bluuebunny/crossref_metadata_2025 huggingface dataset:
The gradient tensor of potential field anomalies: Some implications on data collection and data processing of maps
Authors: Pedersen L. B. , Rasmussen T. M.
Published: October 2002

The full gradient tensor is presently not measured routinely onboard airplanes or on land. This paper describes some improvements that can be made in strategies of data collection and in processing of potential field maps if such tensor measurements were available. We suggest that, in addition to producing for example standard total field anomaly maps, the invariants of the tensor be mapped. Strikes of magnetic or gravimetric structures may be determined from minimizing the power in the first row and column of the tensor. Invariants can be looked upon as nonlinear filters enhancing sources with big volumes. Their lateral resolution is superior to that of the field proper and, for a given resolution, the flight altitude and separation between flight lines can be increased compared with the standard mode of operation. In airborne surveys the distance between flight lines is normally much larger than the height above the ground. This may introduce severe aliasing effects in the direction perpendicular to the flight lines. By increasing the flight altitude, aliasing effects are reduced at the expense of lateral resolution which, however, may be improved by mapping the tensor invariants in addition to the magnetic field. The estimated gradient tensor from total field magnetic data over the Siljan impact region shows that the magnetic properties of the area are very nonuniform even from a height of 430 m above the topography. The nonlinear filters discriminate major anomalies into separate units.
Limitations of the long‐wavelength components of the North American magnetic anomaly map
Authors: Arkani‐Hamed J. , Hinze W. J.
Published: October 2002

The magnetic anomaly map of North America and its related data set provide the opportunity not only to view the obvious short‐wavelength anomalies (<300 km) in a continental context, but to isolate and analyze the longer wavelength anomalies. However, care must be used in analyzing the longer wavelengths because of the effects of noncrustal sources on these anomalies. Inversion of the anomalies into lateral variations of crustal magnetization suggests that the long‐wavelength anomalies (>2600 km) are strongly affected by core field components that have not been completely removed from the North American data set. Furthermore, the piecewise matching of the magnetic anomalies of adjacent survey areas in the map compilation has contaminated the intermediate wavelength anomalies (300–2600 km).
Occam’s inversion to generate smooth, two‐dimensional models from magnetotelluric data
Authors: deGroot‐Hedlin C. , Constable S.
Published: October 2002

Magnetotelluric (MT) data are inverted for smooth 2-D models using an extension of the existing 1-D algorithm, Occam’s inversion. Since an MT data set consists of a finite number of imprecise data, an infinity of solutions to the inverse problem exists. Fitting field or synthetic electromagnetic data as closely as possible results in theoretical models with a maximum amount of roughness, or structure. However, by relaxing the misfit criterion only a small amount, models which are maximally smooth may be generated. Smooth models are less likely to result in overinterpretation of the data and reflect the true resolving power of the MT method. The models are composed of a large number of rectangular prisms, each having a constant conductivity. [Formula: see text] information, in the form of boundary locations only or both boundary locations and conductivity, may be included, providing a powerful tool for improving the resolving power of the data. Joint inversion of TE and TM synthetic data generated from known models allows comparison of smooth models with the true structure. In most cases, smoothed versions of the true structure may be recovered in 12–16 iterations. However, resistive features with a size comparable to depth of burial are poorly resolved. Real MT data present problems of non‐Gaussian data errors, the breakdown of the two‐dimensionality assumption and the large number of data in broadband soundings; nevertheless, real data can be inverted using the algorithm.
Analysis of gravity anomalies of sedimentary basins by an asymmetrical trapezoidal model with quadratic density function
Authors: Rao D. Bhaskara
Published: October 2002

The decrease of density contrast with depth in many sedimentary basins can be approximated by a quadratic function. The interpretation of gravity anomalies over sedimentary strata can be more realistic if variable density contrasts, rather than constant density contrasts, are assumed. I derive the equation for the gravity anomaly of an asymmetrical trapezoidal model, assuming a quadratic density function, and I develop methods of interpretation, using the Marquardt algorithm. While interpreting a synthetic anomaly profile, the convergence of the algorithm is shown by plotting the values of the objective function, damping parameter, and various parameters of the model with respect to iteration number; the results are superior to those obtained when using constant density contrasts. In addition, I apply the method in the interpretation of gravity anomalies over the San Jacinto graben and the lower Godavari basin.
Automated interpolation of two‐dimensional seismic grids into three‐dimensional data volume
Authors: Kao Jason Chin‐Sen , Schneider William A. , Whitman Walter W.
Published: October 2002

