bluuebunny/crossref_metadata_2025 huggingface dataset:
Inversion of surface NMR data
Authors: Legchenko Anatoly V. , Shushakov Oleg A.
Published: October 2002

The main advantage of the surface nuclear magnetic resonance (NMR) method compared to other geophysical methods in the field of groundwater investigation is the ability to measure an NMR signal directly from the water molecules. An NMR signal stimulated by an alternating current pulse through an antenna at the surface, confirms the existence of water in the subsurface with a high degree of reliability. The NMR signal amplitude depends on the pulse parameter (the product of the pulse amplitude and its duration), bulk water volume, and water depth. Measurements are performed while varying the pulse parameter, and subsequent data processing reveals the number of water‐saturated layers, and data concerning their depth, thickness, and water content. One of the major problems in the practical application of the NMR method is the very weak signal (<3000 nV): hence the problem of signal to noise ratio (S/N). S/N can be improved by stacking the signal, but measurement time is increased. We have developed an algorithm that minimizes the number of measurements (number of different values of the pulse parameter) without a loss of inversion accuracy for a given S/N ratio, making it possible to determine a set of optimal pulses for the measurements. NMR measurements are also sensitive to the electrical conductivity of the subsurface; an electrically conductive subsurface causes variations in the depth of investigation and in the vertical resolution of the method. Experience gained from application of the method has proven that both the inversion algorithm and the analysis of the problem are efficient.
Time-average equation revisited
Authors: Dvorkin Jack , Nur Amos
Published: October 2002

Expressions that relate velocity to porosity and to pore-fluid compressibility are among the most important deliverables of rock physics. Such relations are used often as additional controls for inferring porosity from well logs, as well as in-situ indicators of pore fluid type. The oldest and most popular is the Wyllie et al. (1956) equation: [Formula: see text]where [Formula: see text] is the measured traveltime of a P-wave, [Formula: see text] is the traveltime expected in the solid-phase material, and [Formula: see text] is the traveltime expected in the pore fluid. It follows from equation (1) that [Formula: see text]where ϕ is porosity, [Formula: see text] is the measured P-wave velocity, and [Formula: see text] and [Formula: see text] are the P-wave velocities in the solid and in the pore-fluid phases, respectively.
Wave extrapolation in the spatial wavelet domain with application to poststack reverse‐time migration
Authors: Wu Yafei , McMechan George A.
Published: October 2002

A wavelet transformation is performed over each of the spatial coordinates of the scalar wave equation. This transformed equation is solved directly with a finite‐difference scheme for both homogeneous and smooth inhomogeneous media. Wavefield extrapolation is performed completely in the spatial wavelet domain without transforming back into the space domain at each time step. The wavelet coefficients are extrapolated, rather than the wavefield itself. The numerical solution of the scalar wave equation in the spatial wavelet domain is closely related to the finite‐difference method because of the compact support of the wavelet bases. Poststack reverse‐time migration is implemented as an application. The resolution spaces of the wavelet transform provide a natural framework for multigrid analysis. Migrated images are constructed from various resolution spaces.
Appropriate FFT spectral scales
Authors: Caton Paul W.
Published: October 2002

Improved fast Fourier transform (FFT) spectra are obtained by multiplying a temporal or spatial series by twice the reciprocal length of useful, windowed data. This scaling provides spectral amplitudes that compare with average amplitudes in the original data. The inverse‐transform scale is the reciprocal of the forward scaling divided by the FFT length. True‐amplitude processing is convenient particularly when evaluating sparse data consisting of few traces and waveform types that are to be filtered or compensated for amplitude attenuations.
Reducing 3-D acquisition footprint for 3-D DMO and 3-D prestack migration
Authors: Canning Anat , Gardner Gerald H. F.
Published: October 2002

The acquisition patterns of 3-D surveys often have a significant effect on the results of dip moveout (DMO) or prestack migration. When the spatial distribution of input traces is irregular, results from DMO and migration are contaminated by artifacts. In many cases, the footprint of the acquisition patterns can be seen on the migrated section and may result in incorrect interpretation. This phenomena also has a very significant effect on the feasibility of conducting amplitude variation with offset (AVO) analysis after 3-D prestack migration or after 3-D DMO, and also may affect velocity analysis. We propose a simple enhancement to migration and DMO programs that acts to minimize acquisition artifacts.
Gauss’s theorem, mass deficiency at Chicxulub crater (Yucatan, Mexico), and the extinction of the dinosaurs
Authors: Campos‐Enriquez J. O. , Morales‐Rodrguez H. F. , Domnguez‐Mendez F. , Birch F. S.
Published: October 2002

