ALBERT

Notes: X-ray diffraction (XRD) patterns from nominally β-SiC specimens often differ from those expected for the cubic crystal structure. These differences include the presence of additional peaks, enhanced background intensities, peak broadening, changes in relative peak heights, and shifts in peak positions. It has long been recognized that they are due to the presence of stacking faults, and models relating the experimental observations to stacking fault population have continued to evolve. The presence and relative magnitude of these features vary among different β-SiC specimens. In this work, computer simulations were used to show that the variations are closely related to differences in the type and spatial distribution of stacking faults in each specimen. In these simulations, stacking sequences were generated using a selectively activated 1-D Ising model with a Boltzmann-type probability function for specifying errors, which allows a wide variety of fault configurations to be generated. Direct correlations between different features in the XRD data to the underlying fault population are demonstrated, which are discussed in this paper. It is also shown that this computer model is general, in the sense that many of the models presented in prior work can be interpreted as limiting cases of it.

Notes: The electromagnetic array profiling (EMAP) exploration method can be combined with a direct one-dimensional inversion process for conversion to depth to produce a subsurface resistivity cross-section. This cross-section may then be interpreted in parallel with a seismic cross-section to enhance the prediction of rock type and structure. In complex thrust environments and areas of shallow carbonate rocks, the EMAP method is often used to provide additional data either to help the seismic processor and/or to aid the seismic interpretation. In particular, the electromagnetic (EM) data can be used to build an independent seismic velocity file for depth migration.Three EMAP test areas in the western United States are used to demonstrate such a use of EMAP as an expioration tool. The first shows how a velocity file is estimated from resistivity data for seismic depth migration processing in a complex thrust environment. In the second example, the method is applied in layer-cake geology with high seismic velocity rocks at the earth's surface. The third example is another complex thrust environment, but in this case the velocity file derived from the resistivity data is used for stacking the seismic data.

Notes: A fast inversion technique for the interpretation of data from resistivity tomography surveys has been developed for operation on a microcomputer. This technique is based on the smoothness-constrained least-squares method and it produces a two-dimensional subsurface model from the apparent resistivity pseudosection. In the first iteration, a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. For subsequent iterations, a quasi-Newton method is used to estimate the partial derivatives which reduces the computer time and memory space required by about eight and twelve times, respectively, compared to the conventional least-squares method. Tests with a variety of computer models and data from field surveys show that this technique is insensitive to random noise and converges rapidly. This technique takes about one minute to invert a single data set on an 80486DX microcomputer.

Notes: High-speed photography has been used visually to study the shape, surface, turbulence and behaviour of an underwater oscillating bubble generated by an airgun. The source was a BOLT airgun with a chamber volume of 1.6cu.in., placed in a 0.85m3 tank at 0.5m depth. Near-field signatures were also recorded in order to compare the instant photographs of the oscillating bubble with the pressure field recorded about 25 cm from the gun. Estimations of the bubble-wall velocity and bubble radius estimated from high-speed film sequences are also presented, and are compared with modelled results. The deviation between the modelled and measured bubble radii was at most 9%. In order to check the capacity for transmission of light through the bubble, a concentrated laser beam was used as illumination. We found that the air bubble is a strong scattering medium of laser light, hence the bubble is opaque.

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: We consider the problem of computing the most probable location of a target based on radar measurements of the subsurface. Our algorithm makes use of the maximum likelihood estimator (MLE), which represents a correlation between the measured data and synthetic data generated for the object of interest at different locations. Previous studies assume a plane-wave acquisition geometry and target object(s) embedded in a uniform background. In this paper, a generalization of the MLE method is presented which is valid for discrete point sources (and receivers) and a 2D model (i.e. a 2.5D acquisition geometry). Within this formulation the treatment of a non-uniform background model is also possible. We concentrate on geotechnical ground investigations and assume that the characteristic dimensions of the target object are in the range 1–2λ, (λ being the wavelength). The potential of the method is demonstrated employing cross-hole radar data acquired in a controlled field experiment. The MLE result is also compared with the image obtained employing a full reconstruction method such as diffraction tomography.

Notes: We present a simple method for estimating an effective source wavelet from the first arrival in marine vertical seismic profiling (VSP) data. The method, which utilizes the free-space Green's function of the Helmholz equation, is simple and very computer efficient. We show examples from synthetic and real offset and walkaway VSP data.In the synthetic examples, we show that data modelled with the estimated wavelet give small residuals when subtracted from the reference data. In the real data examples, we show that when modelling with the wavelet estimated from the real data, in a smooth macromodel, we obtain a good fit between the first arrivals in the real and modelled data.

Notes: An expression which is optimum with respect to the simplicity of the numerical computations is obtained for the magnetic field of a polyhedron with constant magnetization. The high accuracy of the results is illustrated using a realistic numerical model.The existence of the magnetic field at points inside the source and on its boundary is discussed and related to real magnetic data modelling.

