ALBERT

Notes: This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR998:GPR_998_mu1"/〉 . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).

Notes: The response of a seismic model to excitation by a source can be represented in terms of the action of reflection and transmission operators for portions of the structure. This approach provides a flexible framework for both modeling and processing problems.The operator development provides a physical description of the wave propagation process and, via the expansion of reverberation operators, gives a mechanism for assessing the accuracy of approximate developments. The representation suggests new ways of developing modeling algorithms by balancing the computational effort expended on minor and major features of the model.For processing problems, the operator representation shows the relation of processing stages to the seismic wave field and thereby indicates effective sequences of operations. For migration it is possible to specify an ideal pre-stack migration procedure in terms of the inverse of the propagation operators and to examine the problems which need to be overcome by practical algorithms.

Notes: A numerical method is presented for direct interpretation of resistivity sounding measurements. The early part of the resistivity transform curve derived from field observations by standard methods is approximated by a two-layer curve. The resistivity of the first layer is determined from the arithmetic mean of the successive computations which are carried on each of three successive discrete values of the resistivity transform curve. Using this mean value of the resistivity, the thickness of the first layer is computed from the sample values in pairs of the resistivity transform curve. After these determinations, the top layer is removed by Pekeris's reduction equation. The parameters of the second layer are obtained from the discrete values of the reduced transform curve (which corresponds to the second part of the resistivity transform curve) by the same procedure as described for the first layer.The same computational scheme is repeated until the parameters of all intermediate layers are obtained. The resistivity of the substratum is determined from the reduction equation.

Notes: In odd-depth structure the two-way traveltime to each boundary is constrained to be an odd integer. The odd-depth property of a model is exposed to possible refutation under a seismogram test. Test function is a simple transformation of a synthetic seismogram. For an odd-depth model the test function has identically the value 1.The testability of a synthetic seismogram over an odd-depth structure provides a method of deterministic deconvolution. There is no need of specialized assumptions, like the minimum-phase property, about the source wavelet. The deconvolution may be performed in the absence of the early segment of a seismogram.

Notes: Zero-offset-source VSP surveys provide information about the subsurface only within the Fresnel zone centered at the well. Offsetting the source location moves the reflection zones away from the well thus providing lateral cover.Conventional processing of this type of data gives rise to a distorted image of the subsurface. Using a simple ray-tracing scheme, this image may be reconstructed into the more familiar coordinate system of the surface seismic section. This simple data-independent mapping is based on the assumption of horizontal layering and requires a vertical velocity profile.The technique of placing the source away from the borehole was first applied to the single-offset-source VSP survey. However, data from any survey geometry (such as deviated well with rig source, walkaway VSP, etc.) can be mapped to the coordinate system defined by the appropriate seismic section.To obtain the best results from this type of survey the target area must be defined and simple modeling techniques used to optimize the source location(s). These pre-survey modeling methods may also be used to anticipate—and hence avoid a number of problem areas which experience has highlighted.The data from any VSP survey is the result of a realizable experiment and as such obeys the wave equation. This implies that the wave equation may be used to migrate the data to its true subsurface location. Theoretically, such a process is more secure than ray-tracing techniques, although its practice presents many difficulties.

Notes: A mathematical expression for potential of a direct current point source in an inhomoge-neous anisotropic earth is derived. The coefficient of anisotropy is given by f= (σr/σz), where σr and σz are the conductivities parallel and perpendicular to the bedding plane. It is assumed that σz varies with depth, whereas σr varies transversely. This potential may be useful in interpretation of geoelectrical data in specified geological situations. Master curves for Wenner and Schlumberger configurations are presented

Notes: Total magnetic intensity contour maps for the study region (between 2°E to 10°E and 56°N to 60°N) were digitized and converted to a regular grid of 285 × 285 points. The study area measures approximately 444 km × 444 km and the grid spacing is thus 1. 56 km. The International Geomagnetic Reference Field for 1975 was gridded for the above-used net, and from the two data sets a further grid of the ▵T field was generated. A large number of profiles were constructed which were suitable for depth determinations. The regular grid ▵T data is also convenient for the computation of the second vertical derivative. Using the method of vertical prisms of Vacquier et al. (1963), a large suite of curvature-depth indices was measured to complement the depths obtained from the intensity slopes and from boreholes which reach the crystalline basement. The depth to the magnetic basement has been contoured, and the resulting map is shown to be in good agreement with what is known about the deeper geology of the study area.The work reported here is part of a research project supported by Amoco Norway, BP Petroleum Development Ltd, Elf Aquitaine, Esso Exploration and Production, Norwegian Gulf, Norsk Hydro, Mobil Exploration Norway, Norwegian Petroleum Directorate, Royal Norwegian Council for Scientific and Industrial Research (NTNF), Norske Shell, and Statoil.

Notes: Geophysical inversion involves the estimation of the parameters of a postulated earth model from a set of observations. Since the associated model responses can be nonlinear functions of the model parameters, nonlinear least-squares techniques prove to be useful for performing the inversion. A common type of inversion applies iterative damped linear least squares through use of the Marquardt-Levenberg method. Traditionally, this method has been implemented by solving the associated normal equations in conventional ways. However, Singular Value Decomposition (SVD) produces significant improvements in computational precision when applied to the same system of normal equations. Iterative least-squares modeling finds application in a wide variety of geophysical problems. Two examples illustrate the approach: (1) seismic wavelet deconvolution, and (2) the location of a buried wedge from surface gravity data. More generally, nonlinear least-squares inversion can be used to estimate earth models for any set of geophysical observations for which an appropriate mathematical description is available.

Notes: In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer.In order to evaluate the closed-form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray-tracing techniques.It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high-velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields.In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples.Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis.The numerical evaluation of the analytical solution of the wave equation as described in this paper has a long history. Most of the work leading to this paper was carried out by one of us (M. J. K.) in the years 1957 to 1968 at the Geophysical Research Corporation. However, the full testing of the various computer codes was carried out only very recently at the Phillips Petroleum Company.

Notes: In South and Central Goa iron ore occurs in two parallel belts with the general NW-SE Dharawar trend. The ore occurrence, however, is not continuous. There are barren zones as well as zones of very high concentration in some of which there are mining activities.Landsat MSS data have been interpreted over a zone covering both mineral belts in order to delineate the ore occurrences. As a guide line a known ore-bearing area has been considered along with the unknown zones.On the basis of two-dimensional plotting of gray level values it has been found that the MSS bands 4 and 7 are most suitable for the studies over iron-rich areas in Goa. Two techniques are described here for the processing of the MSS data; the separation of residual from the regional and MSS band-ratioing. It is observed that (i) the gray level residual maps of MSS bands 4 and 7 are of use in demarcating the iron-ore-bearing zones, and (ii) an existing mine, an abandoned mine, and a proved iron ore zone could be delineated by MSS band-ratioing. On the basis of the latter technique, a few areas with ore occurrence potential have been indicated.