This paper develops an interpolation algorithm for creating three‐dimensional (3-D) seismic data volumes from conventional two‐dimensional (2-D) seismic grids. The creation of a 3-D data volume permits the use of a more accurate 3-D migration process and a better interpretation of the broad geologic features of a prospect area than does applying conventional techniques to 2-D data. A seismic surveying area is divided into a number of polygons by the input 2-D seismic profiles. The interpolation procedure is performed in each polyhedral cylinder, whose cylindrical axis is time and cross‐section is a polygon. The method is local in the time‐space domain, while it is data‐adaptive in theory and requires no prior knowledge of the area. The procedure has two stages: (1) The first stage estimates the interior dips from boundary dip values based on an inverse distance weighting (IDW) method. (2) Based on the estimated interior dips, the second stage extrapolates boundary‐reflection data into the interior of a 3-D volume, using a finite‐difference approach to solve a partial differential equation. Advantages of the method include its accuracy, stability, efficiency, flexibility, and ease of implementation on a digital computer and array processor system. This technique is applied to an example of 2-D profiles which are extracted from a real 3-D marine data volume from the Gulf of Mexico. By comparing with the original 3-D data volume in the example, the reconstructed 3-D data volume suggests the interpolation method can faithfully image the general features of the 3-D structure from the 2-D profiles.
Temperature dependence of the electrical resistivity of water‐saturated rocks
Authors: Llera F. J. , Sato M. , Nakatsuka K. , Yokoyama H.
Published: October 2002

The electrical resistivities of several dacitic tuffs, sandstone, andesite, granite, and crystalline limestone samples, saturated with a 0.001 M aqueous solution of KC𝓁;, were measured in the range from room temperature to 250°C. The experiments were made using a cell technique with platinum electrodes. Of particular interest are the data collected at temperatures above 200°C under high pressure, a region scarcely documented in the literature. Basically the samples used in the present study show a quasi‐exponential decrease of resistivity with temperature up to 200°C. The same temperature dependence is found for the resistivity of the saturating solution, thus confirming that conduction in water‐saturated rocks is essentially electrolytic. At temperatures above 200°C, some specimens of highly porous dacitic tuff still closely follow the saturating solution in the pattern of resistivity variation with temperature, exhibiting a minimum around 220°C; however, the behavior of low‐porosity crystalline rocks (notably granite) where a relatively abrupt decrease of resistivity is observed above 50°C, departs from that of the saturating solution. Hysteresis phenomena are more or less observed in most rock samples; i.e., the resistivity after one complete thermal cycle is systematically lower than its initial value. This experimental evidence points out that mechanisms different from water characteristics, such as growth of microcracks or chemical reactions, contribute to electrical conduction at high temperature. We point out the electrical signature of the thermally induced growth of microcracks (thermal cracking) in welded tuff and granite and suggest the possibility of using electrical measurements to monitor an extension of reservoir fractures in hot dry rock.
Effects of fluid viscosity on shear‐wave attenuation in saturated sandstones
Authors: Vo‐Thanh D.
Published: October 2002

Measurements of shear wave velocity and attenuation as a function of temperature were made in the kilohertz frequency range in sandstones saturated with various liquids. For sandstones partially saturated with glycerol, two attenuation peaks are observed between −80°C and 100°C; they are attributed to viscous shear relaxation and squirt flow. For fully water‐saturated Berea sandstone, the attenuation decreases as the crack density increases. The displacement of the squirt peak, caused by the increase of the central aspect ratio of cracks, is at the origin of this decrease. A simple viscoelastic model, based on the model of O’Connell and Budiansky using a Cole‐Cole distribution of cracks, is proposed for calculation of the shear modulus of fluid‐saturated rocks. This model interprets the experimental data satisfactorily. The data suggest that the shear attenuation and velocity are controlled by the distribution of crack aspect ratios.
Implicit static corrections in prestack migration of common‐source data
Authors: McMechan G. A. , Chen H. W.
Published: October 2002

Static effects due to surface topography and near‐surface velocity variations may be accurately compensated for, in an implicit way, during prestack reverse‐time migration of common‐source gathers, obviating the need for explicit static corrections. Receiver statics are incorporated by extrapolating the observed data from the actual recorder positions; source statics are incorporated by computing the excitation‐time imaging conditions from the actual source positions.
Reflection from a dipping plane—Transversely isotropic solid
Authors: Levin Franklyn K.
Published: October 2002

CMP stacking velocities for a P‐wave reflection from a dipping plane underlying a transversely isotropic solid are, after correction by the cosine of the dip angle, nearly independent of the dip angle if the symmetry axis of the solid is perpendicular to the reflector. If the symmetry axis is perpendicular to the surface, stacking velocities vary, after correction with the cosine of the dip angle, and predicting the amount and dependence on dip angle requires numerical investigation for each solid, since the stacking velocities may increase, decrease, or go through an extremum as the dip increases. The exact behavior depends on the elastic constants of the solid.
Traveltime inversion using transmitted waves of offset VSP data
Authors: Lee Myung W.
Published: October 2002