Using Gauss’s theorem, we estimated the mass deficiencies of the Chicxulub impact structure (Yucatan, Mexico) from its gravity anomaly. The mass deficiency obtained from the residual gravity anomaly map ranges between 1.06 × 1016and 1.67 × 1016kg. Because the gravity anomaly has approximately radial symmetry, we also estimated the mass deficiency from selected profiles. In this way, we obtained slightly lower mass deficiency (6.16 × 1015to 1.35 × 1016kg). The central gravity high, which is supposed to be associated with the central structural high, has a mean excess mass of 1.93 × 1014kg. By assuming a mean density contrast of 100 kg/m3between the country rock and the sedimentary and brecciated rocks, we estimated the equivalent total mass (1.60 × 1017to 4.34 × 1017kg) and volume (6.16 × 1013to 1.67 × 1014m3) of breccias and sedimentary rocks responsible for the gravity anomaly. These figures represent lower bounds on the mass and volume ejected from the impact crater. They represent estimates made from geophysical principles and data, and compare well with independent estimates based on other principles such as scaling relations. According to actual estimations of the sulfur dioxide mass generated by the Cretaceous‐Tertiary impact and our results, only a small fraction (about 1%) of the anhydrite in the target strata was vaporized.
On the computation of the true‐amplitude weighting functions
Authors: Sun Jianguo , Gajewski Dirk
Published: October 2002

True‐amplitude migration is a new development of Kirchhoff‐type migration. By using a proper weighting function, called true‐amplitude weighting function, in the modified diffraction‐stack operator, one can obtain a reconstructed source pulse proportional to the reflection coefficient of the target reflector. According to Schleicher et al. (1993), the true‐amplitude weighting function is complex and consists of two parts. One part is the module of the complex weighting function, given by means of a 2 × 2 ray transformation submatrix called [Formula: see text]. The other is the phase factor of the complex weighting function, determined by the number of ray‐branch caustics. Thus, to obtain the true‐amplitude weighting function, one should compute the matrix [Formula: see text] as well as the number of ray‐branch caustics.
1-D elastic waveform inversion: A divide‐and‐conquer approach
Authors: Xia Ganyuan , Sen Mrinal K. , Stoffa Paul L.
Published: October 2002

Subsurface rock properties are manifested in seismic records as variations in traveltimes, amplitudes, and waveforms. It is commonly acknowledged that traveltimes are sensitive to the long wavelength part of the velocity, whereas amplitudes are sensitive to the short wavelength part of the velocity. The inherent sensitivity of seismic velocity at different wavelengths suggests an approach that decomposes the waveform data into traveltime and amplitude components. Therefore we propose a divide‐and‐conquer approach to the elastic waveform inversion problem. We first estimate the smoothly varying background velocity from the traveltime and the rapidly changing perturbations from the amplitude by amplitude variation with offset (AVO) inversion based on linearized reflection coefficient. Then we combine the perturbation with the background to obtain a starting model to be used in the final waveform inversion that models all converted waves and internal multiples assuming a 1-D earth model. For estimating the background velocity, we use the flatness of events as the objective criterion, and simulated annealing as a search tool. Three different model parameterization schemes (constant velocity blocks, splines, and arctangent models) are compared, with the arctangent having the most flexibility and least artifacts. Having obtained the background velocities, we analyze the AVO effects to estimate the perturbations to the background, for which we use a linearized inversion method. The combination of the perturbation and background should be sufficiently close to the true model so that the inverse problem becomes quasi‐linear. A full elastic waveform inversion is used to fine‐tune the combined model to obtain P-wave and S-wave velocity and density, again using either a nonlinear optimization method or an iterative linearized solution. Application of the inversion algorithm to synthetic data from an 84-layer model was able to predict the full reflectivity data and recover the true model parameters. Application to one seismic line in the Carolina Trough area found a thin gas zone which produces strong Bottom Simulating Reflectors (BSRs).
The equivalent offset method of prestack time migration
Authors: Bancroft John C. , Geiger Hugh D. , Margrave Gary F.
Published: October 2002

A prestack time migration is presented that is simple, efficient, and provides detailed velocity information. It is based on Kirchhoff prestack time migration and can be applied to both 2-D and 3-D data. The method is divided into two steps: the first is a gathering process that forms common scatterpoint (CSP) gathers; the second is a focusing process that applies a simplified Kirchhoff migration on the CSP gathers, and consists of scaling, filtering, normal moveout (NMO) correction, and stacking. A key concept of the method is a reformulation of the double square‐root equation (of source‐scatterpoint‐receiver traveltimes) into a single square root. The single square root uses an equivalent offset that is the surface distance from the scatterpoint to a colocated source and receiver. Input samples are mapped into offset bins of a CSP gather, without time shifting, to an offset defined by the equivalent offset. The single square‐root reformulation gathers scattered energy to hyperbolic paths on the appropriate CSP gathers. A CSP gather is similar to a common midpoint (CMP) gather as both are focused by NMO and stacking. However, the CSP stack is a complete Kirchhoff prestack migrated section, whereas the CMP stack still requires poststack migration. In addition, the CSP gather has higher fold in the offset bins and a much larger offset range due to the gathering of all input traces within the migration aperture. The new method gains computational efficiency by delaying the Kirchhoff computations until after the CSP gather has been formed. The high fold and large offsets of the CSP gather enables precise focusing of the velocity semblance and accurate velocity analysis. Our algorithm is formulated in the space‐time domain, which enables prestack migration velocity analysis to be performed at selected locations and permits prestack migration of a 3-D volume into an arbitrarily located 2-D line.
Geoelectrical fields in a layered earth with arbitrary anisotropy
Authors: Yin Changchun , Weidelt Peter
Published: October 2002

