ALBERT

Notes: Full-wavefield inversion for distributions of acoustic velocity, density and Q on a vertical slice through a25D model is implemented for common-source gathers in a cross-hole geometry. The wavefield extrapolation used is 3D, so all geometrical spreading, scattering, reflection, and transmission effects are correctly and automatically compensated for. In order to keep the number of unknowns tractable, application was limited to 2.5D models of known geometry; the latter assurnes a prior step, such as tomography, to fix the layer geometries. With the model geometry fixed, reliable solutions are obtained using synthetic data from only two independent source locations. Solutions from data with noisy and missing traces are comparable to those from noise-free data, but with higher residuals. When the source locations are spatially widely separated, conunon-source gathers may be summed and treated as a single wavefield to yield the same model estimates as when the individual source wavefields are treated separately, at substantially reduced cost. Inversions for full 3D parameter distributions can be handled with the same software, requiring only solution for more unknowns.

Notes: It is seen that the apparent chargeability (Ma)L anomaly over a 2D graphite body splits into two distinct (Vs)L anomalies which closely follow the apparent resistivity profile. This suggests that the electric field amplitude is distorted due to a superficial inhomogeneity creating a (Vs)L anomaly, which bears no relation to the polarized body. The target depth obtained by continuation of such a profile is therefore, not acceptable.

Notes: The improvement in accuracy and efficiency of wave-equation migration techniques is an ongoing topic of research. The main problem is the correct imaging of steeply dipping reflectors in media with strong lateral velocity variations. We propose an improved migration method which is based on cascading phase-shift and finite-difference operators for downward continuation. Due to these cascaded operators we call this method‘Fourier finite-difference migration’(FFD migration).In our approach we try to generalize and improve the split-step Fourier migration method for strong lateral velocity variations using an additional finite-difference correction term. Like most of the current migration methods in use today, our method is based on the one-way wave equation. It is solved by first applying the square-root operator but using a constant velocity at each depth step which has to be the minimum velocity. In a second step, the approximate difference between the correct square-root operator and this constant-velocity squareroot operator (the error made in the first step) is implemented as an implicit FD migration scheme, part of which is the split-step Fourier correction term.Some practical aspects of the new FFD method are discussed. Its performance is compared with that of split-step and standard FD migration schemes. First applications to synthetic and real data sets are presented. They show that the superiority of FFD migration becomes evident by migrating steeply dipping reflectors with complex overburden having strong lateral velocity variations. If velocity is laterally constant, FFD migration has the accuracy of the phase-shift method. The maximum migration angle is velocity adaptive, in contrast to conventional FD migration schemes. It varies laterally depending on the local level of velocity variation. FFD migration is more efficient than higher-order implicit FD schemes. These schemes use two cascaded downward-continuation steps in order to attain comparable migration performance.

Notes: Simulated annealing is a stochastic combinatorial optimization technique, based on ideas from statistical mechanics, thermodynamics and multivariable probability theory. This paper presents the use of simulated annealing as a means of inversion for both linear magnetics and non-linear resistivity problems. The subsurface is viewed as being constructed of smaller elemental blocks which possess either uniform internal magnetization or conductivity, enabling larger structures to be modelled. Simulated annealing is employed to calculate the distribution of the particular physical property which causes a measured anomalous field curve.A general description of simulated annealing and its application is given, followed by specific descriptions of its application to the magnetics and resistivity cases.For the magnetics case the subsurface consists of 2D prismatic elements as the basis for the forward model. Synthetic model data is used to test the algorithm and an example of actual field data; a survey across an igneous dike is used to demonstrate the use of the method with real data. In the resistivity case, the finite-element method is used to generate the forward models. Synthetic vertical profiling data is used to test the application of the simulated annealing method to the resistivity case. Actual data from an archaeological survey is used to show again the use of the method with real data.Simulated annealing is shown to be capable of inverting both the linear and non-linear methods of magnetic surveying and resistivity surveying respectively.