Notes: The most common source of seismic energy is an explosion at some depth in a borehole. The radiated waves are reflected not only at the subsurface layers but also at the free surface. The earth's surface acts as a generator of both P- and S-waves.If the source depth is much less than the dominant wavelength the reflected waves resemble closely the waves generated by a single force. Theoretical seismograms were computed with different methods to look for the relevance of the surface-reflected waves. The numerical experiments show reflected shear waves even for small shotpoint—receiver distances. Due to their polarization these waves can be detected most easily on in-line horizontal geophones. The existence of these waves was examined during a conventional survey in Northern Germany. Conventional data analysis shows a large variability in the νp/νs ratio. The method used here produced a shear-wave section with a rather good signal-to-noise ratio down to 4 s S-wave reflection time.

Notes: We describe the concept of physico-geological models (PGMs) in geophysical exploration. They represent a “general model”, a spatial combination of a set of particular models (disturbing bodies). The modeling is called complete, incomplete or approximate, depending on the degree of characterization of the PGM by parameters such as dimension, shape and petrophysical property. Each of the three modeling types can be realized as a conceptual, and analytical, or a material PGM. Both deterministic and stochastic PGMs exist; deterministic models are mainly used to investigate the possibilities of a geophysical method, while stochastic models serve to substantiate complex geophysical interpretations.Depending on the geological problem, PGMs are subdivided into multi-alternative models (geological mapping, prediction, general prospecting) and double alternative models (specialized prospecting).An exploration-oriented classification of the PGMs of mineral deposits is discussed. According to this classification the variety of known genetic deposit types is reduced to a limited number of generalized PGM types. The development of typical PGMs is illustrated with examples of magnetitic deposits of Siberia.

Notes: An inverse problem is one in which the parameters of a model are determined from measured seismic data. Important to the solution of inverse problems is the issue of whether or not a solution exists. In this paper we show, in a constructive manner, that a solution does exist to the specific inverse problem of determining the parameters of a horizontally stratified, lossless, isotropic and homogeneous layered system that is excited by a non-normal incidence (NNI) plane wave. Mode conversion between P- and S-waves is included.We develop a seven-step layer-recursive procedure for determining all of the parameters for layer j. These parameters are P-wave and S-wave velocities and angles of incidence, density, thickness, traveltimes, and reflection- and transmission-coefficient matrices. Downward continuation of data from the top of one layer to the top of the next lower layer is an important step in our procedure, just as it is in normal incidence (NI) inversion. We show that, in order to compute all parameters of layer j, we need to (and can) compute some parameters for layer j+ 1. This is a non-causal phenomenon that seems to be necessary in NNI inversion but is not present in NI inversion.

Notes: The suitability of VLF ground surveys in the investigation of shallow two-dimensional structures is analyzed. For such structures the polar formalism is derived, necessary in practice since the transmitters are generally not in the structural strike or profile. A simple vertical dike is considered to demonstrate the striking anisotropy which can be expected over such a structure, in particular the high apparent resistivity along the direction of a well-conducting dike and the low resistivity across it. The theory is then confronted with the practical example of an asymmetrical vertical dike resulting from a strike-slip fault. Modelling of the survey results is very successful and yields good confirmation of the polar behaviour. VLF ground surveys thus provide a quick and powerful tool for the study of geological accidents within about 100 m of the surface.

Notes: A new mode of operation for the Turam electromagnetic exploration system is proposed in which the transmitter loop is placed across the expected trend of a conductor and the receiver is operated along lines parallel to one side of the transmitter. The concept appears to offer several benefits which include greatly extended traverse length, the use of large coil spacing, rejection of the effects of conductive environments, and consistency in the indication of target dip.

Notes: Determination of thickness of sediments (usually of high conductivity) overlying a high-resistivity basement is one of the basic problems of electrical exploration methods. This paper proposes to determine horizontal electrical conductance on the basis of impedance calculated from electrical and magnetic fields of distant quasi-static (low-frequency) point sources. Using the proposed method, horizontal conductance of the sediments can be determined also from artificial quasi-static noise-impulses coming from sources of unknown position and intensity. The results of analogue modeling and field examples prove the potential of the proposed technique.

Notes: Since the early years of seismic surveying, field engineers and observers have been faced with the appearance of interference at power-line frequency (and harmonics) on seismic records: 60 Hz in the Americas, 50 Hz in Eurasia; and 16 2/3 Hz (the train supply frequency in Germany, Austria, and Switzerland) in part of Europe. Such interference is picked up from the ground surface through electric leakage between geophone leads and ground.To minimize power-line interference, the autobalancer automatically performs a balancing procedure by adjusting two potentiometers on each channel—essentially the same operation as manually performed by seismic operators for decades. The first 24-channel system became operational in 1977.The first-generation design comprised two 256-position electronic switching potentiometers. Over 4 years of experience with this system in all parts of the world has shown its value under a variety of field conditions. Improvements up to 30 dB were often found, sometimes even up to 40 dB. Balancing time was about 30 s.A second-generation design was field-tested in 1981. Potentiometer stepping is now performed at three levels: coarse, medium, and fine. This leads to faster operation and better resolution: balancing time is about 10 s; improvements up to 60 dB are occasionally found.A later modification gives a further reduction of the balancing time to 5 s in 60 Hz areas or 6 s in 50 Hz areas.

Notes: The technique of digital linear filtering is used for transformation of apparent resistivity data from one electrode configuration into another. Usually filter spectra are determined via the discrete Fourier transforms of input and output functions: the filter characteristic is the quotient of the spectra of the output function and input function.In this paper, the transformation of the apparent resistivities is presented for four electrode configurations (Wenner, the two-electrode, Schlumberger, and dipole configurations). In our method, there is no need to use the discrete Fourier transform of the input and output functions in order to determine the filter spectrum for converting apparent resistivity in one electrode configuration to any other configuration. Sine responses for determination of the derivative of apparent resistivities are given in analytical form.If the filter spectrum for converting the apparent resistivity to the resistivity transform for one electrode configuration is known, the filter spectra for transforming the apparent resistivity to the resistivity transform for any electrode configurations can be calculated by using newly derived expressions.

Notes: In the western coal-mining area of Ruhrkohle AG, reflection seismic prospecting for the Carboniferous coal measures is severely impaired by structures with halokinetic features. These structures make the interface between Mesozoic and Paleozoic layers, i.e., the top of Zechstein in general, very rugged. Unfortunately the velocity contrast at this interface is very high in that area, the ratio of velocities being 1.5 to 2.0. Therefore, migration and stacking become a problem.Three types of migration are presented:〈list xml:id="l1" style="custom"〉1(f, x)-time-migration with vertical time-to-depth conversion as a second step.2Kirchhoff migration down to a level determined approximately by the highest points of the top of Paleozoics, i.e., 0.35 s, and Kirchhoff-downward continuation for all times exceeding 0.35 s. Intermediate static corrections for these latter times with subsequent (f, k)-time-migration and final vertical time-to-depth conversion.3Direct depth migration in the (f, x)-domain using three interval velocities.In all cases an intermediate picking of the velocity interfaces is necessary. In case 2 this occurs at an earlier stage of the process than in case 1, and in case 3 at a still earlier stage.The results of the second and third migration procedures are superior to those of the first. Possibilities for misinterpretation of faults are reduced considerably when the second or third migration procedure is applied.

