bluuebunny/crossref_metadata_2025 huggingface dataset:
A RAPID GRAPHICAL SOLUTION FOR THE AEROMAGNETIC ANOMALY OF THE TWO‐DIMENSIONAL TABULAR BODY
Authors: Bean R. J.
Published: October 2002

A graphical method of determining the depth and other parameters of two‐dimensional tabular bodies by analysis of aeromagnetic anomalies is outlined. The method uses the inflection and half maximum slope points of anomalies having either two flanks or a single high gradient. Ratios of distances between these points are used to obtain a solution. The problem is simplified by combining angles of dip, magnetization direction and the inclination of the geomagnetic field in the plane of the profile into an apparent inclination angle. By use of the graphs, the depth, width, and apparent inclination angle can be determined rapidly from only a few simple measurements, so the method is especially suited for rapid interpretation of large aeromagnetic surveys by use of the observed profiles. Graphs are also given for locating the center or edge of the block, and the product of the intensity of magnetization and the dip of the body can be obtained by utilizing the maximum slope of the anomaly. By use of alternate values of the apparent inclination angle, the method can be used for any direction of magnetization at any magnetic latitude.
DETERMINATION OF THE ELASTIC CONSTANTS OF AN ISOTROPIC SOLID USING A “PLATE” VELOCITY MEASUREMENT
Authors: Kaarsberg Ernest A.
Published: October 2002

From the longitudinal and shear wave velocities measured in a solid, all of its elastic constants can be determined. Jamieson and Hoskins (1963) have shown how shear wave velocities can be measured in solids with an arrangement which converts high frequency longitudinal wave pulses from axially polarized ceramic transducers into shear wave pulses. This note illustrates how such elastic constants can also be determined with the aid of longitudinal “infinite plate” velocities.
On: “THE GRAVITATIONAL ATTRACTION OF A RIGHT RECTANGULAR PRISM,” BY DEZSÖ NAGY (GEOPHYSICS, APRIL, 1966, PP. 362–371)
Authors: De Bremaecker J. Cl.
Published: October 2002

The recent paper by Dezsö Nagy, “The gravitational attraction of a right rectangular prism,” is certainly of great interest. It might be pointed out, however, that in his textbook published in 1930, MacMillan already gave a formula for computing the potential of this body, as well as an extremely simple method to compute the derivatives along a coordinate axis. The Dover reprint is widely available.
MAGNETIC SURVEY OF THE PUGET SOUND EARTHQUAKE ZONE
Authors: Kaarsberg Ernest A.
Published: October 2002

The Puget Sound earthquake of 29 April 1965 occurred in an area that is part of the Circum‐Pacific Seismic Belt, a region of current crustal instability and adjustment of which earthquakes are one expression. In Figure 1, the location (47.4° N, 122.3° W) of this quake’s epicenter, as determined by Algermisson and Harding (1965), is shown in relation to all the other known epicenters in the area. It is described as having a Richter scale magnitude of 6.5 and a focal depth of 60 km.
GEOPHYSICAL EXPLORATION FOR BURIED VALLEYS IN AN AREA NORTH OF TWO HILLS, ALBERTA
Authors: Lennox D. H. , Carlson V.
Published: October 2002

Geophysical techniques may be used in groundwater exploration for the detection of groundwater itself, for the detection of potential aquifers, and for the detection of geologic situations favorable for the occurrence of aquifers. In Alberta, these buried preglacial valleys commonly contain deposits of permeable sands and gravels which, if of sufficient thickness and extent, can constitute important aquifers. Thus, location of the valleys by geophysical means leads to the identification of areas in which groundwater prospecting stands an improved chance of success. If, in addition, the geophysical methods can be used to indicate whether adequate thicknesses of permeable deposits exist in the valleys—that is, to detect the aquifers—the areas suitable for exploration can be further restricted, possibly to one or more locations with particularly encouraging prospects of a good groundwater supply. Resistivity was useful for the detection of both near‐surface and deeper‐lying permeable deposits and, hence, has some potential for the tracing of buried valley courses wherever these buried valleys contain significant sand and gravel deposits. The method had limited application, however, to the measurement of depths to bedrock because of a lack of resistivity contrast between drift and bedrock materials for a great part of the study area. The seismic refraction method was reasonably successful in the determination of bedrock depths and, thus, in the location of buried bedrock valleys. Success, however, depended on advance knowledge of velocity conditions in the surficial materials and in the uppermost bedrock layers, in order to understand and deal with the interpretative problem presented by a lack of velocity contrast between drift and bedrock materials in regions of elevated bedrock. Anomalously large calculated bedrock depths for regions of elevated bedrock were summarily rejected. Another interpretative problem was posed by the presence of a blind zone within the surficial materials. Blind‐zone velocity segments were introduced on all time‐distance plots on which this characteristic velocity did not originally appear, a method successful in about two thirds of the cases. There was no indication, other than a spurious one discounted by independent evidence, of correlation between the gravity results and the distribution of buried valleys or of any near‐surface materials. The Two Hills investigation effectively demonstrated the importance of adequate control—geophysical as well as geologic—for the successful interpretation of shallow geophysical exploration results in the Alberta plains.
A METHOD OF COMPUTING RESIDUAL ANOMALIES FROM BOUGUER GRAVITY MAP BY APPLYING RELAXATION TECHNIQUE
Authors: Paul M. K.
Published: October 2002