Notes: The posterior probability density function (PPD), σ(m|dobs), of earth model m, where dobs are the measured data, describes the solution of a geophysical inverse problem, when a Bayesian inference model is used to describe the problem. In many applications, the PPD is neither analytically tractable nor easily approximated and simple analytic expressions for the mean and variance of the PPD are not available. Since the complete description of the PPD is impossible in the highly multi-dimensional model space of many geophysical applications, several measures such as the highest posterior density regions, marginal PPD and several orders of moments are often used to describe the solutions. Calculation of such quantities requires evaluation of multidimensional integrals. A faster alternative to enumeration and blind Monte-Carlo integration is importance sampling which may be useful in several applications. Thus how to draw samples of m from the PPD becomes an important aspect of geophysical inversion such that importance sampling can be used in the evaluation of these multi-dimensional integrals. Importance sampling can be carried out most efficiently by a Gibbs' sampler (GS). We also introduce a method which we called parallel Gibbs' sampler (PGS) based on genetic algorithms (GA) and show numerically that the results from the two samplers are nearly identical.We first investigate the performance of enumeration and several sampling based techniques such as a GS, PGS and several multiple maximum a posteriori (MAP) algorithms for a simple geophysical problem of inversion of resistivity sounding data. Several non-linear optimization methods based on simulated annealing (SA), GA and some of their variants can be devised which can be made to reach very close to the maximum of the PPD. Such MAP estimation algorithms also sample different points in the model space. By repeating these MAP inversions several times, it is possible to sample adequately the most significant portion(s) of the PPD and all these models can be used to construct the marginal PPD, mean) covariance, etc. We observe that the GS and PGS results are identical and indistinguishable from the enumeration scheme. Multiple MAP algorithms slightly underestimate the posterior variances although the correlation values obtained by all the methods agree very well. Multiple MAP estimation required 0.3% of the computational effort of enumeration and 40% of the effort of a GS or PGS for this problem. Next, we apply GS to the inversion of a marine seismic data set to quantify uncertainties in the derived model, given the prior distribution determined from several common midpoint gathers.

Notes: The long-wavelength propagation and attenuation characteristics of three geological structures that frequently occur in reservoir environments are investigated using a theoretical model that consists of a stack of fine and viscoelastic plane layers, with the layers being either solid or fluid. Backus theory properly describes fine layering and a set of fluid-filled microfractures, under the assumption that interfaces between different materials are bonded. The effects of saturation on wave attenuation are modelled by the relative values of the bulk and shear quality factors.The anisotropic quality factor in a fine-layered system shows a variety of behaviours depending on the saturation and velocities of the single constituents. The wave is less attenuated along the layering direction when the quality factors are proportional to velocity, and vice versa when inversely proportional to velocity. Fractured rocks have very anisotropic wavefronts and quality factors, in particular for the shear modes which are strongly dependent on the characteristics of the fluid filling the microfractures.When the size of the boundary layer is much smaller than the thickness of the fluid layer, the stack of solid-fluid layers becomes a layered porous media of the Biot type. This behaviour is caused by the slip-wall condition at the interface between the solid and the fluid. As in Biot theory, there are two compressional waves, but here the medium is anisotropic and the slow wave does not propagate perpendicular to the layers. Moreover, this wave shows pronounced cusps along the layering direction, like shear waves in a very anisotropic single-phase medium.

Notes: Responses of a multifrequency, multicoil airborne electromagnetic (AEM) system were modelled numerically for 3D electrical conductors embedded in a resistive bedrock and overlain by an overburden of low to moderate conductivity. The results cover a horizontal coplanar coil configuration and two frequencies, 7837 Hz and 51 250 Hz. The models studied are single or multiple, poor conductors (conductance lower than 0.1 S) embedded in a host rock of high but finite resistivity (5000 Ωm) and overlain by a layer of overburden with finite thickness and low to moderate conductivity (conductance up to 2 S).On the basis of the modelling results, limits of detectability for poor conductors have been studied for the various model structures. The results indicate that the anomaly from a steeply dipping, plate-like conductor will decrease significantly when the conductor is embedded in a weakly conductive host rock and is overlain by a conductive overburden. However, an anomaly is obtained, and its magnitude can even increase with increasing overburden conductivity or frequency. The plate anomaly remains practically constant when only the overburden thickness is varied. Changes in overburden conductivity will cause the plate-anomaly values to change markedly. If the plate conductance is less than that of the overburden, a local anomaly opposite in sign to the normal type of anomaly will be recorded. Another major consequence is that conductors interpreted with free-space models will be heavily overestimated in depth or underestimated in conductance, if in reality induction and current channelling in the host rock and overburden make even a slight contribution to the anomalous EM field.The lateral resolution for the horizontal coplanar coil system was found to be about 1.7 times the sensor altitude. Similarly, the lateral extension of a horizontal conductive ribbon, required to reach the semi-infinite (half-space) behaviour, is more than three times the sensor altitude. Finally, screening of a steeply dipping plate, caused by a small, conductive horizontal ribbon, is much more severe than screening of the same plate by an extensive horizontal layer.