Estimation of layer parameters such as interval velocity, reflector depth, and dip can be formulated as a generalized linear inverse problem using observed arrival times. Based on a 2-D earth model, a computationally efficient and accurate formula is derived for traveltime inversion. This inversion method is applied to offset vertical seismic profile (VSP) data for estimating layer parameters using only transmitted first‐arrival times. As opposed to a layer‐stripping method, this method estimates all layer parameters simultaneously, thus reducing the cumulative error resulting from the errors in the upper layers. This investigation indicates (1) at least two source locations are required to estimate layer parameters properly, and (2) accurate arrival times are essential for computing the dip of a layer reliably. Bulk time shifts, such as static shifts, do not affect the parameter estimation significantly if the amount of shift is not too large. The result of real and modeled VSP data inversions indicates that traveltime inversion using transmitted first‐arrival times from at least two source locations is a viable method for estimating interval velocities, reflector depths, and reflector dips.
The response of an induction dipmeter and standard induction tools to dipping beds
Authors: Gianzero Stan , Su Shey‐Min
Published: October 2002

This theoretical investigation presents the responses in dipping beds of an induction dipmeter and standard induction tools, neglecting the influence of the borehole and invaded zones as well as the mandrel and coil size. The analysis is sufficiently general to determine response characteristics of an induction coil arbitrarily oriented in an arbitrary number of beds. In an induction dipmeter log (IDL) the most useful information is obtained from the out‐of‐phase voltage induced in the receiver coils when they are orthogonally oriented to the transmitter coils. A simple algorithm is developed to convert the crosscoupling signals into the apparent dip and strike information. The agreement between the actual and apparent values is nearly perfect for small transmitter‐to‐receiver spacings, i.e., less than 10 cm. The theoretical results for standard induction tools were consistent with prior work indicating the influence of dip is strongly dependent on the shoulder effect of the device in question. Consequently, dipping beds have less influence on the standard ILm because its shoulder effect is less than the standard ILd. These conclusions are supported by numerous simulations consistent with conditions encountered in the field. Finally, a simple no‐skin‐effect theory is developed for the case of a single dipping interface separating two infinitely thick beds. The results with this approach agree with the exact theory in resistive formations. This simplified theory is a generalization of Doll’s geometrical factor theory.
Differential compaction of Winnipegosis reefs: A seismic perspective
Authors: Anderson N. L. , Franseen E. K.
Published: October 2002

Winnipegosis Formation reefs in southern Saskatchewan are typically encased in the thick, apparently incompressible salts of the Prairie Evaporite. These reefs are characterized by raised rims and reverse drape along the top of the salt. Both features, clearly visible on seismic data, are primarily due to postdepositional compaction. The rims developed principally as a result of differential compaction within the different reef environments; the structural low at the Prairie Evaporite level is attributed to differential compaction between the reef and the encasing salt. If these salts are effectively incompressible, the rim and lagoonal facies are estimated to have been compacted by at least 30 and 44 percent, respectively. This paper illustrates the usefulness of seismic data to separate postdepositional compaction features from primary features to determine the primary morphology of a reef better and to determine the relative amounts of postdepositional compaction within the different reef environments. The degree to which the reef rim and interior areas were compacted can be estimated based on interpretation of the example seismic line. The methods and results of this paper allow for better definition of prime target areas for potential hydrocarbon reservoirs within the reef proper.
Nonlinear one‐dimensional seismic waveform inversion using simulated annealing
Authors: Sen Mrinal K. , Stoffa Paul L.
Published: October 2002

The seismic inverse problem involves finding a model m that either minimizes the error energy between the data and theoretical seismograms or maximizes the cross‐correlation between the synthetics and the observations. We are, however, faced with two problems: (1) the model space is very large, typically of the order of [Formula: see text]; and, (2) the error energy function is multimodal. Existing calculus‐based methods are local in scope and easily get trapped in local minima of the energy function. Other methods such as “simulated annealing” and “genetic algorithms” can be applied to such global optimization problems and they do not depend on the starting model. Both of these methods bear analogy to natural systems and are robust in nature. For example, simulated annealing is the analog to a physical process in which a solid in a “heat bath” is heated by increasing the temperature, followed by slow cooling until it reaches the global minimum energy state where it forms a crystal. To use simulated annealing efficiently for 1-D seismic waveform inversion, we require a modeling method that rapidly performs the forward modeling calculation and a cooling schedule that will enable us to find the global minimum of the energy function rapidly. With the advent of vector computers, the reflectivity method has proved successful and the time of the calculation can be reduced substantially if only plane‐wave seismograms are required. Thus, the principal problem with simulated annealing is to find the critical temperature, i.e., the temperature at which crystallization occurs. By initiating the simulated annealing process with different starting temperatures for a fixed number of iterations with a very slow cooling, we noticed that by starting very near but just above the critical temperature, we reach very close to the global minimum energy state very rapidly. We have applied this technique successfully to band‐limited synthetic data in the presence of random noise. In most cases we find that we are able to obtain very good solutions using only a few plane wave seismograms.
Refraction statics in the wavenumber domain
Authors: Zanzi L. , Carlini A.
Published: October 2002