In many cases in geoelectrical exploration, the standard model of a layered isotropic half‐space is a good approximation to geophysical reality. But sometimes it is useful to extend this model to uniform anisotropic layers. For example, in regions with distinct dipping stratification, one will try to represent this conductivity variation in the form of dipping anisotropic layers. In this paper, the layered isotropic half‐space is extended to a half‐ space with general anisotropy such that to each layer is assigned a symmetrical (3 × 3) resistivity tensor. After formulating the general layered problem, the numerical implementation is treated. A very fast algorithm exists only if the resistivity tensor is rotationally symmetric around a vertical axis (transverse isotropy). In all other cases, one has to calculate a double integral with respect to the horizontal components of the wavenumber vector. Furthermore, we have also calculated the magnetic field. Whereas in the isotropic case this field does not contain any information about the resitivity distribution, in the case of arbitrary anisotropy it carries some information about the distribution of resistivity inside the earth. No correct results are obtained if one interprets data resulting from an anisotropic structure by an isotropic model.
Zero moveout (ZMO) stacking
Authors: Loewenthal Dan , Buchen Peter , Kagansky Alexander , Koren Ilan
Published: October 2002

This work describes a simple stacking procedure based on summing the traces of a common shot or common seismic section without the usual normal moveout (NMO) relative time shifts. We refer to this procedure as zero moveout (ZMO) stacking. A simple horizontal summation with no shift in time results in a stacked trace that is the one‐dimensional seismogram for horizontally layered media. We explore the practical implementation of ZMO stacks for source estimation or wavelet extraction in deconvolution and/or identification of source‐reflector signatures necessary for performing inversion.
Frequency‐dependent shear‐wave splitting in thinly layered media with intrinsic anisotropy
Authors: Werner Ulrich , Shapiro Sergei A.
Published: October 2002

In multilayered media one normally observes two distinct shear‐wave phases that are polarized perpendicularly to each other and propagate at different velocities. One of them, the SH-wave, is a pure shear wave with particle motion parallel to layer interfaces and strictly perpendicular to the incidence plane and the propagation direction. The other one, the qSV-wave, is a so‐called quasi‐shear wave whose particle motion also contains a longitudinal portion. The velocities and attenuations of both phases depend on the frequency and the angle of incidence. However, this dependence is different for SH-waves and qSV-waves.
AVO inversion of a Gulf of Mexico bright spot—A case study
Authors: Mahob Patrice Nsoga , Castagna John P. , Young Roger A.
Published: October 2002

An iterative and linearized inversion algorithm carried out in the x-t domain has been applied to a prestack seismic data set from the central Gulf of Mexico, offshore Louisiana. Sonic and density curves from a well located close to the seismic line are used to generate the initial starting models for the inversion. We tested the geologically realistic hypothesis that the starting models have an accurate impedance structure outside of the potential pay zone and that the prospective pay zone will have mechanical properties consistent with the presence or absence of hydrocarbons. The inversion, performed with starting models with pay zones with a Poisson’s ratio appropriate for 100% brine saturation or with a Poisson’s ratio intermediate between expected values for full brine and hydrocarbon saturation, does not converge to the real seismic gather. However, with a starting model having a Poisson’s ratio appropriate for hydrocarbon saturation in the target zone, there is convergence from the initial to the real seismic gather.
Approaches to defining reservoir physical properties from 3-D seismic attributes with limited well control: An example from the Jurassic Smackover Formation, Alabama
Authors: Hart Bruce S. , Balch Robert S.
Published: October 2002

Much industry interest is centered on how to integrate well data and attributes derived from 3-D seismic data sets in the hope of defining reservoir properties in interwell areas. Unfortunately, the statistical underpinnings of the methods become less robust in areas where only a few wells are available, as might be the case in a new or small field. Especially in areas of limited well availability, we suggest that the physical basis of the attributes selected during the correlation procedure be validated by generating synthetic seismic sections from geologic models, then deriving attributes from the sections. We demonstrate this approach with a case study from Appleton field of southwestern Alabama. In this small field, dolomites of the Jurassic Smackover Formation produce from an anticlinal feature about 3800 m deep. We used available geologic information to generate synthetic seismic sections that showed the expected seismic response of the target formation; then we picked the relevant horizons in a 3-D seismic data volume that spanned the study area. Using multiple regression, we derived an empirical relationship between three seismic attributes of this 3-D volume and a log‐derived porosity indicator. Our choice of attributes was validated by deriving complex trace attributes from our seismic modeling results and confirming that the relationships between well properties and real‐data attributes were physically valid. Additionally, the porosity distribution predicted by the 3-D seismic data was reasonable within the context of the depositional model used for the area. Results from a new well drilled after our study validated our porosity prediction, although our structural prediction for the top of the porosity zone was erroneous. These results remind us that seismic interpretations should be viewed as works in progress which need to be updated when new data become available.
Resistivity and induced polarization monitoring of salt transport under natural hydraulic gradients
Authors: Slater Lee D. , Sandberg Stewart K.
Published: October 2002