Notes: We consider the problem of determining and predicting how the wave speeds in particular directions for a transversely isotropic (TI) medium depend on particular combinations of the density-normalized moduli Aij. The expressions for the qP and qSV velocities are known to depend on four moduli. Normally, we can only determine three independent parameters from qP data, or two from qSZ data, as the others have much lower sensitivity. The resolvable parameters are conveniently described by axial and off-axis parameters: for qP rays, P0°= A11, P90°= A33 and P45°=(A11+ A33)/4 + (A13+2A55)/2; and for qSV rays, S0°= S90°=A55 and S 45°= (A11+ A 33)/4- A13/2. These parameters control the magnitude of the squared-velocities on the axes and at approximately 45°. For an arbitrary TI medium, if the medium is perturbed in a way that preserves a particular parameter, then slowness points in the associated direction and mode witl be approximately preserved in the new medium. we refer to these parameters as ‘push-pins’, i.e. if a parameter is fixed, the associated part of the slowness surface is pinned in place.Because, these five push-pins only contain four independent moduli, we can only fix at most three push-pins. Perturbing one of the other parameters inevitably perturbs the other. Numerical results illustrating the linkage between two push-pins, when three are fixed, are presented.So-called anomalous TI media occur when the roles of the qP and qSV waves are reversed: in some directions the faster ray has transverse polarization. That, in turn, requires anomalous velocities at the push-pins, i.e. S0° 〉 P0°, S45° 〉 P45° and/or S90° 〉 P90° (equivalent to the usual anomalous conditions A11 〈 A55, 〈 0 and/or A33 〈 A55). In the Appendix, we confirm that anomalous sensitivities of the velocities at the five push-pins only occur in such media, although the push-pins still apply if interpreted appropriately. Truly anomalous sensitivities, in which push-pins play no role, only occur in media near the boundary between normal and anomalous.

Notes: Electrical conductivity mapping is a prerequisite tool for hydrogeological or environmental studies. Its interpretation still remains qualitative but advantages can be expected from a quantitative approach. However a full 3D interpretation is too laborious a task in comparison with the limited cost and time which are involved in the majority of such field studies. It is then of value to define the situations where lateral variations are sufficiently smooth for a 1D model to describe correctly the underlying features.For slingram conductivity measurements, criteria allowing an approximate 1D inversion are defined: these mainly consist of a limited rate of variation over three times the intercoil spacing.In geological contexts where the weathering has generated a conductive intermediate layer between the underlying sound rock and the soil, this processing can be applied to determine the thickness of the conductive layer from the apparent resistivity map when the other geoelectrical parameters are known. The examples presented illustrate this application.

Notes: A method to determine the position and magnetization vector of buried objects producing a magnetic anomaly is described. The data used were collected in boreholes. Since the anomaly is due to a number of objects, a ‘stripping’ procedure is employed for finding them, and therefore the process of inversion for finding all objects causing the anomaly consists of a few inversion steps.In each inversion step, two dipoles are considered as a model which approximates an object. The position and magnetic moments of the dipoles are the unknown parameters. The initial parameters are optimized by minimization of an objective function. The optimization procedure consists of a combination of linear and non-linear inversion. The solution of the linear inversion is obtained by singular value decomposition and that of the non-linear inversion by a six-dimensional simplex method (polytope algorithm). After finding one object, its effect is subtracted (‘stripped’) from the data and a new inversion step is started with new initial models and with a reduced data set. The inversion steps for finding different objects are continued until the absolute norm of the data becomes less than some adjustable value.The data will also be inverted assuming a three-dipole model in order to find the effect of using a more complex model in the inversion.The efficiency of the method is demonstrated using synthetic and real borehole data.

Notes: A simple numerical procedure is described for measuring the distance XY in the generalized reciprocal method when there are significant measurement errors in the refracted arrival times. It is applicable when the XY value is of similar magnitude to or less than the receiver spacing. Such conditions frequently occur in using the reciprocal or generalized reciprocal methods to estimate static corrections from first-break times measured in multifold seismic reflection profiling. The use of the method is illustrated with data from both deep and high-resolution seismic reflection profiles.

Notes: An analytical transient solution is obtained for propagation of compressional waves in a homogeneous porous dissipative medium. The solution, based on a generalization of Biot's poroelastic equations, holds for the low- and high-frequency ranges, and includes viscoelastic phenomena of a very general nature, besides the Biot relaxation mechanism. The viscodynamic operator is used to model the dynamic behaviour associated with the relative motion of the fluid in the pores at all frequency ranges. Viscoelasticity is introduced through the standard linear solid which allows the modelling of a general relaxation spectrum. The solution is used to study the influence of the material properties, such as bulk moduli, porosity, viscosity, permeability and intrinsic attenuation, on the kinematic and dynamic characteristics of the two compressional waves supported by the medium. We also obtain snapshots of the static mode arising from the diffusive behaviour of the slow wave at low frequencies.