A new method for refraction statics reduces the computational time without reducing accuracy. The first arrivals, common‐offset organized, form the data space. The method involves Fourier transforming any common‐offset data vector with respect to the common mid‐point. As a result, the data are decomposed in a number of subspaces, associated with the wavenumbers, which can be independently inverted to obtain any wavelength of the near‐surface model. The main advantage of the subspace decomposition is a remarkable reduction of the computation time. It also helps us to derive the following conclusion about the ill conditioning of the inverse problem: the uncertainty in estimating refractor velocity is proportional to the wavenumber, whereas estimation of refractor depth is practically unaffected by ill conditioning on the whole spectrum. To reduce the null space of the problem, the solution is further constrained by assuming, for any station, the local symmetry of the weathering within the range of half the critical distance. Final local corrections, applied to the resulting depths and velocities, may improve the accuracy for complex interface geometries. The effects of noisy data, i.e., mispicks and events roughly picked, are also analyzed with respect to the wavelength. This leads to the main conclusion that noise mostly affects the short wavelengths of the velocity. An upgrade of the basic method allows vertical gradients of the velocity to be accounted for. Experimental results validate the theory and prove that good quality and solution robustness can be achieved with this method while computing time is reduced.
Frequency‐wavenumber migration in laterally heterogeneous media
Authors: Wenzel F.
Published: October 2002

In a recent paper, Stoffa et al. (1990) presented a split‐step Fourier migration method. It takes laterally varying migration velocities into account by splitting the reference slowness into an average slowness, constant within the migration interval, and a perturbation term which accounts for the lateral variations. The method works accurately only if the lateral slowness variations are smooth and angles of propagation are near‐vertical. The restriction to steep propagation angles stems from the fact that the wavefield is accurately propagated with respect to the reference slowness but a five‐degree approximation is used to accommodate the lateral variations. This note presents a theory that avoids the five‐degree assumption and thus generalizes the split‐step algorithm.
Stable explicit depth extrapolation of seismic wavefields
Authors: Hale Dave
Published: October 2002

Stability has traditionally been one of the most compelling advantages of implicit methods for seismic wavefield extrapolation. The common 45-degree, finite‐difference migration algorithm, for example, is based on an implicit wavefield extrapolation that is guaranteed to be stable. Specifically, wavefield energy will not grow exponentially with depth as the wavefield is extrapolated downwards into the subsurface. Explicit methods, in contrast, tend to be unstable. Without special care in their implementation, explicit extrapolation methods cause wavefield energy to grow exponentially with depth, contrary to physical expectations. The Taylor series method may be used to design finite‐length, explicit, extrapolation filters. In the usual Taylor series method, N coefficients of a finite‐length filter are chosen to match N terms in a truncated Taylor series approximation of the desired filter’s Fourier transform. Unfortunately, this method yields unstable extrapolation filters. However, a simple modification of the Taylor series method yields extrapolators that are stable. The accuracy of stable explicit extrapolators is determined by their length—longer extrapolators yield accurate extrapolation for a wider range of propagation angles than do shorter filters. Because a very long extrapolator is required to extrapolate waves propagating at angles approaching 90 degrees, stable explicit extrapolators may be less efficient than implicit extrapolators for high propagation angles. For more modest propagation angles of 50 degrees of less, stable explicit extrapolators are likely to be more efficient than current implicit extrapolators. Furthermore, unlike implicit extrapolators, stable explicit extrapolators naturally attenuate waves propagating at high angles for which the extrapolators are inaccurate.
Four shallow‐depth, shear‐wave feasibility studies
Authors: Hasbrouck W. P.
Published: October 2002

Studies using a hammer‐impact source were made to evaluate the feasibility of using shallow‐depth, seismic shear‐wave methods to (1) detect earth fissures, (2) map an aguiclude, (3) locate a bedrock channel, and (4) study the fault and fracture system within a highly fractured welded tuff. For detecting earth fissures, a V/V (vertical‐impact, vertical‐geophone—recording both P-waves and vertically polarized shear waves, SV), 6-m common‐offset procedure was used; for mapping the aquiclude, an R/R (radial‐impact, radial‐geophone—recording predominantly SV), unbalanced‐split‐spread procedure; and for the bedrock channel search, a wide‐angle, T/T (transverse‐impact, transverse‐geophone—recording horizontally polarized shear waves, SH) reflection procedure. The principal result of these investigations is that it is technically feasible through use of shear‐wave methods to obtain reasonable solutions to the first three problems. For the tuff study, wave tests showed phase velocity differences between R/R and T/T recordings indicating shear‐wave splitting, and revealed a fault between blocks of seemingly similar lithology.
A microgal approximation for the Bullard B—earth’s curvature—gravity correction
Authors: Whitman Walter W.
Published: October 2002

An approximation of the Bullard B—earth’s curvature—gravity correction is expressed in terms of fractions of the standard Bouguer slab terrain correction. The Bullard B correction is appropriate for either high‐resolution surveys or for rugged terrain such as the Rocky Mountains, where the correction can be as much as 1.5 mGal. The approximation has three terms, each separated from the others by roughly an order of magnitude, indicating a substantial segregation of physical effects. An analysis indicates that physically the three correction terms are for the curvature effect, the Bouguer slab truncation, and the thickness effect on curvature. The approximation is accurate to within 1 μGal for Bullard caps of less than 4-km thickness. The accuracy of the approximations is illustrated for the parameters of thickness and Bullard radius.
Evaluation of the three‐dimensional configuration of a subsurface artificial fracture by the triaxial shear shadow method
Authors: Niitsuma Hiroaki , Saito Hiroyuki
Published: October 2002