We demonstrate the use of resistivity/induced polarization (IP) monitoring of salt transport under natural hydraulic loads. Electrical monitoring of saline tracer transport during forced injection has been demonstrated previously. Detection of tracer transport under natural hydraulic loading is difficult because neither the hydraulic load nor the tracer resistivity can be controlled. In one study, we identify the electrical response to salt transport in a dynamic beach environment. Resistivity/IP imaging resolved the structure of the saltwater‐freshwater interface and evidence for tide‐induced groundwater transport. Resistivity increases in the near surface and at depth, upbeach of the high‐tide mark, accompanied by tidal transgression. We attribute this to desaturation and decreasing salinity in the near surface and to decreasing salinity at depth, despite tidal transgression. Monitoring of groundwater levels indicates a phase lag between the tide level and groundwater level, supporting the electrical data. IP was insensitive to groundwater salinity variation. In a second study, we identify the electrical response to recharge‐induced salt transport from a road‐salt storage facility. Conductivity and IP models for monitoring lines, located on the basis of an EM31 survey, resolved the subsurface salt distribution. IP modeling resolved the sediment‐bedrock interface. Modeling of monthly conductivity differences revealed conductivity increases and decreases at the locations of salt contamination, which correlate with the recharge pattern. We attribute near‐surface conductivity increases after heavy rainfall to increasing saturation and ion dissolution. Corresponding conductivity decreases at depth are attributed to flushing of the bedrock with freshwater. Essentially, the opposite response was observed during a quiet monitoring period following heavy recharge. Near‐surface IP changes are consistent with this interpretation. Salt transport occurring under natural hydraulic conditions was monitored with resistivity imaging. IP improved characterization of the hydrogeologic framework but was of limited value in monitoring salt transport in these environments.
Anisotropic effects on full and partial stacks
Authors: Chen He , Castagna John P.
Published: October 2002

Nonhyperbolic moveout resulting from localized variations in anisotropy can create many misleading artifacts such as apparent faults, folds, channels, flat spots, dim spots, bright spots, and AVO anomalies on fully and partially stacked seismic sections. This tutorial shows how these interpretation pitfalls may result when isotropy is assumed in processing.
A model for seismic velocity and attenuation in petroleum source rocks
Authors: Carcione José M.
Published: October 2002

Petroleum source rock is modeled as a viscoelastic transversely isotropic medium composed of illite/smectite and organic matter. The wave velocities and attenuation of petroleum source rocks are obtained as a function of excess pore pressure, initial kerogen content, and water saturation. The model generalizes a previous approach based on a pure elastic formulation of Backus averaging and introduces the pressure effect and the presence of fluids (oil and water). The model allows the simulation of different maturation levels induced by pore‐pressure changes caused by the conversion of kerogen to oil. The higher the oil saturation, the higher the maturation level. Assuming that the source rock has a very low permeability, the excess pore pressure can be calculated as a function of the conversion factor. Then the bulk modulus and density of the kerogen/oil mixture are obtained with the Kuster and Toksöz model, assuming that oil is the inclusion in a kerogen matrix. Finally, Backus averaging of this mixture with the illite/smectite layers gives the complex stiffnesses of the transversely isotropic and anelastic medium. Computed P- and S-velocities and quality factors parallel to bedding are higher than those normal to bedding, with attenuation anisotropy higher than stiffness anisotropy. In particular, for the North Sea Kimmeridge Shale and at maximum anisotropy, P and S parallel velocities are approximately 0.7 km/s higher than the corresponding P and S normal velocities. The maximum attenuation and stiffness anisotropies are obtained for 18% and 30% volumetric kerogen content, respectively. Both velocities and quality factors decrease with increasing kerogen content at a given pore pressure. The decrease in wave velocity is 2 km/s for P-waves and 1 km/s for S-waves when kerogen increases from zero to 100%. Moreover, anisotropy increases and velocities decrease with increasing pore pressure, i.e., with higher kerogen‐to‐oil conversion. Finally, the presence of water affects the normal‐bedding velocity, i.e., higher water saturation implies lower velocities.
Predicting the seismic implications of salt anisotropy using numerical simulations of halite deformation
Authors: Raymer Daniel G. , Tommasi Andréa , Kendall J‐Michael
Published: October 2002

In the past, the potential for seismic anisotropy in salt structures and its effect on their seismic imaging has received little attention. We consider the plausibility of salt anisotropy through linked numerical studies of salt deformation and its seismic consequences. Numerical models are used to predict lattice preferred orientations (LPOs) in halite polycrystalline aggregates subjected to axial extension and simple shear. The elastic constants for the deformed polycrystalline aggregate are then calculated. Simple models representing a salt sill and the stem of a diapir are created using these elastic constants. Ray tracing is used to investigate the effects of halite LPO on the propagation of seismic waves. The results suggest that salt anisotropy can cause significant traveltime effects and could lead to significant errors in seismic interpretation in salt environments if this anisotropy is ignored. We also investigate potential amplitude variation with offset and azimuth (AVOA) for the reflection from the top and bottom of an anisotropic salt sill. Ray paths with a shear‐wave leg within the salt display strong AVOA effects with a clear four‐fold symmetry.
3-D prestack Kirchhoff beam migration for depth imaging
Authors: Sun Yonghe , Qin Fuhao , Checkles Steve , Leveille Jacques P.
Published: October 2002