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: The widespread use of common depth point techniques has emphasized the need for accurate static corrections. Manual interpretation methods can give excellent results, but a computer technique is desirable because of the great volumn of data recorded in common depth point shooting. The redundancy inherent in common depth point data may be used to compute a statistical estimate of the static corrections. The corrections are assumed to be time-invarient, surface-consistent, and independent of frequency. Surface consistency implies that all traces from a particular shot will receive the same shot static correction and all traces from a particular receiver position will receive the same receiver correction.Time shifts are computed for all input traces using crosscorrelation functions between common depth point traces. The time shift for each trace is composed of a shot static, a receiver static, residual normal moveout if present, and noise. Estimates of the shot and receiver static corrections are obtained by averaging different sets of the measured time shifts. Time shifts which are greatly in error are detected and removed from the computations.The method is useful for data which has a moderate to good signal to noise ratio. Residual normal moveout should be corrected before estimating the statics. The program estimates the statics for correctly stacking common depth point traces but it is not sensitive to constant or very slowly changing static errors.

Notes: The principle of the mise-á-la-masse method is to earth one current electrode of a pair in a conducting mineral show (in a borehole, in an outcrop etc.) and measure the resulting distribution of electric potentials. The distribution will, to some extent, reflect the geometry of the ore mass of which the mineral show forms a part.In a mise-á-la-masse survey of a lead-zinc deposit in Central Sweden electric potentials were measured on the surface of the ground as well as in some 25 drillholes, in either case with earthings (successively) in three different parts of the irregular ore deposit. Besides this, measurements were made in drillholes with earthings in two further drillholes.Geologic correlation between the drillholes is difficult in the present case on account of the irregular geometry of the ore deposit. However, the mise-á-la-masse measurements clearly showed the dip and the pitch of the ore body, established connections between the different ore widths encountered in the various holes, and yielded information about the shape of the ore mass.In particular, the survey showed that the ore lenses must be crescent-shaped rather than tabular, and the dip was indicated to be westerly, instead of easterly as originally presumed.Three-dimensional models of equipotential surfaces were constructed from the observed drillhole and surface potentials (using transparent plastic sheets and thin copper wire) and these helped to elucidate the mass geometry further.The surface and underground potential data collected in the present case should be of nterest to geophysicists working on analytic continuation problems.

Notes: The author comments the techniques and methods used in continuous seismic profiling by the Monaco Oceanographic Museum during the last five years.Pinger probe give informations on the Mud layering and thickness. On the shelf or in abyssal plains, boomer and sparker are employed and allow to rise various geological conclusions. South coast of France, continental shelf in the Gulf of Lion, abyssal plain of the Ligurian Sea and Lake of Geneva are the areas concerned to with the results.

Notes: The author proposes the parameter Δ2/ΔT1 for possible application in aeromagnetic surveying making use of already available gradiometer systems equipped with sensors separated vertically.

Notes: Geophysical field equipment has undergone rapid changes in the past decade; from simple AGC amplifiers and galvo cameras to binary gain switching amplifiers and digital recorders, all in an attempt to keep pace with the new geophysical interpretive methods developed, and the growing acceptance of the terminology, methods, and philosophy of communication theory.The additional tools of the digital recorder and digital computer make it possible to utilize these new techniques in geophysical processing. Accomplishing these new techniques demands severe requirements on the digital field recording process in handling the decreasing energy return from the seismometer, and to fully realize the capabilities of digital techniques in reducing data. Simple automatic gain control may be used. However, in the more sophisticated interpretive methods, such as autoregression and deconvolution, it is necessary to reconstruct the actual energy levels in the computer. Recording the control signal used in master AGC or programmed gain control may prove satisfactory; however the accuracy of control versus gain is limited to I% for such analog instrumentation.To utilize the computer to its fullest extent, and to accurately perform these new techniques, requires an accuracy of I% or better. This accuracy is obtainable by using a step gain control where the gain is increased by fixed steps in which each step represents a gain in amplification by a constant factor. The accuracy in this case can be made dependent only on the tolerance of resistors used as attenuators or feedback elements. Preferably the constant factor of gain steps should be a number easily handled by the computer. By using 6 db steps it becomes a simple matter to shift binary numbers, such as multiplying or dividing by 10 in the decimal system.The requirements or parameters for such an amplifier system, and the elements of the amplifier necessary to achieve these requirements are presented.

Notes: Spurious reflections showing a residual move-out are generally present on both corrected seismic cross-sections and common depth point composites.We propose to determine a space-time filter satisfying the following conditions: to attenuate as much as possible reflections presenting a given move-out, to retain intact reflections whose time gradient is zero (or has a predetermined value), to be applicable efficiently even to a small number of traces, not to amplify random noise unduly.After briefly indicating the design principle of these filters, we shall give the results of their application to the theoretical examples, in order to bring out: the influence of sampling interval and filter length (possibility of achieving efficient filtering using an apparatus with a small number of terms), the effect of filtering on dipping reflections (reduction in amplitude and distortion increasing with the time gradient), the range of reflection move-out that can effectively be filtered with the same apparatus, the disturbing influence of random noise.〈section xml:id="abs1-2"〉〈title type="main"〉RESUMEOn constate généralement, tant sur les films sismiques corrigés que sur les résultats de couverture multiple, la présence de réflexions parasites présentant une courbure résiduelle d'indicatrice.Nous nous sommes proposé de déterminer un opérateur de filtrage spatio-temporel satisfaisant aux conditions suivantes: filtrer le plus possible les réflexions présentant une courbure donnée, conserver intégralement les réflexions dont le gradient temps est nul (ou a une valeur déterminée), pourvoir être appliqué efficacement à un petit nombre de traces, ne pas amplifier outre mesure les bruits inorganicés.Après avoir indiqué brièvement le principe du calcul de ces filtres, nous présenterons les résultats de leur application à des exemples théoriques, afin de mettre en évidence:ľ'influence du pas d'échantillonnage et de la longueur du filtre (possibilityé d'obtenir un filtrage efficace avec un opérateur comportant un petit nombre de termes),ľ'effet du filtrage sur les réflexions pentées (réduction d'amplitude et distorsion croissant avec le gradient temps),ľ'ouverture de ľ'éventail des réflexions courbes que ľ'on peut filtrer efficacement avec un même opérateur,ľ'influence perturbatrice de bruits inorganicés.