Notes: Airborne electromagnetic methods are most commonly used in mineral exploration. However, new developments, such as multifrequency capability and digital on-board field recording, as well as improvements in instrumentation resulting in high signal-to-noise ratios in recorded data, have made their application in geological mapping possible.A three-frequency airborne EM survey carried out over an area northwest of Timmins, Ontario, was interpreted in terms of thickness and resistivity of the layers of a two-layer earth section. Since both in-phase and quadrature components are measured, this provides six independent parameters at each point in space. Based on prior geological information and a preliminary interpretation of the field records, two two-layer models of the subsurface seemed to be appropriate for most of the survey area. An automatic computerized interpretation procedure was devised to interpret the field data at each point in terms of thickness and resistivity parameters of those two models. When the geology is more complex, the data do not fit the models and no interpretations are made. Two maps illustrating the variation of the resistivity and the thicknesses of the layers were constructed from the interpreted data. These maps agree with the known geological information about the distribution of glacial clay in the area. Areas where the layered models do not fit are known to be areas where the geology is complex with a large number of dykes and other lateral inhomogeneities. The study shows that multifrequency airborne EM surveys can be very useful in geological mapping over inaccessible terrain and can significantly help the mapping geologist where outcrops are scarce.

Notes: Shear (= S) wave studies in addition to compressional (= P) wave surveys have revealed that S-wave velocities are much more variable than P-wave velocities. This strongly affects Poisson's ratio σ, especially in young sediments. It is shown that σ has a great influence on the directivity pattern, i.e., on the radiation and receiving characteristic of horizontal sources and receivers. For their calculation, well-known surface boundary conditions and White's statement of the reciprocity relation (White 1965) are used. They also form the basis for the combination of source and receiver patterns essential for practical field work. The various combinations of horizontally and vertically arranged sources and receivers are investigated with regard to their directivity pattern, their amplitude ratio and, in general, to their usefulness in seismic prospecting.

Notes: Previously ignored characteristics of the seismic recording instrument are presently experienced as limitations as more sophisticated interpretive methods using wider frequency ranges are developed to extract stratigraphic information from seismic land data for hydrocarbon and mineral exploration. Most of these limitations arise from inadequate characteristics of the first element of the seismic instrument: the geophone. A geophone does not faithfully follow the motion of the earth for higher frequencies due to poor geophone-earth coupling. This filtering effect brings about time shifts that are dependent on the frequency and the soil type. A geophone can also produce spurious outputs, brought about by the motion of the suspended part of the geophone, with a magnitude comparable to that of the desired output. The suspension is made very compliant to obtain the required sensitivity. A compliant suspension, however, gives a large sag. The geophone can therefore only be used in one position, tolerating little tilt. A compliant suspension also widens the traveling range of the movable part. Minor sensitivity changes with travel are then noticeable as nonlinearity, since the surface wave is large with respect to the reflected wave. A compliant suspension is usually realized in the form of thin, spirally shaped spring-spiders. Such suspensions exhibit transverse or rotational resonances that are in or close to the seismic frequency band. Excited by ground roll, they can produce considerable undesirable output.The novel geophone we describe is a light-weight (17 g) acceleration-sensitive transducer which gives good ground coupling and partial correction for the increasing damping in the earth with increasing frequencies. It employs internal hybrid electronics for a magnetodynamic velocity-nulling feedback system. Velocity nulling makes the movable part of the geophone virtually rigid with respect to the housing. This makes the geophone characteristics independent of the suspension. The springs used are stiff in a transverse and rotational direction so that the suspension resonances are well outside the useful frequency band. This suspension also allows the geophone to be used in any orientation while being only sensitive to the vibration component along the main axis. The feedback system makes the sensitivity flat within 1 dB from 2 Hz to 500 Hz, with a phase tolerance smaller than 5°. The geophone is robust, has no moving internal wires, employs a current output [sensitivity 1 mA/(m s−2)] and internal gain so that the signal-to-cable-noise ratio is improved. This type of output allows parallel connection without any interaction between the geophones.

Notes: There are two types of masked layers in seismic refraction work: the velocity reversal (low-velocity layer) and the hidden layer (insufficient velocity contrast or layer thickness). On the basis of an analytical formulation of the general case of a masked layer under an overburden of plane and parallel multiple refractors the two limiting cases are discussed: the solution resulting from an uncritical interpretation of the measured time-distance curve and the blind zone solution. Between these two limiting cases there is a variety of possible masked layer solutions. These no-blind zone solutions—as well as the blind zone solution itself—are formulated separately for the velocity inversion and the hidden layer case.For the evaluation of some no-blind zone solution a diagram is presented which can be used for any case of multiple refractors in the overburden of the masked layer. However, it is only for the three- and the four-layer case that a blind zone interpretation by use of diagrams is advisable. Such diagrams are presented together with the basic sets of formulae which contain as parameters only ratios of velocities and layer thicknesses. As the velocity of the masked layer is usually unknown the diagrams are principally constructed to show the dependence on the masked layer velocity. This is useful for estimation of the largest possible error.

Notes: Wave equation migration techniques have shown the limits of traditional stacking methods with data from tectonically complicated areas. An improved stack can be obtained utilizing the dip-moveout correction technique based on offset continuation. The properties and the limits of the algorithms used are summarized briefly.Several synthetic and real data examples are shown and compared with the results obtained using conventional processing in order to show the focusing effects and the strong improvement in signal-to-noise ratios, both at the stacked and migrated section level. The possibility of exploiting this technique to transform multiple coverage into increased spatial resolution is illustrated with examples.

Notes: The far-field signatures from a comprehensive and systematic airgun pulse test have been analyzed. Empirical relations between the characteristic signature parameters and depth (5–12 m), pressure (100–137 bar = 10–13.7 MPa) and total chamber volume (0.65–9.5 l) have been derived. Also, the influence of using waveshape kits in different positions within the chamber has been tested.The results indicate that:〈list xml:id="l1" style="custom"〉1 The amplitude is proportional to chamber pressure to the power 3/4.2 The bubble period is nearly independent of the position of the waveshape plate.3 The increase in primary/bubble amplitude ratio is inversely proportional to the chamber volume above the waveshape plate.4 The amplitude is independent of airgun depth.Suggestions and comments regarding this work from Dr B. Ursin and Dr A. Ziolkowski are appreciated. The field work was supported by the Norwegian Petroleum Directorate through the Continental Shelf Project at the Seismological Observatory, University of Bergen.An airgun allowing for continuous variation of the chamber volumes was supplied by GECO (Geophysical Company of Norway). The purchase of two airguns was financed by Norske Getty Exploration A/S.

Notes: The accuracy of short length digital linear filter operators can be substantially increased if the sampling interval as well as the abscissa shift are properly adjusted. This may be done by a trial and error process of adjustment of these parameters until the error made by the filter operator, applied to a suitably chosen test function, is smallest.As an illustration of the application of this method, 7-, 11- and 19-point filters for the calculation of Schlumberger apparent resistivity from a known resistivity transform are designed. Errors with the new 7-point filter are seen to be less than those with a 19-point filter of conventional design. The errors with the new 19-point filter are two to three orders of magnitude smaller than those made by the conventional 19-point filter.The new method should provide digital linear operators that allow significant improvements in accuracy for comparable computation efforts, or substantial reduction in computation for comparable accuracy of results, or something of both.