We have determined the three‐dimensional configuration of a single fracture in the hot dry rock model field at Higashi‐Hachimantai, Japan, by the triaxial shear shadow method. The crack was created by hydraulic fracturing in intact welded tuff at a depth of 370 m. We have carried out crosshole seismic measurements by using a downhole air gun and a triaxial seismic detector. Extinction at a special polarization direction and the dependency of transmissivity in shear wave component on incident angle were determined by a triaxial hodogram analysis of detected signals. We have evaluated the orientation and distribution of the fracture using the shear wave extinction, and the three‐dimensional configuration of the fracture by a continuation of the evaluated orientations. The results are in good agreement with the data obtained by independent experiments in the field.
Interface conditions for acoustic and elastic wave propagation
Authors: Sochacki J. S. , George J. H. , Ewing R. E. , Smithson S. B.
Published: October 2002

The divergence theorem is used to handle the physics required at interfaces for acoustic and elastic wave propagation in heterogeneous media. The physics required at regular and irregular interfaces is incorporated into numerical schemes by integrating across the interface. The technique, which can be used with many numerical schemes, is applied to finite differences. A derivation of the acoustic wave equation, which is readily handled by this integration scheme, is outlined. Since this form of the equation is equivalent to the scalar SH wave equation, the scheme can be applied to this equation also. Each component of the elastic P‐SV equation is presented in divergence form to apply this integration scheme, naturally incorporating the continuity of the normal and tangential stresses required at regular and irregular interfaces.
Depth filtering of first breaks and ground roll
Authors: McMechan G. A. , Sun R.
Published: October 2002

Much of the energy removed in a typical standard seismic data preprocessing sequence corresponds to approximately horizontal propagation in very near‐surface structure. Such energy includes direct (first‐break) compressional waves, direct shear waves, and ground roll; these may be effectively separated from deeper reflections by downward continuation of the recorded common‐source wavefield, by reverse‐time extrapolation, to a depth beneath which these waves propagate. The subhorizontally traveling waves get left behind in the shallow part of the model. Subsequent upward continuation of the wavefield reconstructs the original surface‐recorded wavefield with the subhorizontally traveling waves removed. Only a very simple (even constant) velocity distribution is required for the wavefield extrapolation; no net distortion is produced since both downward and upward continuations are performed using the same velocity model.
Correspondence between membrane potential and conductivity
Authors: Sen P. N.
Published: October 2002

Combining the membrane potential [Formula: see text] with the corresponding ideal membrane potential [Formula: see text] and the liquid junction potential [Formula: see text], for the same activity ratio, gives [Formula: see text]. [Formula: see text] and [Formula: see text] are the reciprocal of the average of the reciprocal water conductivity and reciprocal of cation and anion conductivities, and [Formula: see text]; and [Formula: see text] is the average of the ratio of the water to the rock conductivity [Formula: see text] with respect to [Formula: see text], where t is the transport number for the Na ion, [Formula: see text] is the ionic concentration, and [Formula: see text] is the activity coefficient. This relationship is independent of any model and does not even refer to the value of clay counterion concentration. Combining σ with [Formula: see text] gives the saturation dependent formation factor F, and thus the interpretation of shaly sands becomes no more difficult than for clean sands. Experimental data on 27 rocks for which both membrane potential and conductivity were measured by Smits (1968) and Waxman and Smits (1968) over a large salinity range are used to verify this relationship.
Compressional and shear‐wave logging in open and cased holes using a multipole tool
Authors: Chen S. T. , Eriksen E. A.
Published: October 2002

We have found in field observations that the multipole sonic logging tool can effectively measure formation P‐wave and S‐wave data in a cased hole. The multipole tool, containing both monopole and quadrupole source‐receiver systems, was originally designed to log P‐ and S‐waves directly, in all lithologies, for an open borehole. The monopole source‐receiver system (P‐wave) operates at 7–10 kHz, as compared with 15–25 kHz for a conventional sonic tool, while the quadrupole source‐receiver system (S‐wave) operates at 3–7 kHz. These lower operating frequencies enable the signals to penetrate the well casing and cement more effectively than signals from a conventional sonic tool. As a result, the formation P‐ and S‐waves recorded by the multipole tool are generally much stronger than the unwanted waves which travel along the well casing and cement. Formation arrivals can be easily identified and separated from the casing arrivals for a wide range of lithologies. Logs run before and after the wells were cased show remarkable agreement even in severely washed out zones.
On: “A calculus for finely layered anisotropic media” by M. Schoenberg and F. Muir (GEOPHYSICS, 54, 581–589, May 1989)
Authors: Hudson John A. , Crampin Stuart
Published: October 2002