Notes: An iterative process is proposed that computes a distribution of masses giving rise to a certain gravitational field. The possibility of applying a similar procedure to magnetic and electric fields is also discussed.

Notes: The method presented takes the influence of refraction rigidly into account. All travel-times available are used in an application of the method of least squares. The solution is illustrated by a computer flow diagram.

Notes: Charts are presented for the computation of the vertical component of the attraction of horizontal laminas and of horizontal cylinders bounded by irregular w-sided polygons. Contrary to older methods no restricting conditions are made for the directions of the sides of the polygons.

Notes: It was found in Part I of this paper that approximating the sharp cut-off frequency characteristic best in a mean square sense by an impulse response of finite length M produced a characteristic whose slope on a linear frequency scale was proportional to the length of impulse response, but whose maximum overshoot of ±9% was independent of this length (Gibbs' phenomenon). Weighting functions, based on frequency tapering or arbitrarily chosen, were used in Part II to modify the truncated impulse response of the sharp cut-off frequency characteristic, and thereby obtain a trade-off between the value of maximum overshoot and the sharpness of the resulting characteristic. These weighting functions, known as apodising functions, were dependent on the time-bandwidth product Mξ, where 2ξ, corresponded to the tapering range of frequencies.Part III now deals with digital filters where the number 2N–1 of coefficients is directly related to the finite length M of the continuous impulse response. The values of the filter coefficients are taken from the continuous impulse response at the sampling instants, and the resulting characteristic is approximately the same as that derived in Part II for the continuous finite length impulse response. Corresponding to known types of frequency tapering, we now specify a filter characteristic which is undefined in the tapering range, and determine the filter coefficients according to a mean square criterion over the rest of the frequency spectrum. The resulting characteristic is dependent on the time bandwidth product Mξ= (N–1/2)ξ up to a maximum value of 2, beyond which undesirable effects occur. This optimum partially specified characteristic is an improvement on the previous digital filters in terms of the trade-off ratio for values of maximum overshoot less than 1%. Similar to the previous optimum characteristic is the optimum partially specified weighted digital filter, where greater “emphasis is placed on reducing the value of maximum overshoot than of maximum undershoot”. Such characteristics are capable of providing better trade-off ratios than the other filters for maximum overshoots greater than 1/2%. However these filters have critical maximum numbers 2.NC–1 of coefficients, beyond which the resulting characteristics have unsuitable shapes. This type of characteristic differs from the others in not being a biassed odd function about its cut-off frequency.

Notes: In Part I of this paper, we examined the properties of the best mean square approximation to the sharp cut-off frequency characteristic by an impulse response of finite length. It was found that the sharpness of cut-off for the resulting frequency characteristic depended on the length of the impulse response–but because of the discontinuous nature of the specified frequency characteristic, this best mean square approximation always had a maximum overshoot of ± 9%, independent of the length of the impulse response (Gibbs phenomenon).In Part II, we investigate ways of reducing this ± 9% overshoot at the expense of a reduced sharpness of cut-off. The discontinuous frequency characteristic is first approximated by a continuous characteristic with linear or cosine frequency tapering. The impulse response for such tapered characteristics consists of the impulse response of the discontinuous frequency characteristic weighted by a certain function corresponding to the type of tapering employed. The best mean square approximation to the tapered characteristic by an impulse response of finite length M will produce a frequency characteristic whose properties are now dependent on the time-band width product Mζ, where 2ζ is the tapering range.A trade-off exists between the maximum overshoot and the sharpness of cut-off for the resulting characteristic for both forms of frequency tapering. Instead of considering other forms of tapering in the frequency domain, we now investigate arbitrarily chosen weighting functions in the time domain to determine the minimum length of impulse response for a minimum value of maximum overshoot and a maximum value of sharpness of cut-off.Part III will discuss the digital realization of the above finite length impulse responses together with the optimum partially specified digital filter approximation to the desired frequency characteristic.