A new method of computing residual anomalies for gravity prospecting data from a Bouguer gravity map has been evolved. In arriving at the proposed method, we have at first examined the behavior of the regional gravity field from an analytical point of view. With the concepts acquired therefrom in mind, we consider the case of square grids with such separation of stations that in an elementary area, formed by joining the four nearest stations around a central station, the regional field may be represented by a linear function of the Cartesian coordinates in the horizontal surface of observation. Making use of the formal relationship between the residual, regional, and Bouguer gravity values, we have been able to formulate in this case a set of simultaneous linear equations—one for each station of observation—with the residual values at the grid corners as the unknowns in the left hand sides of these equations and some linear function of the Bouger values at the grid corners as the known quantities in the right hand sides. With some plausible estimates of the residual values at the stations on the boundaries at hand, these equations can be solved efficiently with the aid of the relaxation technique as has been exemplified in the cases of theoretical model as well as field data.
SIGNAL STRENGTH OF MARINE SEISMOGRAPH EXPLOSIVES
Authors: Barnhard Philip
Published: October 2002

The impulse of the shock wave from an underwater explosion, as recorded under laboratory conditions, has been used to predict the signal strength of heterogeneous explosives of the nitro‐carbo‐nitrate type used in offshore seismic exploration. The changes in relative magnitude of the shock‐wave impulse due to changes in composition and to varying shot‐firing depths are reported; compositions that maximized the impulse were found for a mixture of aluminum, dinitrotoluene, oil, and ammonium nitrate. Increasing shot‐firing depth from 6 to 9 ft increased measured impulse 16 percent for charges having identical weights and compositions.
CONVERGENCE IN DOWNWARD CONTINUATION FOR SOME SIMPLE GEOMETRIES
Authors: Roy Amalendu
Published: October 2002

Laplacian fields can be continued either by the use of Taylor series, or by spectral analysis and synthesis. While the first method is applicable to non‐Laplacian fields as well, the second, as it is presently developed, is not. The convergence properties of downward continuation by these methods have been investigated for some source geometries that frequently occur in nature. The cases treated include gravity, magnetic, electrical, and electromagnetic fields. When the spectral method is used, the boundary between regions of convergence and divergence is always a plane that is parallel to the plane of observation. With the Taylor series method, on the other hand, the boundary is a hyperboloid or a combination of hyperboloids. The position of these boundaries—plane or hyperboloid—depends upon the shape of the anomaly‐causing body. For bodies with corners and edges, the plane passes through the shallowest corner or edge, or there is a hyperboloid apexed at each corner or edge so that the outermost envelope constitutes the boundary of convergence. For smooth bodies, like spheres and cylinders, these boundaries are positioned at some internal point, which, in the case of artificial‐field methods, may correspond to an image. For instance, for the gravity effect of a sphere or a two‐dimensional horizontal circular cylinder, or their magnetic and electrical effects under the influence of a uniform primary field, the plane or the hyperboloid passes through or is apexed at the center or the axis, as the case may be. The results of this paper provide the theoretical justification for using the method of continuation in interpretation of mining geophysical data, as reported empirically earlier.
THE GEOMAGNETIC GRADIOMETER
Authors: Slack Howard A. , Lynch Vance M. , Langan Lee
Published: October 2002

The geomagnetic gradiometer is a new geophysical prospecting tool which measures directly the vertical gradient of the earth’s magnetic field and the total field intensity. The system is composed of two simultaneously recording, optically pumped and monitored magnetometer sensors suspended from a helicopter. The sensors are separated vertically by a known distance so that the magnetic gradient can be determined from the difference in total magnetic intensity between the two sensors. Since the gradient is measured directly, the gradiometer allows geophysicists to make better use of LaPlace’s and Euler’s equations. The gradiometer increases the value of magnetic prospecting by: (1) greatly increasing resolving power, (2) discriminating between intrabasement and suprabasement anomalies, and (3) eliminating problems caused by diurnal variations.
On: “Geophysical Exploration for Buried Valleys in an Area North of Two Hills, Alberta” by D. H. Lennox and V. Carlson (GEOPHYSICS, April, 1967, pp. 331–362)
Authors: Burke Kenneth B. S. , Wyder J. E.
Published: October 2002

The paper “Geophysical Exploration for Buried Valleys in an Area North of Two Hills, Alberta” by D. H. Lennox and V. Carlson is a welcome addition to the literature on the application of geophysical exploration to groundwater problems. However, we must disagree with one of the statements made in this paper, and also with the presentation of widely scattered resistivity readings in the form of isoresistivity contours maps. We also wish to comment on the authors’ observation of a gradual decrease in apparent resistivity with increasingly electrode spacing in spite of there being no marked decrease in resistivity with depth in the electric‐log results.
APPLICATION OF DINOSEIS IN CANADA
Authors: Godfrey L. M. , Stewart J. D. , Schweiger E.
Published: October 2002