A beam implementation is presented for efficient full‐volume 3-D prestack Kirchhoff depth migration of seismic data. Unlike conventional Kirchhoff migration in which the input seismic traces in time are migrated one trace at a time into the 3-D image volume for the earth’s subsurface, the beam migration processes a group of input traces (a supergather) together. The requirement for a supergather is that the source and receiver coordinates of the traces fall into two small surface patches. The patches are small enough that a single set of time maps pertaining to the centers of the patches can be used to migrate all the traces within the supergather by Taylor expansion or interpolation. The migration of a supergather consists of two major steps: stacking the traces into a τ-P beam volume, and mapping the beams into the image volume. Since the beam volume is much smaller than the image volume, the beam migration cost is roughly proportional to the number of input supergathers. The computational speedup of beam migration over conventional Kirchhoff migration is roughly proportional to [Formula: see text], the average number of traces per supergather, resulting a theoretical speedup up to two orders of magnitudes. The beam migration was successfully implemented and has been in production use for several years. A factor of 5–25 speedup has been achieved in our in‐house depth migrations. The implementation made 3-D prestack full‐volume depth imaging feasible in a parallel distributed environment.
A new insight into the reciprocity principle
Authors: Arntsen Børge , Carcione José M.
Published: October 2002

Reciprocity is usually applied to wavefields associated with concentrated point forces and point receivers, but, reciprocity has a much wider application potential. In many cases, however, it is not used at its full potential because (1) a variety of source and receiver types are not considered or (2) its implementation is not well understood. We obtain reciprocity relations for inhomogeneous, anisotropic, viscoelastic solids and for distributed sources and receivers, and test these relations with a full‐wave numerical modeling algorithm. The theory and the numerical experiments show that, in addition to the usual relations involving directional forces, (1) the diagonal components of the strain tensor are reciprocal for dipole sources (single couple without moment), (2) the off‐diagonal components of the stress tensor are reciprocal for double couples with moments, (3) the dilatation due to a directional force is reciprocal to the particle velocity due to a dilatational source, and (4) some combinations of the off‐diagonal strains are reciprocal for single couples with moments.
Past, present, and future of geophysical inversion—A new millennium analysis
Authors: Treitel Sven , Lines Larry
Published: October 2002

Geophysicists have been working on solutions to the inverse problem since the dawn of our profession. An interpreter infers subsurface properties on the basis of observed data sets, such as seismograms or potential field recordings. A rough model of the process that produces the recorded data resides within the interpreter’s brain; the interpreter then uses this rough mental model to reconstruct subsurface properties from the observed data. In modern parlance, the inference of subsurface properties from observed data is identified with the solution of a so‐called “inverse problem.” In contrast, the “forward problem” consists of the determination of the data that would be recorded for a given subsurface configuration and under the assumption that given laws of physics hold. Until the early 1960s, geophysical inversion was carried out almost exclusively within the geophysicist’s brain. Since then, we have learned to make the geophysical inversion process much more quantitative and versatile by recourse to a growing body of theory, along with the computer power to reduce this theory to practice. We should point out the obvious, however, namely that no theory and no computer algorithm can presumably replace the ultimate arbiter who decides whether the results of an inversion make sense or nonsense: the geophysical interpreter. Perhaps our descendants writing a future third Millennium review article can report that a machine has been solving the inverse problem without a human arbiter. For the time being, however, what might be called “unsupervised geophysical inversion” remains but a dream.
The new millennEM
Authors: Christopherson Karen R.
Published: October 2002

Writing this piece about the state of electromagnetic (EM) geophysics in the year 2000, I am influenced by the fluctuation in commodity prices and other factors that affect our part of the industry. In the past two years, oil prices have halved and then nearly doubled, gold prices have dropped by about 15%, the geothermal industry has been hit hard by Asian economics and politics, and government policies control environmental concerns.
A Bayes tour of inversion: A tutorial
Authors: Ulrych Tadeusz J. , Sacchi Mauricio D. , Woodbury Alan
Published: October 2002

It is unclear whether one can (or should) write a tutorial about Bayes. It is a little like writing a tutorial about the sense of humor. However, this tutorial is about the Bayesian approach to the solution of the ubiquitous inverse problem. Inasmuch as it is a tutorial, it has its own special ingredients. The first is that it is an overview; details are omitted for the sake of the grand picture. In fractal language, it is the progenitor of the complex pattern. As such, it is a vision of the whole. The second is that it does, of necessity, assume some ill‐defined knowledge on the part of the reader. Finally, this tutorial presents our view. It may not appeal to, let alone be agreed to, by all.
A comparison of performances of linearized and global nonlinear 2-D inversions of VLF and VLF-R electromagnetic data
Authors: Kaikkonen P. , Sharma S. P.
Published: October 2002