Notes: The application of McClellan transformations considerably reduces the computational cost of 3D wavefield depth extrapolation by explicit convolutional methods. The accuracy of migration methods based on McClellan transformation depends on how well the transformation filter (cos !;κ!;) is approximated; errors in this approximation cause anisotropy in the extrapolation operator and frequency dispersion in the migrated results. The anisotropy can be greatly reduced by rotating the approximate filter by 45° and averaging the rotated filter with the original filter. The application of the rotated filter yields a migration method that correctly images very steep dips, with little or no additional computational cost. McClellan migration with the improved circular response enhances the imaging of synthetic and real data.

Notes: It is often very useful to be able to smooth velocity fields estimated from exploration seismic data. For example seismic migration is most successful when accurate but also smooth migration velocity fields are used. Smoothing in one, two and three dimensions is examined using North Sea velocity data.A number of ways for carrying out this smoothing are examined, and the technique of locally weighted regression (LOESS) emerges as most satisfactory. In this method each smoothed value is formed using a local regression on a neighbourhood of points downweighted according to their distance from the point of interest. In addition the method incorporates ‘blending’ which saves computations by using function and derivative information, and ‘weighting and robustness’ which allows the smooth to be biased towards reliable points, or away from unreliable ones.A number of other important factors are also considered: namely, the effect of changing the scales of axes, or of thinning the velocity field, prior to smoothing, as well as the problem of smoothing on to irregular subsurfaces.

Notes: A fast imaging technique is developed to deduce the spatial conductivity distribution in the earth from low-frequency (〉 1 MHz) cross-well electromagnetic measurements. A sinusoidally oscillating, vertically orientated, magnetic dipole employed as a source, and it is assumed that the scattering bodies are azimuthally symmetric about the source dipole axis. The use of this model geometry reduces the 3D vector problem to a more manageable 2D scalar form. Additional efficiency is obtained by using the Born series approximation which is derived from nonlinear integral equations that account for the scattered magnetic fields generated by inhomogeneities embedded in a layered earth. Stabilization of the inversion problem is accomplished through the use of bounding constraints and a regularization method which results in a smooth model that fits the data to the desired noise level.The applicability of cross-well electromagnetics for imaging and monitoring changes caused by subsurface processes has been tested by simulating plumes of conductive fluid with 2D models. The images that result from inverting these synthetic data indicate that the vertical resolution of the method is better than the horizontal, increasing the noise decreases the image resolution, and incorporating a priori knowledge in the form of positivity constraints improves the results. Although higher operating frequencies are usually associated with better resolution, frequencies as low as 100 Hz can produce acceptable images in simulated oilfield environments.The imaging scheme has been applied to data collected during a salt-water injection experiment at the Richmond Field Station test site in Richmond, California. Both the data and the resulting images clearly reveal the presence of the plume and indicate that it is migrating towards the north-northwest rather than spreading symmetrically about the injection well. Applying the imaging code to synthetic data generated by a 3D sheet model verifies the interpretation of these results.

Notes: An accurate analytical expression for shot-gather dip-moveout (DMO) in the timespace log-stretch domain has until now not been published. We present a simpler, alternative derivation of the exact DMO relationships of Black et al. which correctly take account of the repositioning of the midpoint. A new computationally efficient frequency-wavenumber (F-K) DMO operator for shot profiles is then derived, based on these DMO relationships in the time-space log-stretch domain. The newly derived DMO operator is, unlike most other log-stretch DMO operators) accurate for the full range of reflector dips. Along with other schemes which are performed in the log-stretch domain, it offers considerable time savings over conventional DMO processing. We have compared numerically the impulse response of the new operator with those of a number of other shot-gather DMO operators, and found it to be superior and well match to the theoretical elliptical DMO response.