An experimental program was conducted to determine if a seismic system consisting of a Dinoseis, a digital recorder, and digital processing was adequate for solving exploration problems in Alberta and Saskatchewan. Several miles of data were collected and processed from three areas—Edson, Alberta; Bellshill Lake, Alberta; and Central Saskatchewan. Certain aspects exist which must be considered when using a low power, low frequency, surface source. These are ambient and coherent noise reduction, resolution of reflected events, and penetration of subsurface. They are attacked at different places in the total system by use of carefully‐designed field procedures and processing techniques. Methods of attack include stacking of multiple pulses taken at each shotpoint, selection of appropriate source and receiver arrays, common‐depth‐point coverage, and application of deconvolution and velocity and frequency filtering in the processing sequence. After processing the experimental data, a match was obtained between Central Saskatchewan Dinoseis traces and a synthetic seismogram over a frequency bandwidth of 20 to 65 cps. In Bellshill Lake and Edson, processed Dinoseis sections were comparable to processed dynamite sections, indicating that Dinoseis data was adequate to solve the geologic problem in both areas. Results are promising, and, coupled with favorable economics, warrant further exploitation of DinoSeis in Canada.
SEISMIC EXPERIMENTS WITH VERTICAL ARRAYS
Authors: Roden Robert B.
Published: October 2002

Experiments with vertical arrays of seismometers were conducted from 1963 to 1965. Data of exceptionally high quality were obtained through the use of special 1‐cps, deep‐well seismometers and direct digital recording techniques. Arrays studied experimentally contained up to 7 vertical‐component seismometers and extended to depths as great as 3.1 km. P‐wave signals observed at depth are generally distorted because of interference between incident and surface‐reflected waves. It is shown that the outputs of two or more deep‐well instruments can be combined to reconstruct signal waveforms. Small additional improvements were obtained through the application of optimum multichannel filtering to vertical array outputs, but the best signal‐to‐noise ratios obtained were never more than 6 db above those available from single deep‐well seismometers located at points of constructive signal interference. Results obtained from analysis of experimental data support the hypothesis that severe attenuation of seismic noise with depth is a characteristic only of sites where ambient noise is very intense at the surface. It is concluded that improvements in record quality which can be obtained through the application of vertical array processing at noisy sites are probably not greater than the improvements which would result from careful selection of a quiet site.
COMPUTED RESPONSE OF AN ACOUSTIC LOGGING TOOL
Authors: White J. E. , Zechman R. E.
Published: October 2002

Transient waveforms have been computed for a family of source and receiver types and for geometry corresponding to plausible acoustic logging tools in oil wells. The acoustic tool now in commercial use is one member of the family. The computations also treat flexural waves and torsional waves. All quantities are expressed in terms of appropriate vector and scalar potentials, and output waveforms are obtained by numerical evaluation of triple Fourier transforms. When loss parameters are included in the stress‐strain relations, the Fourier inversion formulas are free of singularities and numerical integration is straightforward. For the purely elastic case, it is necessary to cope with the singularities of the integrands in performing the numerical integrations. Dispersion curves and other features agree with earlier publications on wave propagation along concentric cylinders.
HOW VELOCITY LAYERING AND STEEP DIP AFFECT CDP
Authors: Cressman Kenneth S.
Published: October 2002

Normal moveout may be used to distinguish primary from multiple reflections when the average velocity changes with depth. Approximate values of normal moveout may be found using an average velocity formula, but such values are always too large. The error appears to be controlled by the ratio of the standard deviation of the velocities within the section to the average velocity. Ray tracing provides normal moveout values which agree much better with observations. As a consequence of large dip, the reflections added by the CDP method do not represent identical areas of the dipping bed. However, if the various reflection zones lie on an inclined plane, they are added in‐phase and assume the time of a reflection from a point on the plane.
EFFICIENT DECONVOLUTION OF MARINE SEISMIC RECORDS
Authors: Kunetz G. , Fourmann J. M.
Published: October 2002

Insofar as the deconvolution of marine seismic records is applied to the elimination of the effects of near‐surface layers, two methods are available to improve operator efficiency. One method is the iterative determination of a gapped deconvolution operator using a generalization of the three‐point “Backus Filter.” Another method is the derivation, by division in the z‐transform domain, of the operator that “removes” the surface and near‐surface reflectors from the section.
AUTOMATIC CONTOURING OF IRREGULARLY SPACED DATA
Authors: Pelto Chester R. , Elkins Thomas A. , Boyd H. A.
Published: October 2002

Machine contouring of irregularly spaced observations can be performed in three basic steps: (1) In large areas with no data points, control values are interpolated by a specified mathematical rule. These values keep the next step “well behaved.” (2) A regional polynomial surface is fitted by least squares to the original and interpolated points. (3) The surface of step (2) is deformed smoothly to pass through the original observations. The final product is similar in appearance to hand‐drawn maps. The complete mathematical theory is developed in an appendix.
THERMAL AND ELECTRICAL CONDUCTIVITIES OF SANDSTONE ROCKS AND OCEAN SEDIMENTS
Authors: Hutt Jeremy R. , Berg Joseph W.
Published: October 2002