The performances of linearized (local) and global nonlinear joint 2-D inversions of very low frequency (VLF) and VLF resistivity electromagnetic measurements are analyzed. A stable iterative inversion scheme is used in linearized inversion while the very fast simulated annealing approach is used in global nonlinear inversion. Synthetic noise‐free and noisy data due to three different models in complexity and two field examples are considered. Synthetic examples show that linearized inversion reveals the subsurface structure better than global nonlinear inversion provided the model has only a few parameters under inversion. Both linearized and global nonlinear inversions must be performed combining all available data in order to obtain the most reliable estimates of the subsurface parameters. Complex models with a large number of parameters are better to invert using global nonlinear inversion although the CPU time needed is always much longer than the one used in linearized inversion. Contrary to global nonlinear inversion, success in linearized inversion requires the good a priori information of all the model parameters under inversion. Noise in data influences the linearized inversion results more than those provided by global inversion. Linearized inversion using as an initial model the mean model due to a few global inversion runs is also a good approach. Even in this case, if there are a large number of model parameters in inversion, linearized inversion can lead to an unstable solution. To overcome such a problem, one can fix the important and stable model parameters from the first step of linearized inversion and then vary and stabilize unstable parameters in the second step.
THE RELATIVE PLACE OF EMPIRICAL AND ANALYTIC METHODS OF GEOPHYSICAL INTERPRETATION
Authors: Weaver Paul
Published: October 2002

The pioneer in geophysics has, in most cases, used empirical methods on his first jobs in the field. Frequently, such an initial campaign has been successful in that valuable evidence has been obtained as to the position of a new ore‐deposit. Thereupon the method has received recognition so that additional parties have gone into field work; also, analytic methods have then been applied to show why the particular method succeeded in some cases and now far it would be likely to succeed in border‐line problems. After a discussion of the difference between empirical and analytic procedure, the author reviews the history of one geophysical project—the search for iron ore in the Lake Superior region by magnetic methods—describing the empirical efforts and the subsequent analysis. He then suggests that failures on certain other jobs might be less if the analysis be made earlier, and that there will be an economy, if this analysis be made before field work begins.
GRAVITY EXPRESSION OF THE HATCHETIGBEE ANTICLINE
Authors: McCollum E. V.
Published: October 2002

A reconnaissance gravity survey is presented of the Hatchetigbee Area of Southwestern Albama, which discloses two gravity minima associated with the Hatchetigbee Anticline and the neighboring Jackson Fault. A study of the gravity data, together with geologic and magnetic information, leads to the possibility that a salt ridge exists in the general Hatchetigbee Area, and that the gravity minima represent individual salt domes.
PROGRESS OF COOPERATION BETWEEN THE BUREAU OF MINES AND THE GEOPHYSICAL INDUSTRY WITH REGARD TO THE FEDERAL EXPLOSIVES ACT
Authors: Kintz G. M.
Published: October 2002

A year ago in Denver, I had the privilege of discussing with a number of the members of this Society the probable requirements of the Federal Explosives Act as they were understood at that time. As a result of this discussion you appointed a committee with your president, Mr. Goldstone, as chairman, to draw up and submit to D. Harrington, chief of the Health and Safety Service of the Bureau of Mines, suggestions embodying the thoughts of this organization as to how the geophysical industry might be able to change its methods of handling, storing, and transporting explosives, to conform with the Federal Explosives Act without excessive cost.
SECONDARY ARRIVALS IN A WELL VELOCITY SURVEY
Authors: Horton C. W.
Published: October 2002

Seismograms obtained in a well survey of the Shell‐Longleaf Lumber Co. #1, Vernon Parish, Louisiana, showed well‐developed secondary arrivals which satisfied a velocity formula V = (2000+0.27Z) feet per second. If these arrivals are assumed to be transverse waves, a value of 0.43 for Poisson’s ratio is obtained. On this same assumption, values of the modulus of rigidity and bulk modulus are computed for various depths. It is shown that the velocity of the secondary wave does not satisfy the equation developed by Lamb for thick‐walled tube waves.
On: “Shallow Stratigraphic Variations over Gulf Coast Structures”
Authors: Seager A. A.
Published: October 2002

During my residence in Southern Oklahoma I had occasion to note that over many of the structural features secondary cementation and leaching of the surface beds had occurred. A list of the structures exhibiting this phenomenon follows.
On: “THE RELATIVE PLACE OF EMPIRICAL AND ANALYTICAL METHODS OF GEOPHYSICAL INTERPRETATION”
Authors: Coffin R. Clare
Published: October 2002