The calculation of the overall anisotropic response of materials with variations in properties on a scale short compared to the wavelength of the imposed stressfield is complicated but, when the variations in structure are one‐dimensional, a straightforward averaging technique exists. This method, originated by Riznichenko (1949) and Postma (1955), and further developed by Backus (1962), has been cast into a convenient matrix form by Helbig and Schoenberg (1987). Schoenberg and Douma (1988) have shown that distributions of parallel cracks may also be incorporated into the system by representation as layers in the limit of vanishing thickness and stiffness. Finally, Schoenberg and Muir (1989) cast the whole calculation into a form in which the rules of group theory apply, and suggest that distributions of intersecting sets of parallel cracks in fine layering can be manipulated in this way.
An improvement on D norm deconvolution: A fast algorithm and the related procedure
Authors: Wang C.‐S. , Tang J. , Zhao B.
Published: October 2002

A criterion for simplicity, D norm criterion [Formula: see text], and a noniterative algorithm (MEDD) proposed by Cabrelli, are based on the Varimax norm [Formula: see text] of the minimum entropy deconvolution (MED). Mathematical analysis of the MEDD algorithm reveals that some part of the MEDD computation is unnecessary. In this paper, we present a fast algorithm (FD) which gives the same results as the MEDD algorithm but is ten times more efficient than MEDD. To improve the results of the MEDD algorithm, a new computational procedure (FD-MEDP) is also advanced and some numerical examples show the advantages of the new procedure.
An explicit, unconditionally stable, 15‐degree depth migration and modeling algorithm implemented in poststack, directional, and prestack modes
Authors: Benson Alvin K.
Published: October 2002

An explicit, unconditionally stable, finite‐difference depth migration and modeling algorithm is formulated and implemented for the fifteen‐degree wave equation in poststack, directional (rotational), and prestack modes for inhomogeneous media. It is about two times faster than implicit schemes. The simplicity, unconditional stability, and speed of the algorithm are appealing for numerous applications, especially prestack and three‐dimensional data sets.
Geophysical diffraction tomography at a dinosaur site
Authors: Witten Alan , Gillette David D. , Sypniewski Josef , King Wendell C.
Published: October 2002

In 1979 two hikers discovered the partially exposed bones from the tail of a dinosaur in the high desert of New Mexico. Excavation in 1985 led to the recognition that the dinosaur, informally named “Seismosaurus,” was new to science. It is by far the longest dinosaur on record. Excavations continued in 1986 with the discovery that additional bones leading forward from the middle region of the tail, potentially toward the remainder of the skeleton, remained entombed in the 145 million year old sandstone. The site has been the subject of intensive experimentation to assess the feasibility of geophysical remote sensing in exploration paleontology. The efforts of numerous investigators at the site may serve to change the century‐old methods of hammer and chisel, in part, to those based on more modern technology. One of the methods tested is geophysical diffraction tomography (GDT). Unlike the more common straightray algorithms of geophysical tomography that map subsurface properties by projecting received signal amplitude or time of the first signal arrival back to the source, GDT treats the problem as one of wave propagation by inverting the linearized wave equation to compute the spatial distribution of refractive index. Excavation of the “Seismosaurus” skeleton continues. The purpose of our most recent GDT study is to further test the method and to guide paleontologists in their future excavations by locating and identifying the buried skeletal remains. A total of eleven imaged vertical cross‐sections displayed features of sufficient acoustic contrast to be tentatively identified as dinosaur bone. Although the GDT resolution is insufficient to characterize bone shape, bone identification was subjectively accomplished on the basis of size, aspect ratio, and position. Based on this interpretation, it is believed that much of the remaining skeleton exists and is in near articulation.
On: “The use of Hartley transform in geophysical applications” by R. Saatcilar, S. Ergintav, and N. Canitez (GEOPHYSICS, 55, 1488–1495, November 1990) and “Solving elastic wave equations with the Hartley method” by R. Saatcilar, and S. Ergintav (GEOPHYSICS, 56, 274–278, February 1991).
Authors: Zhou Binzhong
Published: October 2002

Since Kosloff and Baysal (1982) introduced the Fourier or so‐called pseudo‐spectral method to the geophysical industry for solving wave‐equation modeling problems, it has become one of the major tools in computational seismology. Recently, Saatcilar et al. and Saatcilar and Ergintav presented some geophysical applications of the Hartley transform (HT). From their papers, it is clear that the HT is an alternative tool to the Fourier transform (FT).
A dynamic programming approach to first arrival traveltime computation in media with arbitrarily distributed velocities
Authors: Schneider W. A. , Ranzinger Kurt A. , Balch A. H. , Kruse Curtis
Published: October 2002