Relationships between electrical and thermal conductivities of consolidated sandstone rocks and sediments were investigated. Equations given by Archie (1942) and Woodside and Messmer (1961) were combined to give an equation which relates the two conductivities for the rocks. Equations relating conductivity and porosity, given by Maxwell (1881), Bruggeman (1935), and Woodside and Messmer (1961) were combined to give two equations which relate thermal and electrical conductivities for sediments. Data from 65 rock samples and 105 sediment samples (including data for 37 rock samples published by Zierfuss and Van der Vliet, 1956) were use establishing the reliability and parameter values of the equations. The derived equations can be used to determine thermal conductivities from electrical conductivities providing thermal conductivities of the solid constituents can be approximated. For samples of sandstone rock, deviations of the data from values predicted by the equations are shown to be related to the variations in composition of the samples. Within the accuracy of the data, the thermal conductivities of sediment samples seem to be controlled more by the water content than by the mineral composition.
On: “Preferential excitation of refracting interfaces by use of a source array” by S. J Laster and A. F. Linville (GEOPHYSICS, February 1968, p. 49–64)
Authors: Meyer Robert P. , McCamy Keith
Published: October 2002

While we have no quarrel with the content of the paper (actually hearty agreement), we think that it is important that some acknowledgment of previous work in quite exactly the same field be made in articles published in Geophysics.
SECTIONAL CORRELOGRAMS AND CONVOLUTIONS BY A SIMPLE OPTICAL METHOD
Authors: Jackson Philip L.
Published: October 2002

Sectional correlograms, which have been shown recently to be interpretively valuable in several ways, can be obtained with a simple optical method. A visual presentation of sectional correlograms can be obtained from variable‐density or variable‐area record sections. Individual autocorrelations, selected crosscorrelations, or sums of selected correlations can be displayed simultaneously for all channels in a conventional section. The display is economically and simply achieved by using an elaboration of the Robertson technique of optical correlation. A two‐dimensional correlation function is obtained with the basic Robertson technique. With the addition of a cylindrical lens and an adjustable slit, many simultaneous selective one‐dimensional correlations can be obtained; thus, sectional correlograms with seismic transparencies can be produced. Because a broad‐band, incoherent light source is employed, this optical method can be used with a pattern on a CRT as data input.
On: “Refraction Determination of Water Table Depth and Alluvium Thickness” by James Otto Duguid (GEOPHYSICS, June 1968, p. 481–488)
Authors: Sendlein Lyle V. A.
Published: October 2002

Mr. Duguid’s study provides an opportunity to compare borehole information with shallow seismic refraction data. The single geophone technique is well adapted to very shallow refractors such as those present in this study.
GEOPHYSICAL ACTIVITY IN 1967 APPLIED TO MINING EXPLORATION
Authors: Hood Peter J. , Kellogg William C.
Published: October 2002

Data on world‐wide geophysical activity in mining exploration programs is collected annually by the SEG Geophysical Activity Committee as part of a continuing service to the industry. The data is obtained by sending out questionnaires to all organizations which are known to be carrying out mining geophysical work; the organizations canvassed include mining companies, contractors, government departments and universities. The questionnaire is divided into three sections, namely ground methods, airborne methods, and research. The data compiled from the questionnaires shows that world‐wide utilization of mining geophysical methods reached a new high in 1967 with total expenditures of U.S. $32,323,240. This was divided as follows: ground methods—$18,106,785; airborne methods—$10,123,405; and research $4,093,050. For the ground methods, most money was spent on the induced‐polarization technique ($5,681,780); electromagnetic methods were second in reported expenditure ($2,010,900). Total reported geophysical line‐mileage flown was 1,275,072 line‐miles, with aeromagnetic surveying being the most popular airborne method. Total amount spent on aeromagnetic surveys was $5,832,564 for 895,420 line‐miles. This gives an average cost for aeromagnetic surveys of $6.50 per line‐mile.
GEOPHYSICAL ACTIVITY IN 1967 APPLIED TO ENGINEERING, CONSTRUCTION, AND GROUNDWATER PROJECTS
Authors: Melickian G. E.
Published: October 2002

1967 marks the third year that the Society has attempted to survey geophysical activity applied to groundwater, engineering, and construction projects. For the last two years, these data were developed from a separate questionnaire. For 1965 activity, the information was obtained from the mining questionnaire.
LINEAR PHASE FILTERING OF MULTICOMPONENT SEISMIC DATA
Authors: Mercado E. J.
Published: October 2002

The phase relationships between the vertical and horizontal components of motion at a free surface differ between the various modes of propagation. These differences in phase between the components of motion may be made the basis for a linear filtering technique to separate P, S, and Rayleigh waves when the components of motion at the free surface are recorded in reproducible form. In this paper, a set of linear filters is derived and applied to some three‐component reflection seismograph field data that separate P and Rayleigh wave motion on the basis of their phase relations between horizontal and vertical components of motion at the free surface. A comparison is made between the linear phase filtering technique, and the “Polarization Filtering” technique of Shimshoni and Smith, and a multichannel Wiener deconvolution using the vertical and horizontal components of motion as input channels.
NORMAL‐MOVEOUT AND VELOCITY RELATIONS FOR FLAT AND DIPPING BEDS AND FOR LONG OFFSETS
Authors: Brown Robert J. S.
Published: October 2002