Notes: A well-known technique for the migration of normal-incidence two-way travel-time maps is extended to common-source-point travel-time data. The travel time and the travel-time gradient are used to compute the parameters defining the tangent plane of the reflecting interface. It is also shown how the curvature matrix of the received wavefront can be used to compute the curvature of the reflecting interface. The method is initially derived for common-source-point data and then extended to common-midpoint data.In a three-dimensional medium the wavefront curvature matrix is computed by solving a 2 × 2 symmetric matrix Riccati equation. In a two-dimensional medium and in a medium with constant velocity gradient, the wavefront curvature matrix is computed by solving a scalar Riccati equation and two linear equations. The migration procedures are also simplified.When the velocity function is unknown, the migration procedures cannot be used. An inverse modeling algorithm which simultaneously performs the migration and estimates the velocity function must then be applied. Two different inversion schemes are discussed briefly.

Notes: Time-domain-induced polarization (IP) laboratory measurements were performed on about 200 fine sediment samples with varying water content. The results permitted an analysis of IP properties of clays, loams, silts, and sands.Particular emphasis has been given to the analysis of the chargeability m as a function of lithotype and the water content.By analyzing decay curves, a new parameter was identified. It is a statistically specific characteristic of the lithotype and is independent of the water content. Therefore, it provides a diagnostic parameter for lithotype identification. In association with the values of chargeability and electrical resistivity, this parameter permits a reliable evaluation of water content and yields useful information about the porosity and permeability of the lithotype.

Notes: Approaches to the reduction of bias in the computation of the elements of the magnetotelluric impedance tensor have been proposed in the past by several authors. In this paper a clear distinction is made between random errors and bias errors. No effort is made to reduce either, but the emphasis is on their estimation. Both types of errors depend critically upon the polarization of the magnetic field. The random error increases with increasing noise-to-signal ratio in the electrical field, and it is rather insensitive to noise in the magnetic field. The bias error increases with increasing noise-to-signal ratio in the magnetic field. Expressions for random errors and maximum bias errors are developed and discussed using a single station set-up. Random errors with a reference station set-up are also calculated.

Notes: Dipole-dipole induced polarization (IP) data are displayed typically as multi-level profiles, or as contours on vertical sectional plots referred to as pseudo-sections. The dipole-dipole array tends to yield IP anomalies in which the most anomalous values are displaced laterally from the source body. The data patterns are fairly interpretable on pseudo-sections or on multi-level profiles but are sufficiently complex to discourage the contouring of the data in plan.A method was developed for the presentation of dipole-dipole IP data on a contour map. The method consists of a simple averaging of data which can be performed manually if desired. It yields a single output value per station which reflects all levels of the pseudo-section, and is suitable for contouring in plan. The advantage of the technique is that it provides a quantitative picture of IP anomalies in their background or regional setting.

Notes: Constant offset sections can be mapped to a fixed offset and compared in order to provide a method of velocity analysis. The direct mapping to zero offset prior to stack might provide an alternative processing procedure to NMO and stack. The main advantage of such a procedure would lie in the correct treatment of cross-dips, but interpretational advantages might also follow from the performance of partial stacks biased to either high or low offset information.

Notes: Induced polarization and resistivity model studies over thin dykes for varying resistivity contrasts, depth of burial, and dip angles show striking parallelism of the surface apparent resistivity contours with the boundary of the body. This effect may be utilized for the estimation of strike length of the body. Results show that intermediate values of the electrode spacing is satisfactory for detection under widely varying conditions of resistivity contrast and depth. The percentage frequency effect (P.F.E.) and the metal factor (M.F.) responses are found to be more sensitive to the variation in the depth of burial than the resistivity responses. Pseudosections for P.F.E. and M.F. are concentrated much closer to the body than the resistivity pseudo-sections.

Notes: A direct interpretation scheme is developed which is capable of determining most of the geological features of a ground which can be assumed to be two dimensional in structure. This scheme extends the earlier work of Pekeris (1940) and Koefoed (1968) to the case where the basal layer of a ground is undulating. It also has a limited use for finding the parameters of a dipping dyke in the lower medium. Though the top and dip of the dyke can be determined, this is not true for the thickness.

Notes: Laboratory studies of absorption-frequency behavior in rocks often use spectral ratios of digitally recorded ultrasonic signals which have been transmitted through a rock sample and a reference sample of very low absorption, respectively. It is proposed to treat the digitally recorded signals as an autoregressive-moving average (ARMA) process which, using recursive filter concepts, can be represented as a ratio of two polynomials in the z-transform variable z. The numerator polynomial contains only that part of the signal that is modified by anelastic effects, whereas the denominator contains the elastic effects of the physical apparatus such as reverberations. Examples are given which show that this separation of the recorded signal greatly facilitates the laboratory investigation of loss mechanisms and absorption-frequency behavior based on spectral ratios.

Notes: The generalized integral equation for the electric potential governed by a quasi-harmonic equation can be derived via a variational formulation. For surface current distributions it is not always a Fredholm integral equation of the second kind. Numerical solutions of the general heterogeneous problem can be obtained with the “reciprocal averaging technique”, where the solution is obtained a second time after exchange of source and field points.

Notes: A method to calculate the resistivity transform of Schlumberger VES curves has been developed. It consists in approximating the field apparent resistivity data by utilizing a linear combination of simple functions, which must satisfy the following requirements: (i) they must be suitable for fitting the resistivity data; (ii) once the fitting function has been obtained they allow the kernel to be determined in an analytic way.The fitting operation is carried out by the least mean squares method, which also accomplishes a useful smoothing of the field curve (and therefore a partial noise filtering). It gives the possibility of assigning different weights to the apparent resistivity values to be approximated according to their different reliability.For several examples (theoretical resistivity curves in order to estimate the precision of the method and with field data to verify the practicality) yield good results with short execution time independent of shape the apparent resistivity curve.

Notes: We present a new method for the extraction and removal of the source wavelet from the reflection seismogram. In contrast to all other methods currently in use, this one does not demand that there be any mathematically convenient relationship between the phase spectrum of the source wavelet and the phase spectrum of the earth impulse response. Instead, it requires a fundamental change in the field technique such that two different seismograms are now generated from each source-receiver pair: the source and receiver locations stay the same, but the source used to generate one seismogram is a scaled version of the source used to generate the other. A scaling law provides the relationship between the two source signatures and permits the earth impulse response to be extracted from the seismograms without any of the usual assumptions about phase.We derive the scaling law for point sources in an homogeneous isotropic medium. Next, we describe a method for the solution of the set of three simultaneous equations and test it rigorously using a variety of synthetic data and two types of synthetic source waveform: damped sine waves and non-minimum-phase air gun waveforms. Finally we demonstrate that this method is stable in the presence of noise.

Notes: In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression.As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.

Notes: The Hankel transform theorem can be applied to the inversion of gravity data for the buried sphere, the horizontal cylinder, and the vertical rod. This new approach leads to exact solutions of the transforms for the assumed bodies. A comparison with the classical procedure by Fourier transform reveals that for the sphere and the vertical rod, the Hankel transform is preferable.