Notes: Book reviewed in this article:Le Filtrage en Sismique, Tome IJ. AUBOUIN “Geosynclines” (Developments in Geotectonics 1). Elsevier Publishing CompanyEarth and Planetary Science Letters Vol. 1. Nr. 2H. Ramberg Gravity, Deformation and the Earth's Crust Academic Press“Potassium Argon Dating” Compiled by O. A. Schaeffer and J. Zähringer

Notes: Deep seismic sounding was performed along two profiles which cross at the Dinarides area right angles. One of the profiles goes far into the Adriatic Sea.Besides considerations on the lithophysical conditions, characteristics of the registered waves are analysed. The amplitude curves and curves of amplitude ratios are shown. Special attention was paid to the frequency of the registered waves.In order to obtain a better knowledge of the registered wave pattern three-component recordings of waves were carried out. The analysis of the records obtained is given, with particular regard to the possibility of creating converted waves.The Earth's crust structure along the profiles II and III is given.

Notes: Nomograms for solving equations in multilayer and dipping layer cases are presented. The nomograms constructed are used to solve the following equations: I. Intercept-time formula. 2. Critical distance formula. 3. Critical angle formula. 4. Critical angle and dip angle formula. 5. Vertical depth formula.

Notes: Consideration is given to the use of a configuration of four electrodes set in a square array for resistivity measurements.It is found that, by passing current successively between different pairs of electrodes, an apparent resistivity can be determined which is both more sensitive to the position of the array centre and less dependent on orientation than the measures usually obtained with colinear arrays of electrodes. At the same time the observations made enable the degree of the departure of local conditions from conditions of lateral homogeneity to be assessed.Theoretical and practical examples of the use of this electrode system are given and the use of the system both as a tool in mapping and in depth investigations is considered.It is shown that provided electrode spacings are suitably arranged the results of a probe carried out using the square array can be interpreted by conventional methods.The system is shown to have particular advantages in the investigation of lateral resistivity variations and the reduced dependence on orientation makes possible the recasting of interpretation data in an orientationally invariant form with a consequent drastic reduction in the number of type curves required for a particular problem.

Notes: A large self-potential anomaly was outlined in 1963–64 at Tantahuatay near Hualgayoc in the Andes of northern Peru. Peak value recorded was–1842 millivolts–thus making it one of the strongest, or perhaps the strongest, SP anomaly ever measured. A lack of detailed geological data precludes the formulation of an adequate explanation for the Tantahuatay anomaly, but geological and mineralogical similarities with the well-documented Venencocha anomaly near Cerro de Pasco, Peru (Kruger and Lacy, 1949), suggest that the anomaly arises from sulfuric acid associated with the mineral alunite. The anomaly obviously cannot be explained by the half-cell mechanism of Sato and Mooney (1960), who place a limit of 700 millivolts on self-potential anomalies over sulfide bodies. Further study of the Tantahuatay anomaly would be of interest in understanding self-potential mechanisms in general.

Notes: Book review in this articleF. S. Grant and G. F. West, Interpretation Theory in Applied Geophysics, McGraw-Hill Comp., New York, 1965, 583 pp., price $ 17.50.Archaeo-Physica. Technische und naturwissenschaftliche Beiträge zur Feldarchäologie. Mit Beitragen von E. Le Borgne, I. Scollar, J. D. Mudie, J. Görier, H.-J. Appel, G. Strunk-Lichtenberg, Böhlau Verlag, Köln, Graz, 1965, 202 pp., 124 fig.H. Takeuchi, Theory of the Earth's Interior, Blaisdell Publishing Company, Waltham (Mass.), Toronto, London, 1966, 131 pp.G. D. Garland, The Earth's Shape and Gravity, The Commonwealth and International Library, Geophysics Division, Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfurt, 1965, 183 pp., price: 17s 6d.

Notes: According to a study of seismic velocities in the Alpine Foreland of Eastern Switzerland, the initial velocity is rather high in comparison with other Tertiary basins and shows an exceptionally high increase rate. When analysing the average and the interval velocities, especially of Tertiary strata, and when comparing them with velocities of strata of the same age and a very similar facies of the Northern Rheintalgraben, it has been found that the increase of velocity is closely related to the distance to the Subalpine Molasse. The conclusion is that the velocity of the Tertiary strata is strongly influenced by the folding pressure of the Subalpine Molasse or of the Alps. The same method has been applied to a relatively large number of wells in the area of the “German Molasse”. Not only the results in Eastern Switzerland have been confirmed, but also it has been proved that the diagenesis of the Tertiary strata and, hence, their velocities are influenced only partially by the specific depth of the basin. Velocities increase towards the Folded Molasse or the Alps. Consequently they depend on lateral folding pressure, which decreases from west to east with the increasing width of the basin. The tertiary strata of the basin have been affected by lateral folding pressurefrom south to north. However, structures with lateral compression have not been discovered yet in the German Alpine Foreland.

Notes: In a paper by Koefoed and Kegge (1968), which was based on previous work of Wesley (1958), the electrical current pattern has been derived that is induced by an oscillating magnetic dipole in a semi-infinite thin plate of infinitesimal resistivity.In the present paper, the range of validity of the assumptions, on which the work of Wesley is based, is subjected to a theoretical analysis. It is found that the decisive factor for the validity of Wesley's derivation is the quotient of the square of the penetration depth of the electrical current over the product of the thickness of the plate and a distance that is indicative of the size of the current loops in the plate. Wesley's derivation is shown to be valid only when this factor is negligible. It is also shown that in this condition the imaginary component of the anomaly must be negligible.Model experiments are described in which the electrical current pattern is studied also in the range in which the derivation of Wesley is not valid. The procedure used in these model experiments was to measure the tangential component of the magnetic field strength very close to the metal plate that simulated the conductive dyke.In order to express the results of the measurements in terms of the imaginary to real ratio, these results are compared with an interpretation graph for field measurements that was published by Hedström and Parasnis (1958). It is found that the current pattern in the plate is essentially the same as that which follows from Wesley's derivation, provided that the imaginary to real ratio is less than one third. The measurements do not permit to draw conclusions regarding the current pattern in the plate in conditions that correspond to larger values of the imaginary to real ratio.