Notes: In order to investigate the possibility of using low-frequency electromagnetic waves to detect and monitor oil contamination of soils, a series of laboratory measurements were performed. A new measurement system to monitor the resistivities of soil and sand samples while samples are being contaminated by diesel oil is presented. The frequency used in measurements is 100 kHz. Since the measurement system is composed of coil-type transmitters and receivers, there is no need for electrodes to be in contact with samples. The contamination process is simulated using diesel oil dripping on top of soil and sand samples. The conductivity distributions in samples along the sample length are recorded as a function of time. Water-wet sand and soil samples were measured during diesel oil contamination. The measured data show that the conductivities of soil and sand samples change during the contamination process. The change in resistivity for measured samples before and after diesel oil contamination is in the range of 20% to 50%, giving a reflection coefficient change in the low-frequency limit of 4.7% to 7%. This amount of change in the reflection coefficient makes it very challenging to detect and monitor oil contamination based on EM reflection from the contaminants. The results suggest that EM methods based on propagation and induction, such as tomography and borehole induction, could be used for this purpose.

Notes: A simple expression ties the midpoint of a surface spread to reflection points on a dipping plane. If we use two coordinate systems, an unprimed one with a z-axis perpendicular to the surface and a primed one with a z-axis perpendicular to the reflector, we have 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR831:GPR_831_mu1"/〉where θ is the dip angle, φ is the profile angle, X is the source-to-receiver separation, and D is the depth of the reflector. The reflection point is (x, yp, D) and the surface midpoint is (xc, yc, 0).Using the expression, I show that if complete azimuthal coverage is required at a CMP position, the reflection points lie on an ellipse. Similarly, a fixed reflection point generates a circle of surface midpoints. A circle of CMP positions for fixed θ and φ becomes an ellipse of reflection points and a circle of reflection points becomes an ellipse of midpoints. A user can easily find the shape and location of the reflection area generated by a surface aperture.

Notes: An integrated electromagnetic and nuclear magnetic resonance (NMR) method is proposed for investigating highly conductive soil areas. Using a simple model of a homogeneous half-space and the same antenna for both methods, a significant improvement in the NMR data interpretation is obtained. A case study has shown fair agreement between the results from computer modelling, field tests, and data from a nearby observation well. The electromagnetic method and the half-space model were selected for easy integration into an existing instrument used for the NMR method. A more accurate knowledge of the conductivity distribution with depth will further improve the final result.

Notes: A new method is proposed for the quantitative interpretation of SP field data produced by a polarized ore body and simulated by an inclined sheet. The theoretical concept is based on the study of the amplitude Spectrum. It is shown that the SP amplitude Spectrum is not continuous at zero frequency; this leads to the dip angle determination of the inclined sheet. It is also shown that the SP amplitude spectrum is practically nullified at a characteristic amortization frequency that depends on the depth of the polarized body. The maximum amplitude Spectrum value of the SP gradient is used to estimate the depth to the bottom of the polarized body. Thus, the geometrical parameters h and H, the depths to the top and bottom, respectively, as well as the dip angle of the inclined sheet, can be satisfactorily determined. Some problems may arise in the determination of these parameters, affecting their accuracy, whenever unwanted frequency noise is present.

Notes: Twelve ground penetrating radar (GPR) experiments were conducted on the modern, wave-influenced William River delta, on the Southern shore of Lake Athabasca in northern Saskatchewan, Canada. The delta is a well-sorted, quartzoserich, clean, sand-dominated, water-saturated geomorphic feature which provided an ideal site to test GPR. Penetration depths, resolution and continuity of reflections were compared for different antennae frequencies (25, 50, 100, 200 MHz) and transmitter powers (pulser voltage: 400 V, 1000 V). The data show significant variations in vertical resolution from 0.15 m to 0.76 m (200-25 MHz), depth of penetration from 14 m-28 m (200-25 MHz), and continuity of reflections. Increasing the transmitter power from 400 V to 1000 V increases the depth of penetration by 5 to 14% and improves the continuity of reflections with little effect on the resolution.