Notes: Air guns have been used in various applications for a number of years. They were first used in coal-mining operations and were operated at up to 16000 psi charge pressures. Later, single air guns, operated at 2000 psi, found application as an oceanographic survey tool. Air gun arrays were first used in offshore seismic exploration in the mid-1960's. These early arrays were several hundred cubic inches in total volume and were operated at 2000 psi; they were either tuned arrays or several large guns of the same size with wave-shape kits. Today's arrays have total volumes greater than 5000 cu in. and are typically operated at 2000 psi. Recently, higher-pressure, lower-volume arrays operated at 4000–5000 psi have been introduced; guns used in these arrays are descendants of the coal-mining gun.On first thought one would equate increased gun pressure linearly with the amplitude of the initial pulse. This is approximately true for the signature radiated by a “free-bubble” (no confining vessel) and recorded broadband. The exact relation depends on the depth at which the gun is operated; from solution of the free-bubble oscillation equation, the relation is 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu1"/〉 If Pc,1= 6014.7 psia, Pc,2= 2014.7 psia and PO, 1=PO, 2= 25.8 psia (corresponding to absolute pressure at 25 ft water depth), then 〈displayedItem type="mathematics" xml:id="mu2" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu2"/〉 Experiments were conducted offshore California in deep water to determine the performance of several models of air guns at pressures ranging from 2000 to 6000 psi and gun volumes ranging from 5 to 300 cu in. At a given gun pressure, the initial acoustic pulse Pa correlated with gun volume Vc according to the classical relation 〈displayedItem type="mathematics" xml:id="mu3" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu3"/〉 For 1 ms sampled data the ratio 〈displayedItem type="mathematics" xml:id="mu4" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu4"/〉 varied between 4.5 and 5.5 dB depending on gun model. Pulse width of the 2000 psi signatures indicated they are compatible with 2 ms sample-rate recording while pulse width of the 6000 psi signatures was greater, indicating they are less compatible with 2 ms sample-rate recording.Conclusions reached were that 2000 psi air guns are more efficient than higher pressure guns and are more compatible with 2 ms sample-rate requirements.

Notes: Numerous electrodes, already used in geophysics or just perfected by us, have been compared by measuring the three main characteristics which interest the user: noise spectrum, temperature coefficient and polarization with its stability versus time.Among the most used unpolarizable electrodes, silver-silver chloride (Ag-AgCl) are the best ones. But a systematic research of all different possible metal-salt couples, have led us to use lead-lead chloride (Pb-PbCl2) for the following reasons: noise as low as the one of Ag-AgCl at 1 Hz and even lower for the low frequencies (0.4 μV at 1 Hz and 1.2 μV at 0.01 Hz for peak to peak value and ΔF=F), temperature coefficient about ten times weaker (−40 μV/°C instead of −450 μV/°C) and also better long time stability of the polarization (1 mV/month instead of 2 at 10 mV/month).We have been using these electrodes since 1977 as “tube” electrodes which are very easy to use. They allow us to record correctly the fast variations thanks to their low noise, the very slow variations, their low temperature coefficient and their stability, and this with telluric lines only about 100 m long.

Notes: The compression of seismic signals which have propagated through a dispersive medium can be achieved by a frequency-domain transformation. This transformation is formally related to the dispersion characteristic of the medium and is independent of phase and group velocities. By defining a suitable cost-function to measure the degree of dispersion of a time- signal, an iterative technique can be employed to find that transformation which gives minimum dispersion.In this paper, we assume that the inverse of the dispersion characteristic can be adequately approximated by a finite polynomial in the region of maximum signal energy density. The coefficients of this polynomial are the parameters of dispersion of the medium. These parameters can be estimated both in the presence of noise and in the case of signals made up of multiple arrivals.The techniques developed in this paper are applied to seismic signals which have been recorded underground by a set of geophones designed to detect and map discontinuities in coal-seams. Results of dispersion estimation and signal compression are discussed for data collected in the Blackshale seam, Pye Hill Colliery, near Derby, in the United Kingdom.

Notes: Sign reversals have been observed with the one-loop version of the TEM method in an area near Cloncurry, Queensland. This is the only area in which such a response has been recorded in seven years of field surveys by the Australian Bureau of Mineral Resources.The geology of the area consists mainly of pyrrhotitic graphitic shale, which has resistivities as low as 0.1 Ωm and frequency effects up to 30%. The sign reversals could be due to magnetic phenomena, reflections from layers, or complex conductivity effects.

Notes: A crucial step in the use of synthetic seismograms is the estimation of the filtering needed to convert the synthetic reflection spike sequence into a clearly recognizable approximation of a given seismic trace. In the past the filtering has been effected by a single wavelet, usually found by trial and error, and evaluated by eye. Matching can be made more precise than this by using spectral estimation procedures to determine the contribution of primaries and other reflection components to the seismic trace. The wavelet or wavelets that give the least squares best fit to the trace can be found, the errors of fit estimated, and statistics developed for testing whether a valid match can be made.If the composition of the seismogram is assumed to be known (e.g. that it consists solely of primaries and internal multiples) the frequency response of the best fit wavelet is simply the ratio of the cross spectrum between the synthetic spike sequence and the seismic trace to the power spectrum of the synthetic spike sequence, and the statistics of the match are related to the ordinary coherence function. Usually the composition cannot be assumed to be known (e.g. multiples of unknown relative amplitude may be present), and the synthetic sequence has to be split into components that contribute in different ways to the seismic trace. The matching problem is then to determine what filters should be applied to these components, regarded as inputs to a multichannel filter, in order to best fit the seismic trace, regarded as a noisy output. Partial coherence analysis is intended for just this problem. It provides fundamental statistics for the match, and it cannot be properly applied without interpreting these statistics.A useful and concise statistic is the ratio of the power in the total filtered synthetic trace to the power in the errors of fit. This measures the overall goodness-of-fit of the least squares match. It corresponds to a coherent (signal) to incoherent (noise) power ratio. Two limits can be set on it: an upper one equal to the signal-to-noise ratio estimated from the seismic data themselves, and a lower one defined from the distribution of the goodness-of-fit ratios yielded by matching with random noise of the same bandwidth and duration as the seismic trace segment. A match can be considered completely successful if its goodness-of-fit reaches the upper limit; it is rejected if the goodness-of-fit falls below the lower one.

Notes: If the conductivity of any one of the layers of a horizontally stratified earth varies exponentially with depth with or without a discontinuity at the interface, the corresponding expressions for apparent resistivity for Wenner- and Schlumberger-sounding arrays can be formulated. The general case has been broadly divided into three categories for mathematical simplicity. All previous discussions of this problem can be regarded as particular cases of the present study.

Notes: The physical properties of the serpentinized pyroxenitic and saxonitic rocks from stratiform ultramafic complexes of Roro, Singhbhum distrct, India, are examined using principal factor (R-mode) analysis technique. The variations and inter-relations of these properties reflect the compound effects of two processes—(a) degree of serpentinization, and (b) mineralogical and other changes attendant to serpentinization. Factor analysis is thus shown to be an effective tool for petrophysical inferences.