I agree with Mr. Weaver in the relative merits of an analytical procedure as opposed to an empirical procedure in the analysis of geophysical data. However, the pioneer in geophysical exploration in entirely unexplored areas may be obliged to resort to the empirical approach to his data. This he may do sometimes to his advantage, but his errors come in applying the method over too large a territory. Certainly, he should use the empirical method with caution and abandon it in favor of the analytical method when data are available for such procedure.
Authors’ Reply
Authors: Nettleton L. L. , Elkins T. A.
Published: October 2002

We are very glad to receive a petrologist’s generally favorable comments on our paper. Perhaps, in our extremely limited petrographic knowledge, we have “rushed in where angels fear to tread,” although not without some appreciation of the pitfalls in our path. Our excuses are, first, that to a certain extent, these pitfalls may be bridged by a broad statistical base and second, that our aim has been to find a way of making a geophysical application of the great body of existing fact in petrographic literature rather than to make new measurements of the particular properties discussed. Since we agree with most of the criticisms stated, apparently we did not emphasize certain points as much as may be desirable and, therefore, we shall take this opportunity to explain some details more fully.
Reply to discussion by L. deWitte on “Log Interpretation in Sandstone Reservoirs”
Authors: Wyllie M. R. J.
Published: October 2002

My sketchy discussion of the rather involved history of the “shaly sand problem” may indeed appear to underestimate Leendert deWitte’s contributions and to favor unduly those of his brother Adriaan. I must crave Leendert’s indulgence for I did not intend to leave an impression of fraternal discrimination. I drew particular attention to Adriaan’s work because it was presented in the form of nomographs well suited to practical use and was, therefore, an easily available alternative to the familiar Schlumberger shaly‐sand nomographs.
Reply by authors to discussion by Dr. Nelson C. Steenland
Authors: Slack Howard A. , Lynch Vance M. , Langan Lee V.
Published: October 2002

We wish to thank Dr. Nelson Steenland for his interest in, and his comments on, our recent paper. We also acknowledge the written, but unpublished, comments of Messrs. Helmut Linsser and M. S. Reford and the oral communication with Dr. R. J. Bean and others.
Reply by authors to discussion by A. Grover
Authors: Thomson Ker C.
Published: October 2002

Our answers to these points follow in sequence.
Reply by authors to discussion by John F. Hermance
Authors: Price Albert T. , Jones F. Walter
Published: October 2002

We do not regard the criticism by J. F. Hermance of our interpretation of the results of our H‐polarization calculations ( nor the alternative “explanation” given by him of our results) as valid, for the following reasons.
Reply by author to the discussion by Edson S. Sampaio
Authors: Naudy H.
Published: October 2002

The comment of Prof. Sampaio is quite useful because until now I did not notice an error which has remained in the paper. The true formula is not [Formula: see text] but [Formula: see text].
Reply by authors to the discussion by G. Gudmundsson
Authors: Spector Allan , Grant Fraser S.
Published: October 2002

We wish to thank Mr. Gudmundsson for his continued interest in our paper. It is unfortunate that in this paper we allowed ourselves to use the term “power spectrum” erroneously in referring to what (in the formulas) was actually an “energy spectrum.” This was a mistake for which the second author bears the responsibility. The distinction between power spectrum and energy spectrum is merely that the former is a normalized version of the latter (see, e.g., Bracewell, chapter 6), and thus they are related to each other by a constant.
Reply to I. R. Qureshi by the Authors
Authors: Bhattacharyya B. K. , Navolio M. E.
Published: October 2002

In order to determine expressions for magnetic and gravity anomalies generated by a body of known shape, it is the general practice to integrate the dipolar magnetic field or the gravitational field due to a point mass over the volume occupied by the body. The digital convolution approach, as discussed in the above paper, makes it unnecessary to perform the integration analytically and to use a complicated expression for computing the anomalous potential field.
Reply by authors to discussion by Douglas J. Guion
Authors: Rudman Albert J. , Mead Judson , Blakely Robert F. , Whaley Joseph F.
Published: October 2002

The authors’ model studies depended primarily on downward continuation of the magnetic field (p. 884). Satisfactory results were obtained for magnetic models, but certain discrepancies were observed for gravity (p. 887). Mr. Guion’s comments on some differences between the observed and model gravity anomalies are, therefore, well taken. In his view these differences cannot be attributed to the manner in which the regional gradient is removed or to the choice of density contrast used in constructing the model. Our opinion is that he underestimates the importance of both of these parameters.
Reply by author to Discussion
Authors: Cribb J. L.
Published: October 2002

I apologize for leading Shuey and Wannamaker up an alluring blind alley but they do seem to have made a contribution by deriving results similar to mine but more directly by application of the Euler‐Lagrange differential equation. An earlier draft of my paper contained the disclaimer, “No claim is made that the distribution found is of any practical use, although this was hoped at the beginning of the research”. This was edited out by me during the course of revisions.
Reply by authors to Mr. Cheh Pan
Authors:   Delegation Members
Published: October 2002

The authors appreciate Mr. Pan’s interest in their report and his comments regarding governmental organization and terminology. A conscientious effort was made by the authors to be as exact as possible in all details, using various authoritative sources. Unfortunately, some of the information was conflicting and arbitrary decisions were required.
Reply by the authors to R. P. Singh and D. Rankin
Authors: Thiel David V. , Chant Ian J.
Published: October 2002

