large dynamic range in the presence of noise. The sweep signal encoding technique using complementary codes was first proposed for Vibroseis® by Bernhardt (1977). The coding allows a complete correlation noise suppression after a predetermined time interval which is completely independent of the amplitude characteristic of the subsurface and the recording arrangement. Binary and quaternary codes have been investigated. Moreover, the quaternary encoded sweep allows the advantages of the encoding technique to be combined with the preferences of the Combisweep technique in order further to reduce correlation noise in the ± τ range (τ = code member length). The encoded sweep technique has been applied in several areas. The technique effected improvements in those areas where reflections with long traveltime had to be recorded. ®Trademark of Conoco Inc.
Refined finite‐difference simulations using local integral forms: Application to telluric fields in two dimensions
Authors: Hermance John F.
Published: October 2002

This paper describes a new finite‐difference form for simulating the behavior of telluric fields near electrical inhomogeneities. The technique involves a local integration of the electric current density crossing a closed surface surrounding a mesh node. To illustrate the concept, a two‐dimensional (2-D) model is considered, but it is readily possible to generalize to three dimensions. The resulting expressions, which are accurate to second degree everywhere, have the form of nine‐point finite‐difference operators, but they have a higher precision than those derived from the usual differential forms which result in five‐point operators. In particular, the new form accounts for cross‐derivative [Formula: see text] effects in the region about each node. Including this term can provide significant improvements in accuracy near sharp, localized discontinuities, where the anomalous field decays rapidly (as 1/r or [Formula: see text]) with distance. An analytical solution is compared to finite‐difference calculations using both the conventional five‐point differential form and the new nine‐point integral form developed here. The results suggest that, in some cases, one might expect at least a factor of three improvement when using the nine‐point operator instead of the five‐point operator. This is particularly true in the vicinity of localized structures where the curvilinear character of the distorted field is most pronounced and one would expect the cross‐derivative term to be large.
Gravity measurements in an airplane using state‐of‐the‐art navigation and altimetry
Authors: LaCoste Lucien , Ford James , Bowles Robert , Archer Keith
Published: October 2002

In 1976 the U. S. Naval Oceanographic Office made experimental gravity measurements over the Atlantic in an airplane using a LaCoste and Romberg shipboard gravity meter, a Honeywell electrostatic gyro inertial system, a Rosemont pressure port altimeter, a Honeywell radar altimeter, Loran C and other electronic navigational aids. Preliminary results were reported at the 47th Annual International SEG Meeting in Calgary, Canada, in 1977. These preliminary results were compared with sea gravity data furnished by the Naval Oceanographic Office and were found to be in general agreement. However, there were some unexplained systematic errors of about 15 mgal and the airplane gravity profiles were considerably more noisy than helicopter gravity profiles reported by William Gumert (1977, personal communication). After the paper was given, we found that corrections for Schuler oscillations in the inertial system significantly reduced the systematic errors. We also found that by making full use of a half‐second sampling rate of the radar altimeter, we could make meaningful vertical acceleration corrections relative to sea level as well as relative to an atmospheric pressure surface. A comparison of the two corrections showed that variations in the isobaric surfaces were the main cause of the noise in the airplane gravity profiles. It also became apparent that the noise could be reduced by flying slower or making successive flights at different speeds.
Quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces
Authors: Ursin Bjørn
Published: October 2002

A quadratic approximation for the square of the traveltime from a source region to a receiver region is given for a three‐dimensional (3-D) medium consisting of inhomogeneous layers with curved interfaces. The square of the traveltime, being a function of source and receiver coordinates, is developed in a Taylor series around a reference source and receiver point. The relationships of the traveltime parameters to the ray parameters and the wavefront curvature matrices are shown. Using midpoint, half‐offset coordinates gives a simplified traveltime function compared to using source‐receiver coordinates only in the case that the reference source point and the reference receiver point coincide (zero‐offset approximation). For a medium consisting of homogeneous layers with plane dipping interfaces, the traveltime approximation is further simplified. The derived traveltime approximation is shown to be exact for a reflection from a plane dipping interface in a homogeneous medium. Explicit expressions for the traveltime parameters in terms of the layer parameters are derived for a horizontally layered medium. The traveltime errors of two different approximations are compared for a given layered model in a numerical example.
Time‐variable dispersion processing through the use of “phased” sinc functions
Authors: Robinson John C.
Published: October 2002

A technique for the continuous representation of dispersion in seismic data was introduced in Robinson (1979). The basic dispersion relation is that derived by Futterman (1962) for an absorption model which is linear with frequency, the so‐called “constant Q model.” The technique allows one either to remove from, or introduce into, seismic data the effects of dispersion at a constant rate related to some specified absorption quality factor Q.