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: 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: 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 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: Gravity data are often acquired over long periods of time using different instruments and various survey techniques, resulting in data sets of non-uniform accuracy. As station locations are inhomogeneously distributed, gravity values are interpolated on to a regular grid to allow further processing, such as computing horizontal or vertical gradients. Some interpolation techniques can estimate the interpolation error. Although estimation of the error due to interpolation is of importance, it is more useful to estimate the maximum gravity anomaly that may have gone undetected by a survey. This is equivalent to the determination of the maximum mass whose gravity anomaly will be undetected at any station location, given the data accuracy at each station. Assuming that the maximum density contrast present in the survey area is known or can be reasonably assumed from a knowledge of the geology, the proposed procedure is as follows: at every grid node, the maximum mass whose gravity anomaly does not disturb any of the surrounding observed gravity values by more than their accuracies is determined. A finite vertical cylinder is used as the mass model in the computations. The resulting map gives the maximum detection error and, as such, it is a worst-case scenario. Moreover, the map can be used to optimize future gravity surveys: new stations should be located at, or near, map maxima. The technique is applied to a set of gravity observations obtained from different surveys made over a period of more than 40 years in the Abitibi Greenstone Belt in eastern Canada.

Notes: Restoration of missing offsets and trace interpolation is an interesting and important problem in seismic data processing. Based on the parabolic Radon transform, a method is presented for missing offset restoration, resampling and regularization of prestack individual CMP gathers. The method is also valid for resampling spatially aliased seismic data.The method is based on the parabolic assumption of the seismic events which is generally verified after a partial NMO correction in the CMP organization of the data. The essence of the method consists of a band-limited forward parabolic Radon transform of the data containing zero traces at the missing offset locations. The curvature range is chosen to map properly the coherent energy while the zero traces map beyond that range. After inverse transform the originally zero traces are partly filled with information. Several iterations of forward and inverse transform, every time replacing the zero traces in the original gather with the partially reconstructed ones, almost fully restore the zero traces.Efficient and fast algorithms can be built up to process data having a uniform geometry. Examples on synthetic as well as on field data demonstrate clearly the robustness of the method.

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: 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: The quality of results of migration before stack is sensitive to inaccuracies in the velocity field applied. This does not hold if only traces of similar sources-receiver distances (common offset traces) enter the migration process. In this case, velocity deviations generate minor shifts in travel times of migrated interfaces but no deterioration in quality. These time shifts are proportional to both the velocity error and the square of the source-receiver distance.The above observations suggest the following migration scheme: migrate separately the traces of the various common offset planes or groups of neighbouring common offset planes; for every common midpoint plane and as a function of travel-time perform a residual NMO search to find trajectories t) =t)o+px)2 of maximum coherency along which migrated events are aligned; correct for residual NMO and stack the migration results obtained in the various common offset planes to obtain the final migration result.This process not only takes care of inaccurate migration velocities but also corrects partly for effects of refraction.It is shown by means of an example that good migration results are generated even with a considerably deviating velocity field.

Notes: It is shown that the so-called Kirchhoff-summation operator is of a very wide-band nature and even contains an evanescent part. As a consequence, discretization may cause serious aliasing errors, particularly for small extrapolation steps. It is proposed to use in all practical cases band-limited versions of the summation operator, the spatial cut-off frequency being determined by the spatial Fourier spectrum of the coherent noise.

Notes: In the Andes mountains of North Chile seismic refraction measurements revealed the existence of a buried graben structure. The special geological environment permitted the deduction, by detailed analyses of diffraction patterns and delayed arrival times, of a low velocity layer underneath a high velocity ignimbritic sheet.The gravity method was chosen as an economic secondary aid to trace the course of the buried structure. This unusual combination of detailed gravity measurements following a general seismic survey was not only successful in detecting and tracing a buried structure, but also provided complementary data about the deeper subsurface conditions.

Notes: A Kunetz equation is often used as the starting point in the development of solutions for the inversion of one-dimensional, noise free, normal incident seismograms, for which |ro|= 1. In this paper we demonstrate a need for a Kunetz-type equation in which filtered signals can be used, so that noise effects can be reduced. We then show that an infinite number of Kunetz-type equations exist for the lossless wave equation in layered media. Finally, we show that it is indeed valid to formulate and solve the inverse problem using filtered signals.