Curved‐ray tomographic traveltime inversion, reverse‐time migration and various other seismic modeling applications require the calculation of traveltime and raypath information throughout a two‐ or three‐dimensional medium. When arbitrary velocity distributions and curved rays are involved, traditional ray shooting or bending procedures can be time consuming and error prone. A two‐dimensional dynamic programming traveltime computation technique, based upon Fermat’s principle, uses simple calculus techniques and a systematic mapping scheme to determine first‐arrival times on a uniform grid, given an arbitrary, discrete velocity distribution. It accurately handles large contrast, discontinuous velocity distributions, including those that generate caustics. First arrival seismic energy can travel either as transmitted waves, diffracted waves, or headwaves, and this technique models all types. The traveltime computations begin with starting values computed near the source location. Then, the mapping systematically steps through the grid, where each new arrival time is calculated using two previously computed “neighbor” traveltimes. We present two mapping procedures, a brute force approach that advances across the grid one column (or row) at a time and a more natural approach that computes times along expanding rectangles. Isotime lines within the traveltime grid represent wavefronts, and seismic raypaths can be numerically computed through the traveltime grid as orthogonal trajectories to the wavefronts. Such a forward model was used in a curved‐raypath tomographic inversion program to successfully invert a physical model crosshole data set. The traveltime computation algorithm also performed successfully on several difficult velocity models. On a discontinuous, large contrast velocity model, traveltimes agreed to within 0.12 percent with those of an accurate ray‐tracing program.
Thermal state in the north Viking Graben (North Sea) determined from oil exploration well data
Authors: Brigaud F. , Vasseur G. , Caillet G.
Published: October 2002

We can deduce thermal conductivities and thermal gradients from extensively available oil exploration data: geophysical well logs, cores, cuttings, formation thicknesses and temperatures. Thermal conductivity is predicted at three significant scales. First, it is computed at the scale of well‐log electrofacies (thicknesses from 1 to 10 m) using a geometric mean model calibrated on laboratory measurements made on the main sedimentary rocks—the electrofacies conductivity is calculated as a function of the mineralogy, the porosity and the saturating fluids. Second, it is estimated at formation scale at each well site (thicknesses from 100 to a few thousand meters) using a serial model that accounts for the anisotropy due to sediment stacking and for temperature effects. Finally, for each formation (thicknesses on the order of 1 km), the average conductivity field is mapped at basin scale (extent on the order of 100 km) using a geostatistical treatment accounting for lateral facies and/or porosity changes. For thermal gradient field reconstruction, the systematic errors associated with the drilling history are removed from temperatures (bottom‐hole temperatures) using various techniques depending on data quality. The formation thermal gradient fields are then estimated using a stochastic inversion for temperatures and thicknesses, considering lateral correlations between thermal gradients at well sites. The technique is applied to the Norwegian Viking Graben, a multistage rift basin in the North Sea, where previous studies indicate large lateral and vertical variations in thermal conductivity and thermal gradient fields.
Comparison of four least‐squares inversion schemes for studying equivalence in one‐dimensional resistivity interpretation
Authors: Simms J. E. , Morgan F. D.
Published: October 2002

The problem of equivalence in dc resistivity inversion is well known. The ability to invert resistivity data successfully depends on the uniqueness of the model as well as the robustness of the inversion algorithm. To study the problems of model uniqueness and resolution, theoretical data are inverted using variations of a nonlinear least‐squares inversion. It is only through model studies such as this one, where the true solutions are known, that realistic and meaningful comparisons of inversion methods can be undertaken. The data are inverted using three schemes of fixed‐layer thickness where only the resistivity varies, and the results are compared to the variable parameter inversion where both the layer resistivities and thicknesses are allowed to vary. The purpose of fixing the layer thicknesses is to reduce the number of parameters solved for during the inversion process. By doing this, nonuniqueness may be reduced. The fixed‐layer thickness schemes are uniform thickness, geometrical progression of thickness, and logarithmic progression of thickness. By applying each inversion scheme to different models, the layer thickness that minimizes the data rms error for various numbers of layers is determined. The curve of data rms error versus model rms error consists of three general regions: unique, nonunique, and no resolution. A good inversion routine simultaneously minimizes the data rms and model rms errors. The variable parameter scheme is best at simultaneously minimizing the data rms and model rms errors for models that can be resolved through the inversion process. The optimum number of layers in the model can be determined by using a modified F‐test.
P‐wave anisotropy of the Pierre Shale
Authors: Levin Franklyn K.
Published: October 2002

Experimental evidence for the existence, at seismic frequencies, of transverse isotropy with a vertical symmetry axis is not overwhelming. Anisotropy of this type has been inferred for SH‐waves from a consistent overestimation of reflector depths. Because of the shape of transverse isotropy velocity surfaces for P‐waves and the accompanying tendency to obtain vertical velocities (Krey and Helbig, 1956), only a few field measurements of P‐wave anisotropy are in the literature.
Noncausality of the discrete‐time magnetotelluric impulse response
Authors: Egbert Gary D.
Published: October 2002