Accurate relations between NMO and velocity are needed in modern exploration seismology, especially in long‐offset CDP work, where accurate NMO corrections must be made for stacking, and where several types of velocity averages may be computed with accuracy from NMO data. The velocity average associated with NMO is the time‐rms velocity [Formula: see text]. Even for long offsets the straight‐ray computation using [Formula: see text] is usually adequate, but a closer approximation for horizontal reflectors is obtained by reducing the NMO calculated from [Formula: see text] or reducing the value of [Formula: see text] calculated from NMO by the factor [Formula: see text], where σ is the rms deviation of the velocity from its mean, T is zero‐offset traveltime, and ΔT the NMO. The difference between time‐average and time‐rms velocities is often several percent. For the velocity function [Formula: see text] and for reflectors of arbitrary dip and strike, the NMO is shown to be [Formula: see text] where X is offset, α is emergence angle, and ψ is the angle between the offset direction and the reflector dip direction. The terms that contain angles can be used as a correction ΔΔT to the NMO value computed as if the seismic energy were reflected from a horizontal reflector, even for offset greater than those for which an NMO expression quadratic in offset is accurate. A further approximation gives [Formula: see text], where δT is dip moveout over a spread of length L, and [Formula: see text] is the angle between the receiver line and the dip direction, differing from ψ only if there is substantial perpendicular offset of the source point. An expression for the degradation of the stacked signals in CDP stacks because of NMO errors is given. It is shown that the criterion that the signal‐to‐random‐noise ratio could not be improved by dropping the longest‐offset trace(s) requires that the NMO error be not much larger than one‐quarter of a dominant period.
MODEL STUDY OF RADIATION FROM AN EXPLOSION IN A CIRCULAR DISK
Authors: Bahjat Dhari S. , Kisslinger Carl
Published: October 2002

The effect of the medium immediately surrounding the shot on the properties of the primary compressional waves has been studied by means of two‐dimensional models. Circular disks of Plexiglas and Styrofoam of various diameters were inserted in large sheets of aluminum and of Plexiglas, respectively. Charges were fired in the center of the disk. An approximate theory for radiation from a simple harmonic line source of P waves on the axis of a solid circular cylinder embedded in an infinite homogeneous solid medium has been developed. The transfer function of the disk has been calculated from the observed spectra in order to compare it with the frequency response calculated from theory. The results show that for these cases of a low‐velocity disk a peak frequency exists which decreases with increasing diameter. The maximum peak frequency is that for a shot in an infinite sheet of the high‐velocity material, and the minimum peak frequency is that for a shot in a sheet of the low‐velocity disk material. This minimum peak frequency is approached rapidly as the disk diameter increases. The geometric effect of radiation from the circular inhomogeneity is important only over a narrow range of cavity diameters for which the resonance associated with the cavity happens to fall near the peak of the spectrum of the explosion‐generated wave.
HRVA—A VELOCITY ANALYSIS TECHNIQUE APPLIED TO SEISMIC DATA
Authors: Robinson John C.
Published: October 2002

A High‐Resolution Velocity Analysis (HRVA) has been developed which can be employed for the determination of the rms subsurface velocity energy spectrum from gated seismic data which has been NMO corrected. All calculations are performed in the frequency‐space or frequency‐wavenumber domain; seismic gates are transformed from the time‐space domain via the Fast Fourier Transform algorithm. HRVA is not restricted to the investigation of apparent horizontal velocities which have associated stepout values that are integral multiples of the time sampling interval, as are the existing correlation techniques. The technique liberally exploits the usual inexistence of significant energy in the higher frequency harmonics of seismic data, resulting in a considerable time saving. The technique is illustrated with West Texas seismic data. The results are discussed as a means for deriving a more accurate rms subsurface velocity function for NMO corrections and subsequent stacking, and as a means for various lithologic investigations.
SCATTERING OF A TRANSIENT, SPHERICAL P WAVE BY A RANDOMLY INHOMOGENEOUS, ELASTIC HALF‐SPACE
Authors: Dunkin John W.
Published: October 2002

Random inhomogeneities in an elastic half‐space generate scattered P and S waves when excited by a spherical P wave initiated at the surface. The scattered energy can be characterized by statistical correlations of the displacement components at two receivers on the free surface. Based on the assumptions of far‐field Rayleigh scattering, a simple perturbation theory, and the neglection of boundary effects, simple expressions can be obtained for the correlations. They are composed of weighted sums of partial correlations which are associated with combinations of P and S waves arriving at the two receivers. The partial correlations depend on the times at the two receivers, the distance between the source and the receivers, and the separation between the receivers. The weighting factors depend on the statistical properties of the random elastic parameters. Although the analysis is carried out for an impulsive source, the correlations for a more general source can be found by performing a single convolution. If the transient input pulse is appropriately prefiltered before convolution, the effects of energy loss during propagation can be taken into account, approximately.
On: “A Method of Computing Residual Anomalies from Bouguer Gravity Map by Applying Relaxation Technique,” by M. K. Paul (GEOPHYSICS, August 1967, p. 708–719)
Authors: Biesheuvel K.
Published: October 2002