Notes: A theory for the bipole-dipole method of resistivity sounding is developed. Bipole-dipole apparent resistivities are related to Schlumberger apparent resistivities at two spacings. The theory can also be used to compute exact dipole-dipole apparent resistivity curves providing an improvement over the existing techniques which involve far field approximations. A comparison of bipole-dipole and dipole-dipole systems reveals the similarity between the two. However, the resolution of the bipole-dipole system depends on the azimuth angle. The flexibility of the theoretical expressions lead to a generalized field scheme independent of the bipolar or dipolar nature of the current source.

Notes: The combined observation of first and later arrivals in shallow seismic refraction surveys, particularly on hard rock terrains, is discussed. Details of experimental weathered-zone investigations by the correlation refraction method in a granite terrain (i.e. field procedure, seismograms obtained, plotting of the data, and identification of the waves are presented). Complete travel time data and interpreted subsurface sections of a few test refraction surveys are included. In one instance the interpreted results of normal and converted refracted wave data have been tested by drilling at three points along a 220 m long profile.

Notes: A Bremmer Series decomposition of the solution y(t) to the lossless wave equation in layered media is 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR71:GPR_71_mu1"/〉 where the yj(t) are physically meaningful constituents (i.e., y1(t) are primaries, y2(t) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact.

Notes: The interpretation of vertical electrical sounding data can be facilitated by the application of the reciprocal geoelectric section. If an apparent resistivity field curve has a descending right end, the apparent resistivity curve of the reciprocal geoelectric section can be obtained by the application of linear filter theory; from this the total transverse resistance of the geoelectric section can be calculated without having to interpret the field curve. In addition, Orellana's auxiliary point method can now be extended to interpret three and four layer apparent resistivity curves of all types.This paper summarizes the properties of the resistivity transform curve, the apparent resistivity curve, and the apparent resistivity curve of the reciprocal geoelectric section, with several new applications.

Notes: Past design of marine source arrays has been based on one or more of the following principles:〈list xml:id="l1" style="custom"〉(i) simultaneous operation of multiple identical sources to increase radiated signal strength by simple addition;(ii) superposition of wavelets of different fundamental frequency to achieve a total pulse of desired, front-loaded form (e.g. mixed volume air-gun arrays);(iii) horizontal spacing of units or groups to achieve spatial filtering effects.The phenomenon of interaction between sources, affecting the loading experienced by each, has usually been ignored, or else avoided by wide spacing of units. However, interactions can significantly affect the efficiency and frequency response, in a way that can be favourable.Calculations are presented for sources emitting continuous or long duration signals, showing the energy efficiency as a function of frequency for arrays in a variety of configurations. Interaction effects are significant for inter-source spacings smaller than or comparable with the wavelength—not, as is often stated, up to a distance related to the radii of the sources. The results show that potential exists for tailoring the frequency response of a source system, according to the application, by simple spatial rearrangement of units.Similar effects occur with interacting impulsive sources, but it is shown that different criteria apply for the optimum arrangements of units.

Notes: This paper deals with the practical problem of processing magnetic data in the field, and it shows how the parameters describing a geological contact can be obtained quickly and conveniently on the basis of five measurements. The complete interpretation can be performed in the field using a programmable calculator. For a small ground-party the method greatly improves the quality of the field-work and the interpretation of the magnetic data. The method has been applied to the data from a magnetic survey over the Mooki Fault (Gunnedah-Manilla, N.S.W.), and the results are discussed as an illustration of the efficacity of the method as a field procedure.

Notes: The iterative estimation process of residual static corrections published earlier is further analyzed.The convergence and convergence rate of the iterative solution are analysed for components of different relative wave length with results of both theoretical and practical value.Relative wave length components practically determinable and indeterminable are defined.One model example is presented for illustrative purposes.

Notes: The observation of shear waves is finding more interest in seismic exploration, especially for the determination of additional lithologic parameters, e.g. Vp/Vs. We demonstrate the observation of converted waves in routine seismic work by means of horizontal geophones. Field technique and data processing permit acquisition and interpretation of converted waves in connection with routine seismic measurements. A special interpretation of the recorded converted waves results in the shear wave velocity and the Vp/Vs relation.