Notes: Electrical resistivity anomalies of a symmetrical four-electrode co-linear system across a single vertical discontinuity are treated in relation to: a) the ratio of potential electrode separation to the current electrode separation that are employed in the system and b) the angle which the electrode alignment makes with the discontinuity. Several conclusions are extracted from this treatment and methods for obtaining an optimum sensitivity of the system, with respect to these parameters, are shown. Disadvantages of special arrangements, such as the Wenner configuration, are indicated. Methods are outlined to utilise variations in the apparent resistivity plot for determining the angle between the electrode alignment and the discontinuity, quantitatively or qualitatively. These variations include certain deviations from the standard curves obtained in longitudinal traverses made at right angles to the discontinuity. Also, a comparison is made between longitudinal and cross traverses, in relation to the discontinuity.

Notes: When, in a two-layer earth, the substratum is insulating or infinitely conducting, the thickness of the top layer can be determined from surface potential measurements along a radius from a single point power electrode. The observed potential needs to be numerically integrated in a direction perpendicular to the said radius, and Figure 4 can then be used to find the thickness. A field example is included.

Notes: In order to increase the seismic efficiency of the Sparker-system developments were made in 1966/67. Results illustrating the main steps of this development are discussed. A new type of electrode called Transploder electrode was field-tested and proved to be promising.

Notes: The theory of electrical dipole soundings proved that this method can produce resistivity measurements, which are comparable with those obtained by electrical soundings of the Wenner or Schlumberger type. Their main advantage is the use of short cable lengths, which is important if the depth of penetration should be large.A considerable disadvantage of the dipole method is the great sensitivity to lateral discontinuities. Though these have an influence on the Schlumberger arrangement as well, they can disturb a dipole sounding to such an extent than an interpretation based on a horizontal layer case is no more possible.There are six different dipole arrays, which differ from each other with respect to the angle enclosed by the two dipole orientations-the current dipole AB and the measuring dipole MN. The theoretical comparison of the dipole arrays with the Schlumberger array concerning their sensitivity to lateral discontinuities is a useful basis for the choice of the most suitable configuration.Considering geological subsurface conditions the right choice of a dipole array can give an optimal result, i.e. a dipole sounding for which the sensitivity to lateral discontinuities is as small as possible under the given circumstances.

Notes: Deconvolution and deringing are well known subjects and it is not necessary to state again their objectives nor the basical methods used to reach them. Let us just remember that, generally, among many others, the two following assumptions are made for simplification purposes:〈list xml:id="l1" style="plain"〉—for deconvolution, it is assumed that the recorded seismic signal is constant, meaning that its shape is the same all along the time interval during which the trace is to be deconvolved;—for de-ringing, it is assumed that the ringing period is constant and that the intensity of the ringing phenomenon is independant of the time.With these two assumptions, a single constant operator can be applied for deconvolving, deringing or both. In most cases, the time variations of the signal or of the ringing are small enough and the error resulting of the application of a constant operator is acceptable. It results into a slight increase of the noise level or into a small residual ringing in the processed trace.When this noise or the residual ringing are too important, the assumption of a constant signal and ringing period must be rejected. This is the case that is examined here according to the following steps:〈list xml:id="l2" style="plain"〉—short definition of the problem;—fast evaluation of some possible solutions;—the selected solution: resulting approximations and how to obviate them, computing method and a remark about the operators;—theoretical example: the efficiency of the process used is evaluated on data in which the results aimed at are known; the influence of the selection of numerical values to be assigned to the parameters is examined;—real cases: comparison of results obtained with the Protee process and with more conventional processes assuming a time invariance or including a weighted composition of several conventional processes each with a different operator.