The following comments on this new method indicate some limitations of the technique as well as a more practical means of solving the equations involved by high‐speed digital computer.
CONTINUATION OF ELECTROMAGNETIC FIELDS—II
Authors: Roy Amalendu
Published: October 2002

Given the values observed on a plane parallel to a horizontal ground surface, solutions are obtained for the continuation of dynamic electromagnetic fields upward in air or downward into a conducting earth. The upward (away from secondary sources) continuation integrals for the real and imaginary parts of any electromagnetic field component with arbitrary frequency and in a medium with arbitrary electrical and magnetic constants are derived and simplified to the case where the conductivity is zero. However, for frequencies normally used in electromagnetic prospecting, the effect of displacement current is negligible and one does not need to use the rigorous formulas derived, because adequate accuracy can be obtained by using the simpler static field formulas for continuation in a nonconducting medium such as air. The central problem in electromagnetic continuation is one of extrapolating the observed field from one medium to another through a physical boundary, namely, the air‐earth interface. From the magnetic field observed in air, one should be able to compute the same within the conducting earth. Conversely, from the electric field observed within the ground or on its surface, one should be in a position to calculate the same in air and also, of course, deeper into the ground. The continuity conditions for the vertical derivatives of the electromagnetic field components, which constitute the basis for continuing an electromagnetic field from one medium to another, are derived. Downward continuation formulas, suitable for practical use, are derived explicitly, through use of a Taylor expansion, for the vertical component of the magnetic field in air, this being the quantity which is commonly measured. Three‐dimensional downward continuation formulations to depths of one and two units of grid spacing and two‐dimensional continuation to a depth of one unit of grid spacing are derived under the assumption that the effect of displacement current can be neglected.
ELECTROMAGNETIC INDUCTION IN A SOLID CONDUCTING SPHERE ENCLOSED BY A THIN CONDUCTING SPHERICAL SHELL
Authors: Wait James R.
Published: October 2002

By means of a straightforward boundary‐value treatment, a solution is obtained for the electromagnetic response of a homogeneous sphere enclosed by a uniform spherical shell. A quasi‐static assumption is invoked at the outset because attention is directed to slowly varying fields. Expressions are derived for the “in‐phase” and “quadrature phase” response of the induced multipoles. These are a function of the radius, conductivity, and permeability of the core, and the radius, conductivity, and thickness of the shell. Some numerical results for the nonpermeable case indicate that the dependence of the dipole response on the normalized core radius is altered significantly by the presence of the shell. On the other hand, the ability to detect the presence of the core is not greatly impaired.
HYDROSTATIC PRESSURIZATION OF MAGNETITE
Authors: Carmichael R. S.
Published: October 2002

Study of the effect of mechanical deformation on magnetic minerals indicates the structure‐sensitive character of a parameter such as coercive force. Magnetoelastic effects and stress‐induced rearrangement of the magnetic domain pattern lead to changes in magnetic remanence. Such work has relevance to basic studies in rock magnetism and paleomagnetism. The effect of increase in hydrostatic pressure on rocks with depth may have application in geophysical prospecting. For example, it could be a factor in the interpretation of magnetic well logging for remanence (Frey, 1951; Khramov, 1957) and susceptibility (Broding et al, 1952; Anderson, 1968), or interpretation of magnetic anomalies from deep‐seated sources.
THE LOCATION OF SPHERICAL CAVITIES USING A TRIPOTENTIAL RESISTIVITY TECHNIQUE
Authors: Habberjam G. M.
Published: October 2002

The surface gravitational and magnetic field anomalies due to a contrasting spherical body at depth are well known and appear in geophysical textbooks. The corresponding problem of the anomaly in apparent resistivity arising from such a body, owing to its conductivity contrast, is less frequently referred to because of the lengthy potential solutions involved. In electrical interpretation, few potential solutions exist for buried bodies of limited three‐dimensional extent, and consequently the simplest of these problems, the buried sphere, has received particular attention. Following early work by Hummel (1928), Webb (1931) produced potential solutions for this problem, and more recently Lipskaya (1949) has derived solutions and computed extensive numerical results. For the particular case of an infinitely conducting sphere, Van Nostrand (1953) has computed comprehensive numerical solutions, and more recently Van Nostrand and Cook (1966) presented a very detailed account of work on the buried sphere.
NEGATIVE ELECTROMAGNETIC SCREENING BY A CYLINDRICAL CONDUCTING COVER
Authors: Negi Janardan G. , Raval Upendra
Published: October 2002

The paradoxical augmentation of the electromagnetic response of an inner core by a conducting cover is reexamined by investigating the behavior of a cylindrical model to establish the geometrical independence of the negative screening phenomenon. The theory is developed for the coaxial cylindrical system in analogy with the spherical case. Results of numerical evaluation of the analytical expressions for the screening factor prove the geometrical independence of the phenomenon of negative screening, as indicated in earlier studies.
On: “Method of Computing Residual Anomalies from Bouguer Gravity Map by Applying Relaxation Technique” by M. K. Paul (GEOPHYSICS, August 1967, p. 708–719)
Authors: Uren N. F.
Published: October 2002