Notes: The transient response of a conductive shell-shell model in the one-loop version was obtained analytically. The results indicate that four zones, namely early, late early, intermediate, and late zone can be identified in the total transient characteristic of the model. In case the measurements are carried out in the late early zone, a conductive target appears as a resistive one. It is suggested that the optimum time of measurement should be so selected as to fall in the intermediate zone.

Notes: A careful examination of the seismic refraction technique details the general assumptions and processes on which it is based. It is apparent that the normal interpretive process of determining velocity by hand fitting time breaks, while necessary to identify the refractors, is subject to imprecision.We describe a digital technique that calculates velocity and its precision from the time break measurements. The technique also facilitates examining for the possibility of systematic errors. Having observed the kind of imprecision that was apparent with velocity we extended our study to layer thicknesses (and thus depth) and found that the imprecision was significantly magnified.The technique and our claims for it are supported by an example of its application to a refraction survey in the Sturt Block, Western Australia.

Notes: A stacked seismic section represents a wave-field recorded at regularly spaced points on the surface. The seismic migration process transforms this recorded data into a reflectivity display. In recent years, Jon F. Claerbout and his co-workers developed migration techniques based on the numerical approximation of the wave equation by finite difference methods. This paper describes an alternative method, termed ASD (for Accurate Space Derivative), and its application to the wave equation migration problem. In this approach to the numerical solution of partial differential equations, partial derivatives are computed by finite Fourier transform methods. This migration method can accommodate media with vertical as well as horizontal velocity variations.

Notes: Field results of shallow seismic reflections obtained with a propane-oxygen detonator (POD) are presented. The survey site was in a tin-mining area of the Kinta Valley in Malaysia. The shallow and irregular limestone bedrock is overlain by alluvial “tailing” and virgin sediments. Sizes of such mining areas can range from about 320 ± 320 m2 to 900 ± 900 m2. The survey was intended to delineate the topography of the bedrock, which is of vital importance in tin ore exploration and exploitation. The equipment included single- and 12-channel signal enhancement seismographs, the POD, a hammer and thumper. The inexpensive and portable POD generates directional waves of reproducible form, variable energy of high frequency, and only a few surface waves at short offsets. Reflections at around 200 Hz were obtained from the shallow bedrock at about 25 m as well as from very shallow lithological interfaces. The interpretation of seismograms is supported by drill-hole lithological sections and synthetic seismograms. The data illustrate the successful use of shallow reflections for mapping irregular bedrock. Reflection seismics can provide better horizontal and vertical details than the refraction method. Further improvements based on the data-processing flexibility of new signal enhancement seismographs and synthetic seismograms are suggested.

Notes: Dynamic elastic moduli like E, μ, K and μ of the foundation rock of a dam have been determined by finding Vp- and Vs-velocities by seismic refraction with a hammer as source. Some parameters such as “fracture frequency” and “rock quality designation” (RQD) of the foundation rock have been derived using “average regression curves” and Vp-velocities. By comparing K/μ with Vp/Vs, a few locations showing weathered conditions have been demarcated. This compares well with RQD values of those locations.

Notes: Using homogeneous full-space and half-space models, we show that induced-polarization properties of the medium influence the inductive coupling between two circuits. It is suggested that existing methods to interpret electromagnetic sounding data should be viewed with caution if the electro-chemical dispersion is not taken into account.