In their discussion of our paper Singh and Rankin appear not to have grasped the primary purpose of the paper, this being to report that measurements of the ratio [Formula: see text] of a VLF signal were constant during the day and night and so can be interpreted in terms of the conductivity of the earth, whereas at dawn and dusk such an interpretation is clearly not possible.
Reply by the authors to V. Babu Rao
Authors: Ku Joe C. , Sharp John A.
Published: October 2002

We would like to thank Dr. Rao for pointing out several errors in our paper. The expressions for [Formula: see text] and [Formula: see text] in equation (26) on p. 761 should read as follows.
Reply by Author to the discussion by Ramesh Chander
Authors: Green William R.
Published: October 2002

The nonuniqueness of potential field inversions makes it desirable to incorporate all available constraints into the inversion problem. Chander has correctly observed that the total mass excess (or defect) may be considered as a constraint in any gravity inversion method. Unfortunately, it does not provide an additional constraint to the gravity observations themselves, since the total anomalous mass is dependent on the gravity anomaly data.
Reply to D. Guptasarma by the author
Authors: Oldenburg Douglas W.
Published: October 2002

I agree with the points made by D. Guptasarma and thank him for bringing them to the attention of the readers.
Reply for the author to D. R. Hutchinson
Authors: Newman B. J.
Published: October 2002

The reference in my paper to “Surface consistency: A solution to the problem of deconvolving noisy seismic data” by D. Hutchinson and B. Link was to illustrate that averaging trace spectra does not eliminate noise contamination, but merely averages it. This is true whether trace autocorrelations or trace log spectra are used, and whether the data reduction is performed with a mean, median, alpha trimmed mean (as proposed in my paper), or a modal analysis. The sensitivity of these methods to excursions in signal and noise level and character varies. The mean is the most susceptible to error from highly contaminated data; the median is the most stable, provided adequate data points are available (more than 100).
Reply to T. Lee and R. Ignetik by the author
Authors: Raiche Art P.
Published: October 2002

We were aware of the “closed‐form” but did not use it for two reasons: First, [Formula: see text] and [Formula: see text] are closed form only for those who do not actually perform numerical computations. Had we used them, we would have had to express them in series form to perform our computations over the range of arguments required.
Reply by the authors to the discussion by Gijs J. O. Vermeer
Authors: Schleicher Jörg , Tygel Martin , Hubral Peter
Published: October 2002

We very much appreciate the competent comments of Mr. Vermeer concerning some topics of our paper. As he points out, the concept of an “experiment,” as used by us, is important. We, therefore, take this opportunity to better clarify it. In fact, the term seismic experiment can be given two different meanings: the first one relates, as Mr. Vermeer correctly points out, to one given source‐receiver pair, which produces a single seismic trace. The second meaning relates to a certain collection of source‐receiver pairs located according to a specific configuration or geometry. In the second case, a seismic experiment produces an organized set of seismic traces, or in other words, a configuration‐dependent seismic record section.
Multidimensional signature deconvolution and free‐surface multiple elimination of marine multicomponent ocean‐bottom seismic data
Authors: Amundsen Lasse , Ikelle Luc T. , Berg Lars E.
Published: October 2002

This paper presents a wave‐equation method for multidimensional signature deconvolution (designature) and elimination of free‐surface related multiples (demultiple) in four‐component (4C) ocean‐bottom seismic data. The designature/demultiple method has the following characteristics: it preserves primary amplitudes while attenuating free‐surface related multiples; it requires no knowledge of the sea floor‐parameters and the subsurface; it requires information only of the local density and acoustic wave propagation velocity just above the sea floor; it accommodates source arrays; and no information (except location) of the physical source array, its volume, and its radiation characteristics (wavelet) is required. Designature is an implicit part of the demultiple process; hence, the method is capable of transforming recorded reflection data excited by any source array below the sea surface into free‐surface demultipled data that would be recorded from a point source with any desired signature. In addition, the incident wavefield is not subtracted from the data prior to free‐surface demultiple; hence, separation of incident and scattered fields is not an issue as it is for most other free‐surface demultiple schemes. The designature/demultiple algorithm can be divided into two major computational steps. First, a multidimensional deconvolution operator, inversely proportional to the time derivative of the downgoing part of the normal component of the particle velocity just above the sea floor, is computed. Second, an integral equation is solved to find any component of the designatured, free‐surface demultipled multicomponent field. When the geology is horizontally layered, the designature and free‐surface demultiple scheme greatly simplifies and lends itself toward implementation in the τ‐p domain or frequency‐wavenumber domain as deterministic deconvolution of common shot gathers (or common receiver gathers when source array variations are negligible).
Reply by the authors to E. Wielandt
Authors: Ziolkowski A. , Parkes G. , Hatton L. , Haugland T.
Published: October 2002

We are very grateful to E. Wielandt for his comments and for pointing out the sloppy mathematics in the Appendix of our paper (Ziolkowski et al, 1982).