Notes: The problem of numerical evaluation of apparent resistivity curves is treated by finite difference modeling. The models proposed are set up in cylindrical coordinates and yield the potential field due to a point source located in a radially symmetric environment. The Schlumberger configuration, widely used for surface measurements, is emphasized. However, the treatment is equally applicable to other similar situations such as the computation of synthetic electric logs when the resistivity of the borehole fluid is different from that of the surrounding uniform or stratified medium. Moreover, the individual layers may not necessarily be isotropic.The medium under investigation is discretized by using a very coarse system of horizontal and vertical grid lines whose distance from the source increases logarithmically; consequently, the physical dimensions of the medium can be made “infinite” without affecting the numerical size of the model. Finer features such as a thin but anomalously resistive or conductive bed which would ordinarily be missed in coarse discretization are accurately taken into account, since the calculations are done in terms of the Dar Zarrouk parameters derived from the exact resistivity distribution of the model. This enables one to compute the potential field by inverting a small sparse matrix. When the medium comprises only a few layers, the efficiency of the finite-difference model is comparable to that of the known analytical methods; for more complicated structures, however, the finite-difference model becomes more efficient. The accuracy of finite-difference results is demonstrated by comparing them with the corresponding analytically obtained data.

Notes: A method is given for solving the dc electric field problem of a point current source in an anisotropic 2 1/2-dimensional structural model. The surface integral equation of the field strength is given. Parallel to the strike the field strength is represented by a Fourier series. On the plane perpendicular to the strike each term of the field strength series is solved by means of the method of sub-sections, where linear behaviour of field strength over the sub-sections is assumed. Some numerical examples for different galvanic effects are given.

Notes: It is proposed that the vertical resolving power of a seismic signal is controlled by three aspects: the width of the central lobe, the side lobe ratio, and the side-tail oscillations. A comparative study of zero-phase signals covering the same frequency range shows that improvement of any one of these aspects inevitably leads to deterioration of one of the other aspects.An analytical simulation model is proposed of zero-phase signals free from side-tail oscillations, in which both the width of the central lobe and the side lobe ratio are adjustable. Analysis of the spectra of this model shows that, while the high frequency content of the spectrum is essential for obtaining a small width of the central lobe, the low frequency content of the spectrum plays an essential part in causing a low value of the side lobe ratio.

Notes: The objective of this study is to generate the separation-distance-domain (r-domain) transformation of the theoretically calculated wave number domain (m-domain) electromagnetic induction field component Bz(m, ω) of a stratified medium and to search for interpretive information which has been absent in the previously achieved numerical solutions of the problem.The r-domain kernel R̃(r, ω) function defining the induction field appears to adequately reflect the layering and electrical properties of the medium if it is expressed as a function of the frequency if the source-receiver separation r is small with respect to the thickness of the first layer. However, exact values of the conductivity cannot be distinguished from those of the neighboring values unless a resistive basement layer is present. This feature is the result of the truncation in series representation of the kernel function R̃(m, ω). However, this truncation is regarded as significant in the case of a conductive first layer. In m-domain static-zone studies, a conductive first layer slightly influences its r-domain correspondent.Although the computational cost of obtaining the kernel B(r, ω) by evaluation of the convolution in a cylindrical coordinate system is high, this semi-analytic solution is still superior to those based on the asymptotic assumptions.

Notes: A new method of estimating seismic stacking velocity from reflection seismograms is based on Fibonacci search technique and provides the highest rate of reduction of the interval of uncertainty of the stacking velocity. A review of the Fibonacci search strategy is presented, the application of the method is illustrated with synthetic and field examples.

Notes: The paper relates primarily to the borehole and the side bed correction charts for Latero-logs 3 and 7. Versions of some of these charts published by different companies—or even by the same company in different years—exhibit significant variations. Usually, such publications do not contain adequate information on how the charts were constructed and do not explain why discrepancies occur.Because of these reasons, an attempt has been made in this paper to reconstruct the borehole correction chart for Laterolog 7 and the shoulder bed correction charts for Latero-logs 3 and 7. For the latter two, the results found differ substantially from those published earlier.The paper demonstrates how departure (response) curves and correction charts for the lateral and the Laterolog 7 sondes can be computed from those for the normal sonde. An apparent resistivity formula is suggested for Laterolog 7 in which all currents that exist in the ground at the time of measurement and that produce the signal are monitored and used. Response curves and correction charts for Laterolog 7, based on such a formula, are presented as illustrations.

Notes: Classical methods of interpretation of reflection seismic data are such that interpretation and processing usually occur in the “collected” frame of reference. However, in recent times other data planes have gained increasing acceptance in seismology as a viable alternative. Through linear transformations applied to a record section, both the t—p- and p—x-planes can be produced. The r—p-domain may be obtained from the t—x-plane by a transformation known as slant stacking. Normal practice has been to do most of the data processing in the t—x-plane and then transforming to the r—p-plane. However, many of the procedures used in the t—x-domain can be modified for use in the t—p-plane to increase the coherence.Velocity inversion may be carried out either in the r—p-domain or further transformed to the p—x-plane where the modified Herglotz-Wiechert inversion may be applied. To perform the inversion, the t—p-wavefield is converted to a p—x-representation by the use of a new linear transformation technique, the cross-stack. By a simple sampling process along a particular p—x-trajectory, the Herglotz-Wiechert method can be used to reconstruct an acceptable velocity model of the subsurface. A comparison of derived velocity structures is made between that produced by the Herglotz-Wiechert technique and that of the Dix method.

Notes: The computation of static corrections requires information about subsurface velocities. This information can be obtained by different methods: surface wave analysis, short refraction lines, downhole times, uphole times and first arrivals from seismograms.For pure shear waves generated by SH sources the analysis of first arrivals from seismograms combined, if necessary, with short refraction lines has proved to be most accurate and economic.A comparison of first-arrival plots from P- and S-wave surveys of the same line measured in areas of unconsolidated sediments in northern Germany illustrates the characteristic differences between the two velocity models. P-waves show a marked velocity increase at the water table from about 600 to 1800 m/s. S-wave velocities of the same strata increase gradually from about 100 to 400 m/s. As a consequence, S-wave models are vertically and laterally more complex and, in general, show no significant velocity increase at a defined boundary as P-wave models do. Therefore, other suitable correction levels with specific velocities must be chosen.A comparison of “tgd-corrections” (correction time between geophone position and datum level) for P- and S-waves in areas of unconsolidated sediments shows that their ratio is different from the P-/S-velocity ratio for the respective correction level because of the greater depth of the S-wave refractor. Therefore, P- and S-waves are influenced by different near-surface anomalies, and time corrections calculated for both wave types are largely independent.

Notes: Forward filters to transform the apparent resistivity function over a layered half-space into the resistivity transform have been derived for a number of sample intervals. The filters have no apparent Gibbs' oscillations and hence require no phase shift. In addition, the end points of the filter were modified to compensate for truncation. The filters were tested on simulated ascending and descending two-layer cases. As expected, “dense” filters with sample spacing of In (10)/6 or smaller performed very well. However, even “sparse” filters with spacing of In (10)/2 and a total of nine coefficients have peak errors of less than 5% for p1:p2 ratios of 10–6 to 106. If a peak error of 5.5% is acceptable, then an even sparser filter with only seven coefficients at a spacing of 3 In (10)/5 may be used.

Notes: The concept of minimum phase is clarified for geophysicists by collecting in one place the properties of minimum phase functions. The “earliest energy arrival” property in the time domain, the “minimum phase-slope property” in the frequency domain, and of the role of causal all-pass filters are demonstrated. The emphasis is placed on keeping the mathematics within the realm familiar to geophysicists and on making clear the somewhat imperfect match between physical continuous time functions and their associated discrete time representations.