Notes: A synthetic seismogram that closely resembles a seismic trace recorded at a well may not be at all reliable for, say, stratigraphic interpretation around the well. The most accurate synthetic seismogram is, in general, not the one that displays the smallest errors of fit to the trace but the one that best estimates the noise on the trace. If the match is confined to a short interval of interest or if the seismic reflection wavelet is allowed to be unduly long, there is considerable danger of forcing a spurious fit that treats the noise on the trace as part of the seismic reflection signal instead of making a genuine match with the signal itself. This paper outlines tests that allow an objective and quantitative evaluation of the accuracy of any match and illustrates their application with practical examples.The accuracy of estimation is summarized by the normalized mean square error (NMSE) in the estimated reflection signal, which is shown to be(/n)(PN/PS)where PS/PN is the signal-to-noise power ratio and n is the spectral smoothing factor. That is, the accuracy varies directly with the ratio of the power in the signal (taken to be the synthetic) to that in the noise on the seismic trace, and the smoothing acts to improve the accuracy of the predicted signal. The construction of confidence intervals for the NMSE is discussed. Guidelines for the choice of the spectral smoothing factor n are given.The variation of wavelet shape due to different realizations of the noise component is illustrated, and the use of confidence intervals on wavelet phase is recommended.Tests are described for examining the normality and stationarity of the errors of fit and their independence of the estimated reflection signal.

Notes: There are numerous modeling techniques commonly employed for the computer simulation of seismic wave propagation. The capabilities of these techniques vary according to the theoretical foundations and subsequent approximations upon which the algorithms are based. This paper constitutes a comparative review of seven modeling methods: geometric ray theory, asymptotic ray theory, generalized ray theory, Kirchhoff wave theory, Fourier synthesis, finite differences, and finite elements.These methods can be categorized as ray or wave, acoustic or elastic, and can be contrasted according to their relative abilities to simulate such behavior as wave interference effects, diffractions, and mode conversions. As is implied by their names, geometric ray theory and asymptotic ray theory are both ray methods. The other five methods provide wave theory simulations. Geometric ray theory and Kirchhoff wave theory are normally implemented in acoustic form, while the other methods are readily adapted for computing elastic theory solutions. Generalized ray theory and Fourier synthesis are more limited in the complexity of geological model they can accommodate than are the other techniques. The methods which typically demand the greatest computer resources are the finite-difference and the finite-element techniques. All methods can incorporate at least some multiple events. Diffractions, however, are only inherent in the solutions computed by Kirchhoff wave theory, finite differences and finite elements. Attenuation is readily incorporated in both the Fourier synthesis and the finite-element methods.As an example of the application of seismic modeling, a geological model representative of a typical petroleum exploration target is used to compare vertical seismic profiles calculated by different modeling methods.

Notes: The cross-hole variant of the magnetometric resistivity (MMR) method requires two bore holes in the vicinity of a conductive target. In the first, two fixed current electrodes are located, one above the other. They are linked to a low frequency current source by cables, the whole system forming a vertical current bipole. In the second, a sensitive coil measures the axial magnetic field as a function of depth. For a uniform earth, if both holes are vertical, the measured component vanishes by symmetry. However, the presence of a local conductor channels the current and causes an anomalous magnetic component which is interpreted to indicate the position, shape and relative conductance of the target.Mineral deposits are often lamellar in form. The conductive disc is the simplest bounded lamella for which MMR responses may be computed. It is excited by a single current source on its axis. The second source and the surface of the earth are assumed to be far away, a valid assumption for down-hole measurements.The numerical method introduces a new integral equation describing the interaction of current dipoles located in the plane of the disc. The equation is solved analytically for a disc of infinite radius, a layer, and the result is compared with a corresponding known boundary value solution.The computed radial current in the disc and the magnetic field generated by it are described in terms of a current channelling number. The magnitude of the computed field is of the order of one nanoTesla for a typical mining problem.

Notes: Time horizons can be depth-migrated when interval velocities are known; on the other hand, the velocity distribution can be found when traveltimes and NMO velocities at zero offset are known (wavefront curvatures; Shah 1973).Using these concepts, exact recursive inversion formulae for the calculation of interval velocities are given. The assumption of rectilinear raypath propagation within each layer is made; interval velocities and curvatures of the interfaces between layers can be found if traveltimes together with their gradients and curvatures and very precise VNMO velocities at zero offset are known.However, the available stacking velocity is a numerical quantity which has no direct physical significance; its deviation from zero offset NMO velocity is examined in terms of horizon curvatures, cable length and lateral velocity inhomogeneities.A method has been derived to estimate the geological depth model by searching, iteratively, for the best solution that minimizes the difference between stacking velocities from the real data and from the structural model.Results show the limits and capabilities of the approach; perhaps, owing to the low resolution of conventional velocity analyses, a simplified version of the given formulae would be more robust.