Dr. M. K. Paul suggests that further investigation of this method may be necessary. The theoretical basis for this method is that [Formula: see text] i.e., that the regional gravity field obeys Laplace’s equation in two dimensions over the plane of observation.
DESIGN OF RECURSIVE FILTERS
Authors: Aguilera Raymundo , Debremaecker J. CL. , Hernandez Salvador
Published: October 2002

Recursive filters are inherently more efficient than purely transverse or purely regressive ones. They can be computed in the frequency domain by a series of simple operations. The roots of the denominator must be computed and the moduli less than unity replaced by their inverses. If such an operation is also performed on the numerator, the resultant recursive filter is minimum phase. The same method can be used to construct a deconvolution operator in the time domain, starting with the autocorrelation. Two examples are given which show the efficiency of the method.
On: “A Method of Computing Residual Anomalies from Bouguer Gravity Map by Applying Relaxation Technique” by M. K. Paul (GEOPHYSICS, vol. 32, no. 4, p. 708–719, August, 1967)
Authors: Meinardus H. A.
Published: October 2002

On page 711 the author, after reference to previous users of the least‐squares method for estimating residuals in a Bouguer gravity map, states, “All of them have used the method for estimating the residual field over the entire area under consideration, while in this case the method will be applied to obtain the same on the boundaries only.” He then proceeds to compute residuals on the boundaries from the second degree polynomial [Formula: see text], (10) representing the regional field over the entire region. However, by this procedure the residuals on the boundaries are influenced by all the gravity observations inside the region, as implied by equation (16) where the vector A is a function of the Bouguer map values over the whole area. In fact, equation (12) could be solved for the vector b, and the condition [Formula: see text] arising from [Formula: see text] (A) could be introduced. The following expression for the regional over the entire area results: [Formula: see text], and there is no need for additional computations by the relaxation technique described.
A PREDICTED PEDESTAL EFFECT FOR PULSE PROPAGATION IN CONSTANT‐Q SOLIDS
Authors: Strick E.
Published: October 2002

Under the assumption of almost constant‐Q behavior of solids over a wide range of frequencies, together with some meaningful assumptions about the linear frequency behavior of the attenuation function, we have been able to obtain theoretical expressions describing the waveform distortion of an impulse‐excited plane wave as it decays and spreads on passing through large distances of the solid. When typical values for the parameters (as obtained from laboratory model or short range field experiments) for a solid having a mechanical Q of about 50 are used, the resulting waveforms at first glance appear to have a simple and not unexpected behavior. The peak amplitude of the waveform in the time domain varies roughly with the inverse of the square of the travel distance (this includes an inverse first power due to geometrical spreading). Also, a spreading of the waveform occurs that varies roughly linearly with the travel distance. This spreading is such that a positive impulse simply broadens as it travels without developing any zero crossings in its wave shape. However, it turns out that the part of the waveform leading up to the visible onset does not admit of a purely elastic interpretation, so that one cannot relate conceptually the arrival time with a purely elastic‐wave velocity. For our solid of Q≈50, about one‐seventh of the arrival time duration is due to a purely inelastic behavior; during this period of inelastic behavior the amplitude is not zero but it is deceptively small. We have designated this portion as a “pedestal.” On observing seismic records, we are never aware of this conceptual division and consequently attribute to the observed arrival an elastic wave velocity, which in our example happens to be about 15 percent less than the actual elastic wave velocity of the solid. Although the existence of the pedestal may not appear to be significant when we restrict our observations to seismic records limited in bandwidth to the low frequencies encountered in exploration or earthquake seismology, an upward curvature which is not associated with a discontinuity in the slope at the time of visual onset will remain and can be of great importance if very accurate arrival time measurements are made. This part of the pedestal can become even more important when we consider refraction arrivals, where the onset undergoes an additional time integration that further enhances the upward curvature of the pedestal.
ELECTROMAGNETIC INVESTIGATION OF THE SEA FLOOR
Authors: Coggon J. H. , Morrison H. F.
Published: October 2002

Numerical evaluation of integral expressions for the fields about a vertical magnetic dipole in the sea allows analysis of the electromagnetic response over wide ranges of sea induction number and sea floor conductivity. Our analysis indicates that a marine electromagnetic system for measurement of bottom conductivity variations could readily be designed, with such applications as oceanographic and geologic studies, and mineral exploration. For a source‐receiver system on a homogeneous sea bottom, it is found that: (i) when the ratio k=(sea‐bed conductivity)/(seawater conductivity) is greater than about 0.03, both horizontal and vertical magnetic fields are useful for measurement of bottom conductivity at sea induction numbers less than 30 [induction number =√2 (horizontal transmitter‐receiver separation/skin depth)]. A separation of 30 m and frequencies in the range 300–3500 hz appear suitable for investigation of the upper few meters of unconsolidated bottom sediments. (ii) When the ratio k is less than 0.03, sea induction numbers from 10 to a few hundred are required for detection of seabed conductivity variations. In this case, the horizontal magnetic field, resulting from energy transmission mainly through the seafloor, is the suitable field to use. Electromagnetic sounding of indurated rocks may thus call for frequencies of 100 to 20,000 hz at a separation of 200 m. Field strengths vary strongly with relative sea depth D/R (D=sea depth, R=horizontal source‐receiver separation) when D/R is small; but sensitivity to bottom conductivity is little affected by D/R. Elevation of source and receiver above a seafloor less conductive than seawater reduces field strengths and sensitivity to seabed properties.
INDUCTIVE SOUNDING OF A LAYERED EARTH WITH A HORIZONTAL MAGNETIC DIPOLE
Authors: Dey Abhijit , Ward Stanley H.
Published: October 2002