Notes: Volcanic maar structures sometimes contain important groundwater reserves. The volcanic formations of the Beaunit maar have a much higher magnetization than their granite substrata. The structure of the maar and its volcanoclastic infill can therefore be defined by magnetic surveying and resistivity soundings. Resistivities of the geological formations present in the Beaunit maar are comparable to those recorded in other volcanic systems. The geophysical data, confirmed by drilling tests, contain useful information on the hydrogeological regime of the volcanic system under investigation.

Notes: In migration procedures, the velocity profile of the subsurface is the most important input information. Since, in general, this information is only approximately known, errors in the migration output due to errors in the velocity input occur in all practical applications. In migration, velocity errors and depth errors can be interchanged. This interchange property is perfect in the paraxial approximation. From this result it follows that migration with incorrect velocities may still yield correctly migrated data if the imaging principle is modified. This attractive property can be used in the stripping version of migration (recursive migration).

Notes: The presence of the water layer in marine seismic prospecting provides an effective waveguide for acoustic energy trapped between the sea-bed and the sea-surface. This energy persists to large ranges and can be the dominant early feature on far-offset traces. On airgun records, there is commonly a lower frequency set of arrivals following the water-trapped waves. These arrivals are not as obvious with higher frequency watergun sources. By using a combination of intercept-time/slowness (τ—p) mapping on observational data and theoretical modelling, we are able to identify the origin of the events. If a very rapid increase in a seismic wavespeed occurs beneath the sea-bed sediments, a new waveguide is formed bounded by the sea surface and this transition zone. The low frequency waves are principally guided within this thicker waveguide. Numerical filtering in the τ—p domain followed by trace reconstruction is very effective in removing the low frequency noise.

Notes: The efficacy of the magnetotelluric and audiomagnetotelluric (MT/AMT) methods for detailing the structure of a hypothetical geological section is investigated by using the singular value decomposition (SVD) technique. The section is representative of southeastern Turkey, which is mostly covered by basalt and is a prime area for oil exploration. One of the geological units, the Germav shale at a depth of 600 m, is a problem layer for electromagnetic surveys because of its very low resistivity (on average 3 Ωm) and highly variable thickness across the area (200–900 m). In the MT frequency range (0.0004–40 Hz) its total conductance—or, since its resistivity is known from resistivity log information, its thickness—is the best resolved model parameter. The total depth to the Germav shale and the resistivity of the Cambrian/Precambrian basement are the marginally resolved parameters. In the AMT frequency range (4–10000 Hz) the resistivity of the surface basalt layer strongly affects the resolution of the other, less important, model parameters which are the total depth to the Germav shale and the total conductance of the Germav shale. The errors in the measurements determine the number of model parameters resolvable, and are also important for interpretation of the geological model parameters to within a desired accuracy.It is shown that statistical evaluation of the MT and/or AMT interpretations by using an SVD factorization of the sensitivity matrix can be helpful to define the importance of some particular stage of the interpretation, and also provides a priori knowledge to plan a proposed survey. Arrangements of MT and AMT observations, together with some Schlumberger resistivity soundings, on a large grid will certainly provide three-dimensional detailed information of the deep geoelectric structure of the area.

Notes: A method for interval velocity analysis is formulated on the basis of wavefield extrapolation, i.e., on the basis of wave-equation migration. When this scheme is applied to multioffset seismic sections or to an ensemble of CMP gathers, it allows for the proper treatment of dipping events. The underlying assumptions are that local velocities should be derived from data associated with events within the interval under consideration. To minimize the effect of the region above the layer of interest, the data are first extrapolated to the top of the analysis interval. Subsequent analysis of these data then pertains to the events within this interval. Velocity estimation consists of repeated wavefield extrapolations through the analysis interval using a set of trial velocities. The optimal velocity is chosen on the basis of coherency measures designed to express the collective phase agreement among a set of offset Fourier modes. The reliability of this approach to interval velocity estimation is demonstrated on synthetic multi-offset data.

Notes: A statistical treatment of MT data from the Pannonian Basin, Hungary, based on the distortion theory of the S-effect suggests that the local increase in crustal conductivity is connected with deep fractures.Field model measurements have recently been carried out in a shallow, quasi two-dimensional basin of well known tectonics using MT station distances of 1–3 km. The results of the investigation and numerical modelling of near surface distortions, support the idea that deep fractures (faults) contain the conducting formations. According to 2-D model computations, several conducting dykes at considerable depths can cause anomalies which are indiscernible from an anomaly due to a conducting layer. The significance of these results is discussed from the point of view of geothermal energy exploitation.

Notes: A principal use of the vertical seismic profile (VSP) is to determine the variation of seismic velocity with depth. Presented here is a discussion of the errors involved with the time picks of a VSP survey and several methods currently used to calculate a velocity section from these time picks. Another technique is proposed, based on the least-squares inversion of the traveltimes, to arrive at a better estimate and statistical description of the velocity section. This technique uses the Levenberg-Marquardt damped least-squares formulation and ray tracing through a horizontally-layered medium to iteratively refine the velocity section. The accuracy and robustness of the procedure are investigated by inverting noisy traveltime curves and comparing these results to the original model velocity section. Agreement is found to be good. One interesting feature of the inverse procedure is that, for certain geometries, it can resolve a few velocity layers, even though there are no measurements made inside those layers. Three actual VSP surveys are analyzed and compared to their corresponding sonic logs. In two of the surveys, it appears that there is some velocity dispersion. Velocity changes associated with gas saturation are evident on one of the surveys.

Notes: It is well recognized that in order to realize the full potential of the Vibroseis technique, one needs to ensure accurate phase locking and a meaningful cross-correlation. To achieve these two important objectives we require an accurate estimate of the compressional stress wave radiated by the vibrator into the ground.In this paper a simple method (subject of a patent application) is developed for predicting the compressional stress waves radiated by a vertical vibrator. The main feature of the proposed method is that it involves the field measurement of the acceleration of the reaction mass and the baseplate, respectively.The method is illustrated by computing the compressional stress waves generated by a typical vertical vibrator radiating into ice, chalk, sand, and mud. It is shown that for a seismic vibrator radiating into hard ground the pressure of the downgoing P-wave is 180° out of phase with the baseplate velocity. It is also shown that when the driving force of the seismic vibrator has a flat amplitude spectrum, the amplitude spectrum of the downgoing P-wave falls off by 6 dB/octave towards low frequencies.

Notes: Bedding on a scale small in comparison to the wavelength results in transverse isotropy. On the other hand, anisotropy has been observed in the field, particularly with horizontally polarized shear waves. In this article velocity data from 23 wells are used to estimate the resulting transverse isotropy and to compare these data with anisotropy observations reported in the literature. Since the well data were compressional velocity (or rather transit time) only, the corresponding shear velocity data were estimated on the basis of a reasonable—though arbitrary—assumption of Poisson's ratio. Actual densities were used wherever they were available; for the remainder of the data, density was assumed to be constant throughout the averaging interval.The anisotropy data estimated on this basis were generally considerably smaller than the observational data that have been reported in the literature. Although both the above assumptions—functional dependence of Poisson's ratio on transit time and constant density—tend to underestimate anisotropy, and although 23 wells is but a small subset of all available data, it appears unlikely that bedding alone could cause anisotropy of the magnitude reported.