Notes: From a great variety of in situ shear wave experiments, i.e., reflection, refraction and borehole surveys in the shallow sediments of the north German plains, several specific properties have been derived. Shear waves (S) differ from compressional waves (P) in that:〈list xml:id="l1" style="custom"〉1they are not affected by the degree of water saturation. Thus, they provide a better correlation between the velocity Vs and (solid) lithology;2they generally have lower frequencies, but shorter wavelength and, hence, a better resolution of thin layers;3they have lower absorption Qs−1 and hence a better penetration in partially saturated and gas-containing sediments than P-waves.Correlations have been established between Vs and the confining pressure and between reduced Vs values and several lithological parameters like the grain size of sandy material. More lithological and hydrological information is obtained by using S- and P-wave surveys along the same profile. The best information on a sedimentological structure is obtained by the simultaneous observation of Vs, Vp, Qs and Qp.

Notes: In the design of linear airgun arrays the interaction between the airguns is usually neglected. We review the different formulae which have been proposed for the minimum separation between airguns at which the interaction is negligible. These formulae can all be approximated by a linear function of a single variable.We have analyzed a large number of measurements in order to establish the amount of interaction between two airguns of various volumes at different pressures and depths. The resulting far-field signature has been measured and compared with the sum of the signatures from the two airguns measured in the same experimental situation. The changes in primary pulse amplitude, bubble period and primary/bubble peak-to-peak amplitude ratio were computed from the measurement data as a function of airgun separation, chamber volume, chamber pressure and airgun depth. The influence of a waveshape kit was investigated, and the effects of interaction and the effects of using a waveshape kit were compared.

Notes: Almost all ray-tracing methods ignore the analysis of the amplitudes of seismic arrivals and therefore utilize only half of the available information. We propose a method which is a combination of ray-tracing imaging and transformation of the amplitudes of wide-aperture data.Seismic data in the conventional X-T domain are first transformed to the domain of intercept time τ and ray parameter p to recover the plane wave response. The next step is the derivation of a series of plane wave reflection coefficients, which are mapped as a function of τ and p. The reflection coefficients R(τ, p) for two arbitrarily chosen traces can then be used in our inversion method to derive a slowness-depth and a density-depth profile. It is shown that the inclusion of amplitudes of seismic arrivals (in this method, we consider the acoustic case) makes the inverse method highly stable and accurate. In a horizontally stratified medium one can recover separate profiles of velocity and density. Since this method utilizes large-offset data, it can be used for separate recovery of velocity and density to a greater depth.

Notes: Random amplitude and phase errors in seismic input data introduce a coherent distribution of migration half-circles or “smiles”, the occurrence of which may cause a significant decrease of signal-to-noise ratio. In addition, the effect of quantization errors is discussed for different wordlengths, used both during acquisition and during data processing. Results of sign-bit recordings are shown.

Notes: A hybrid method for wave field computation in two-dimensional heterogeneous media is proposed. The proposed method is a combination of analytical and numerical techniques. The method is based upon the separation of wave propagation and scattering and upon the description of each process by the most suitable technique. The SH wave scattering problem is used to elucidate the proposed method.Examples of numerical computations using the hybrid method are considered for a number of simple models. The analysis of the results shows that the hybrid method gives both a detailed and a reasonably accurate description of the total wave field.

Notes: After a brief discussion of MT modeling methods, we expose a particular application of finite elements that may be assimilated to a finite-difference method. The resulting linear equations obtained are similar to the transmission network equations for two-dimensional media. The introduction of resistivity discontinuities is more rigorous than in the usual finite-difference development. The consequence is an improved accuracy.We also present some conclusions about various problems encountered in modeling, such as the choice of network boundary conditions, linear system resolution and the final derivation of apparent resistivity. Application of successive over-relaxation is discussed and we detail rules for mesh design that control result accuracy and iterative convergence.