A complete solution of the boundary value problem of a horizontal magnetic dipole over homogeneous and n‐layered half‐spaces is outlined. Quasi‐static expressions for the electric and magnetic fields have been obtained and a comparison of the complete solution with the quasi‐static approximation in practical frequency ranges is made. An analysis of the phases and amplitudes of the magnetic field components and of the polarization parameters of the magnetic field reveals that the phase of the vertical component of the magnetic field and the ellipticity of the magnetic field polarization ellipse are the most sensitive indicators of layering. Amplitude measurements are, in general, less effective than phase measurements for resolution of layered earth structures. Results from both parametric and geometric modes of sounding have been studied in detail for a number of two‐ and three‐layered models of varying thicknesses and conductivity contrasts. Deduction of layering for different thicknesses of the top layer from the measurements of [Formula: see text] and polarization parameters, seems relatively easier when the underlying layer is more conductive than the top layer. For models in which the underlying layer is less conductive than the top layer, the phases of both [Formula: see text] and wave tilt are more diagnostic of changes in layer parameters.
PLANE AND SPHERICAL TRANSIENT VOIGT WAVES
Authors: Balch A. H. , Smolka F. R.
Published: October 2002

The combination of high‐speed digital computers and recursive finite difference schemes has become a powerful tool in the theoretical analysis of seismic wave propagation. Using this tool, we have obtained solutions to the viscoelastic, or Voigt, wave equation under the following conditions: First, a pressure impulse is applied to the surface of a spherical cavity in a spherically symmetric system; and, second, an arbitrary function is applied to the surface of a semi‐infinite body in a rectangular system. At and near the cavity wall, the cavity radius appears to be the dominant factor in determining the wavelet shape. The viscosity of the medium plays a minor role. At large distances from the cavity, the pressure impulse response of the medium is controlled by the viscosity. Poisson’s ratio has a small but noticeable effect on the wavelet shape near the source. In the plane‐wave case, our results are in good agreement with those given by Collins (1960) near the source and those of Ricker (1943, 1953) at large distances from the source.
PHASE MEASUREMENTS OF ELECTROMAGNETIC FIELD COMPONENTS
Authors: Cornille Patrick
Published: October 2002

A method of phase measurement of electromagnetic field components produced by dipoles on a stratified conducting half‐space is described. A symmetric process with a high frequency transmitter and two high frequency receivers is used in order to get a phase reference. This method has been applied to the measurement of the phase of the component [Formula: see text] radiated by a horizontal electrical dipole on a stratified conducting half‐space. The expression for the phase of [Formula: see text] for a N‐layered medium is calculated numerically. Computations for a three‐layered model show good agreement with the measured results.
LEAST SQUARES SMOOTHING OPERATORS
Authors: Wood Lawrence C. , Hockens Sidney N.
Published: October 2002

Smoothing data to extract desired trends has been standard scientific and engineering practice for many years. Use of polynomials in a least squares sense to accomplish this end has also been conventional procedure, and it is well known that smoothing acts as a low‐pass filter. However, detailed analysis of filtering behavior is lacking in the literature and should be useful to geological and geophysical data processors. This paper has two objectives: to review least squares polynomial smoothing and to discuss some z‐transform properties of the convolution operator that implements the smoothing. These operators have real, symmetrical coefficients that lead to z‐polynomials having roots lying in unique patterns. Zeros occur in complex conjugate pairs that are also inverse points with respect to the unit circle. Polynomials of order 2M and 2M+1 produce identical operators; thus, no differences exist in smoothing between polynomials of order 0 or 1, 2 or 3, 4 or 5, . . , 2M or 2M+1. A result of fitting a polynomial of order 2M to n+1 data points in a least squares sense is that exactly n−2M roots lie on the unit circle, whereas 2M zeros have magnitudes other than unity. Of the 2M roots lying off the circle, polynomials of orders, 2, 6, 10, 14… have exactly two positive, real roots while those of orders 4, 8, 12, 16… have no roots that are positive and real. Zeros lying on the unit circle influence principally the passband, reject band, and reject level. Roots lying off the circle, on the other hand, mainly control the rolloff rate. Several figures illustrate how an interpreter can use this knowledge to help in choosing the number of points and orders of polynomials required to smooth data of various kinds: gravity, magnetics, electrical, well log, stratigraphic. The least squares weights also apply to array design.