Under the assumption that the external source magnetic fields are uniform, the electric (E) and magnetic (H) fields observed at the surface of the conducting earth satisfy a time‐invariant linear relation, which may be expressed as multiplication in the frequency domain, [Formula: see text], Eq. (1), or as convolution in the time domain, [Formula: see text], Eq. (2). Here the tilde denotes quantities in the frequency domain; e.g., [Formula: see text] is the frequency‐domain magnetotelluric (MT) impedance, and Z the corresponding time‐domain impulse response. For simplicity in the following discussion, I treat all quantities as scalars, although the operations in equations (1) and (2) generally involve vectors and tensors.
Feasibility of CDP seismic reflection to image structures in a 220-m deep, 3-m thick coal zone near Palau, Coahuila, Mexico
Authors: Miller Richard D. , Saenz Victor , Huggins Robert J.
Published: October 2002

The common‐depth‐point (CDP) seismic‐reflection method was used to delineate subsurface structure in a 3-m thick, 220-m deep coal zone in the Palau area of Coahuila, Mexico. An extensive series of walkaway‐noise tests was performed to optimize recording parameters and equipment. Reflection events can be interpreted from depths of approximately 100 to 300 m on CDP stacked seismic sections. The seismic data allow accurate identification of the horizontal location of the structure responsible for a drill‐discovered 3-m difference in coal‐zone depth between boreholes 150 m apart. The reflection method can discriminate folding with wavelengths in excess of 20 m and faulting with offset greater than 2 m at this site.
Imaging beneath a high‐velocity layer using converted waves
Authors: Purnell Guy W.
Published: October 2002

High‐velocity layers (HVLs) often hinder seismic imaging of deeper reflectors using conventional techniques. A major factor is often the unusual energy partitioning of waves incident at an HVL boundary from lower‐velocity material. Using elastic physical modeling, I demonstrate that one effect of this factor is to limit the range of dips beneath an HVL that can be imaged using unconverted P‐wave arrivals. At the same time, however, partitioning may also result in P‐waves outside the HVL coupling efficiently with S‐waves inside. By exploiting some of the waves that convert upon transmission into and/or out of the physical‐model HVL, I am able to image a much broader range of underlying dips. This is accomplished by acoustic migration tailored (via the migration velocities used) for selected families of converted‐wave arrivals.
Source signature determination by inversion
Authors: Landrø M. , Sollie R.
Published: October 2002

A new method for estimating the pressure wavefield generated by a marine air‐gun array is presented. It is assumed that data is acquired at a ministreamer located below the source array. Effective source signatures for each air gun are estimated by an inversion algorithm. The forward modeling scheme used in the inversion algorithm is based upon a physical modeling of the air bubble generated by each air gun. This means that typical inversion parameters are: gun depths, empirical damping coefficients, and reflection coefficient of the sea surface. Variations in streamer depth are also taken into account by the inversion scheme. The algorithm has been successfully tested on examples with unknown streamer positions, gun parameters, reflection coefficient of sea surface, and ministreamer data contaminated with white noise.
Refractor imaging using an automated wavefront reconstruction method
Authors: Aldridge David F. , Oldenburg Douglas W.
Published: October 2002

The classical wavefront method for interpreting seismic refraction arrival times is implemented on a digital computer. Modern finite‐difference propagation algorithms are used to downward continue recorded refraction arrival times through a near‐surface heterogeneous velocity structure. Two such subsurface traveltime fields need to be reconstructed from the arrivals observed on a forward and reverse geophone spread. The locus of a shallow refracting horizon is then defined by a simple imaging condition involving the reciprocal time (the traveltime between source positions at either end of the spread). Refractor velocity is estimated in a subsequent step by calculating the directional derivative of the reconstructed subsurface wavefronts along the imaged interface. The principle limitation of the technique arises from imprecise knowledge of the overburden velocity distribution. This velocity information must be obtained from uphole times, direct and reflected arrivals, shallow refractions, and borehole data. Analysis of synthetic data examples indicates that the technique can accurately image both synclinal and anticlinal structures. Finally, the method is tested, apparently successfully, on a shallow refraction data‐set acquired at an archeological site in western Crete.
Compressional velocity and porosity in sand‐clay mixtures
Authors: Marion D. , Nur A. , Yin H. , Han D.
Published: October 2002

Laboratory measurements of porosity and compressional velocity were conducted on unconsolidated brine saturated clean Ottawa sand, pure kaolinite, and their mixtures at various confining pressures. A peak in P velocity versus clay content in unconsolidated sand‐clay mixtures at 40 percent clay by weight was found. The peak in velocity is 20–30 percent higher than for either pure clay or clean sand. A minimum in porosity versus clay content at 20–40 percent clay by weight is also observed. Such behavior is explained using a micro‐geometrical model for mixtures of sand and clay in which two classes of sediments are considered: (1) sands and shaley sands, in which clay is dispersed in the pore space of load bearing sand and thus reduces porosity and increases the elastic moduli of the pore‐filling material and (2) shales and sandy shales, in which sand grains are dispersed in a clay matrix. For these sediments, the model reproduces the extrema in velocity and porosity and accounts for much of the scatter in the velocity‐porosity relationship.