Notes: In land seismic surveys spectrum equalization can increase the quality of seismic data in a selected frequency band. The power of lower frequencies in the spectrum of input traces is generally greater than that of higher frequencies, particularly in land seismic surveys because of ground roll. In order to improve the quality of seismic data it is necessary to raise the energy of higher frequencies to the same level as that of lower frequencies, without alteration of the phases.The first step of the method is to compute the amplitude spectrum of each input trace to determine a weighting function which is then applied to the amplitude spectrum in order to balance it. The function is the inverse of the short wavelength variation of the amplitude spectrum. The short wavelength variation can be obtained by interpolation between average values of the modulus of the amplitude spectrum computed in narrow bands within a selected band of frequencies. Another way of obtaining the short wavelength variation is to apply a low-pass filter to the amplitude spectrum. The calculations are readily performed in the frequency domain by the Fourier transform.Spectrum equalization is automatically adjusted to each trace and does not modify the average amplitude in the time domain. However, as the frequency band and energy of the ground roll both vary according to the distance from the shot, spectrum equalization tends to make the spectrum of output traces independent of the offset distance.The use of spectrum equalization before any two-dimensional filtering improves ground roll elimination. Continuity and resolution of horizons are also increased by spectrum equalization before CDP stack.Several examples of applications of spectrum equalization to seismic land and marine surveys are shown.

Notes: A thin superparamagnetic layer on the earth's surface greatly affects the transient electromagnetic response of a conducting ground. The effect of the layer is most evident for singleloop transient electromagnetic data where transient voltages decay as 1/t. Even when a separate transmitter and receiver are used, the effect of the superparamagnetic layer is still pronounced. In this case the effect of the 1/t term in the equation is much less. More dominant now is a 1/t2 term. The effect of the superparamagnetism can readily be seen in the analytical expressions for the apparent resistivities. If the presence of the superparamagnetic layer is not recognized, then the apparent resistivities decrease with time rather than approach the true value of the host rock.

Notes: The use of very long streamers in marine seismic surveys makes the response offset dependent. Line equalization networks are used to balance this effect.In this paper the response of the transformerless streamer system driving a charge amplifier is analyzed. Examples are given for a seismic cable 2500 m long, showing that the delay and the reduction in amplitude of the streamer impulse response in the absence of leakage are of the order of 1 ms and 0.6 dB, respectively. This means that the line equalization network currently used with the transformerless streamer system is not needed. We have also demonstrated that the presence of leakage resistance across the hydrophone group render the sensitivity of the transformerless streamer system offset dependent.

Notes: The suggested interpretation technique is based on discrete linear filtering of VLF data. The output of the described filtering results is expressed in terms of an equivalent current density at a specified depth that would cause the measured magnetic field. The most practical six-point filter gives an accuracy of 8%. The filter is an extension of the commonly used Fraser filter to process VLF dip-angle data.Filtering the same data set for various depths gives an idea about the change of current density with depth. Areas with high current-density correspond to good conductors. The conductor dip can also be determined.The use of the technique is illustrated on theoretical and field examples. In all cases a good correlation with original models and other types of geophysical measurements was obtained. As shown in the last example, the filtering technique is also applicable in interpretation of other electromagnetic methods.

Notes: Different sets of filter coefficients for the linear filter technique for the computations of resistivity and EM sounding curves are evaluated for several electrode and coil configurations. Instead of this procedure, the two-electrode filter can be used for computations of Wenner, Schlumberger, and dipole—dipole apparent resistivity model curves by defining convolutional expressions which contain the new input functions in terms of the resistivity transform function. Similarly, the Schlumberger filter performs the computations of dipole—dipole apparent resistivity model curves. The Wenner, Schlumberger, and dipole—dipole filter functions are defined in terms of the two-electrode filter using the new convolutional expressions. A relationship between the Schlumberger and dipole—dipole filter functions is given.The above arguments are adopted for the computations of EM sounding curves. It is shown that the EM filter for the horizontal coplanar loop system (which is identical to the two-electrode filter) performs the computations of the mutual coupling ratios for perpendicular, vertical coplanar, and vertical coaxial loop systems. In the same way, the Schlumberger filter can be used to compute vertical coaxial sounding curves. The corresponding input functions are defined in terms of the EM kernel for all convolutional expressions presented.After these considerations, integral expressions of the mutual coupling ratios involving zero-order Bessel function are derived. The mutual coupling ratio for the vertical coaxial loop system is given in the same form as the mutual coupling ratio for the vertical coplanar loop system.

Notes: Using approximate boundary conditions, expressions for electromagnetic fields have been derived for a thin, highly resistive layer lying between two homogeneous layers excited by an electric dipole grounded on the surface of the earth. The variations of the fields with the parameter T/T1 (ratio of the transverse resistance of the thin layer to the transverse resistance of the first layer) were studied in relation to frequency, time, the normalized separation source—receiver, and the angle between the source and the radius to the observation point. For a value of h2/h1 (ratio of thickness of second layer to the thickness of the first layer) approximately equal to 0.2, the general three-layer medium case gives the same results as this approach. It was found that the electric fields have a very strong dependence on the parameter T (transverse resistance) which characterizes the thin, highly resistive layer. However, the magnetic fields depend only very weakly on this parameter.

Notes: Microgravity can be used for predicting rock bursts. For the first time gravity anomalies related to rock bursts have been recorded. The methodology developed has lead to the first successful predictions. The depth of the rock-burst focus might be determined on the basis of analytical downward continuation of related gravity anomalies: the focus is treated as a singular point of the gravity potential and its derivatives.The rock-burst gravity anomalies might be explained on the basis of the assumed dilatancy process that causes the rock burst. The mean density change of the rock mass threatened with rock bursts can be estimated from the corresponding rock-burst gravity anomalies.

Notes: A model has been set up for the interpretation of geoelectrical sounding data for certain kinds of clay deposits containing gradually varying amounts of sand. The model assumes that in the so-called gradient layer, resistivity varies linearly with depth. Model calculations show how such a layer can be replaced by two homogeneous layers.An inversion procedure using the Marquardt algorithm has been developed for the interpretation of sounding data obtained with the Schlumberger array; it assumes a gradient layer beneath several covering layers. The procedure is demonstrated on two clay deposits. A comparison is made between the newly developed interpretation, the traditional approach using model curves, and computerized inversion for a homogeneous layer model.

Notes: Gravity data have been transformed into a three-layer, three-dimensional model by using an automatic procedure based on linear filtering. The Bouguer anomaly is first transformed by linear filtering into density variations located between two planes 1100 and 2500 m deep. These densities are then transformed into thicknesses with a constant density contrast of 0.4 g/cm3 with two geological constraints for the second and third interface:—minimum at 2500 m depth;—maximum below a variable limit given by geology.This gives the contact between the second and third layer. Differences between measured and computed gravity are then applied by a similar procedure to a layer located between depths of 0 and 500 m, giving the contact between the first and second layer. Interesting secondary anticlines and transverse faults are shown by various structural maps.

Notes: Migration of an observed zero-offset wavefield can be performed as the solution of a boundary value problem in which the data are extrapolated backward in time. This concept is implemented through a finite-difference solution of the two-dimensional acoustic wave equation. All depths are imaged simultaneously at time 0 (the imaging condition), and all dips (right up to vertical) are correctly migrated. Numerical examples illustrate this technique in both constant and variable velocity media.