Notes: Sharp cut-off frequency filtering is carried out in the discrete time domain on digital computers. A convolution of the digital filter impulse response with the sampled input yields the output. For practical reasons, the length of the filter inpulse response, corresponding to the number of filter coefficients, is limited, and consequently the resulting frequency characteristic will no longer be identical to that originally specified. This is analogous to synthesising some specified frequency characteristic with a finite number of resistive, capacitative and inductive components.In Part I of this paper, we examine the effect of approximating the sharp cut-off frequency characteristic best in a mean square sense by an impulse response of finite length. The resulting frequency characteristic corresponds to the truncated impulse response of the specified frequency characteristic. It has a cut-off slope proportional to, and a mean square error inversely proportional to, the length of the impulse response, and is a biassed odd function about the cut-off frequency point. Because of the Gibbs phenomenon for discontinuous functions, the resulting frequency characteristic will always have a maximum overshoot with respect to the specified characteristic of ± 9%, regardless of the length of the corresponding impulse response. Equal length truncated impulse responses of specified filters with different cut-off frequencies yield frequency characteristics which are almost identical about their respective cut-off points. Now on a log frequency scale (as against a linear frequency scale implied previously) such characteristics may be made almost identical about the respective cut-off points by having the truncated impulse responses composed of an equal number of zero crossings. Results for the low-pass filter are applicable to the high-pass and band-pass characteristics.In the latter case, the mean square error is double that for a single slope characteristic (low-pass or high-pass) and the slopes at both edges of the passband are approximately equal in magnitude to the length of the impulse response (linear frequency scale).Part II of this paper is concerned with reducing the ± 9% overshoot that results from the discontinuous nature of the sharp cut-off frequency characteristic and which is not dependent on the length of the truncated impulse response. The reduction is achieved, at the expense of the steepness of cut-off for the resulting frequency characteristic, by the use of functions which weight the truncated impulse response of the specified frequency characteristic. These functions are called apodising functions. Among other variables, the length of the truncated weighted impulse response will determine the amount of maximum overshoot since the effective frequency characteristic being approximated is no longer a discontinuous function. The digital realization of the finite length impulse responses of Parts I and II is discussed in Part III, together with the optimum partially specified digital filter approximation to the desired frequency characteristic.

Notes: The purpose of this report is to show a method of determining the top of a refractor departing from the times and slopes of the direct and inverse dromocrones. The method does not need topographical correction and can be applied without knowledge of the distance between the geophone and the shot point.These results having been obtained, the commonly accepted point of view is upset: instead of looking for two points on the surface corresponding to one point of the refractor, we try to etablish, starting with only one point from the surface, the two corresponding points from the top of the refractor.This method can be applied to isolated points and does not demand interpretative hypotheses of any kind, excluding the velocity evaluation of the overburden and of the refractor.The necessary calculations can be easily executed by means of a digital computer to which the dromocrone times and the distances between the geophones must be given. These calculations can also be executed by a person having no knowledge of refraction seismology.This report also examines the validity of the approximations involved in the method proposed.

Notes: Determining the shape of a pulse generated by an explosion solely from the data provided by the recorded seismic trace is a difficult and even ambitious task.Knowledge of parameters such as length and number of “arches” of the pulse under study is, in fact, indispensable in solving this problem.These parameters cannot be found directly in the seismic trace, which nevertheless contains a great amount of information. Autocorrelation, with its mathematical and statistical properties, is an efficient way of making the best of this information.We compute all the autocorrelations of reflections having a given number of arches which fulfil certain conditions determined in advance. Then, after statistical testing of some parameters pertaining to the autocorrelations (abcissae of zeros, of extrema …), we select only those with a maximum likelihood. It is sufficient to consider only the reflections whose autocorrelations have been selected and to arrange them in groups according to their shape and arch number in order to obtain average pulses.In so doing several solutions are arrived at, but when considering a given number of traces, a single record for instance, it is possible by comparing these results with each other to considerably reduce their number.In the last part of the paper the nature of the impulse obtained with our method is examined in order to find out whether it is “minimum phase” for carrying out deconvolutions.

Notes: In recent years considerable work has been done to devise a satisfactory non-dynamite seismic system that would replace dynamite in offshore areas. Prior to the advent of digital recording and processing, the non-dynamite sources have generally not provided the depth of penetration or the resolution required for satisfactory seismic interpretation.More recent developments in non-dynamite offshore marine sources include adaptation of the Vibroseis from a land unit to a marine unit, and adaptation of the Dinoseis unit from a land to a marine unit. The SUE (Seismic Underwater Explorer) system is a thermodynamic non-dynamite source utilizing a mixture of propane and oxygen detonated in a special chamber approximately 15 feet below the water surface. This source gives penetration to more than 4 sec in areas typified by Gulf of Mexico type geology and shows deeper penetration than had previously been obtained by dynamite along the western United States in areas with 20 lb charge limitations. A pneumatic source, the airgun, has been in production use in the United States since June 1966. This non-dynamite source provides an intriguing amount of versatility and can be expanded to provide additional energy as necessary to obtain the penetration desired. Tests using systems comprised of from eight to twenty-three airguns show penetration in excess of 5 seconds in many areas. Power spectra comparisons both in amplitude and frequency content demonstrate that this is a controlled source generating a controlled seismic wavelet and a controlled frequency spectrum that can be tailored to fit requirements of particular areas. Sample sections obtained in the Gulf of Mexico and the Pacific Ocean offshore California show adequate penetration to 5.0 seconds reflection time.Quantitative measurements with the airguns demonstrate the effect of:〈list xml:id="l1" style="custom"〉1Variation of the number of guns in the system;2Shaping the frequency spectrum by using different sizes of airguns in the system;3Effects on signal-to-noise ratios as a result of stacking several small energy sources together;4Reproducibility of the initial pulse wavelet from shot to shot.The improvement in record quality as a result of advanced digital processing with non-dynamite sources is comparable to that obtained with dynamite sources. Non-dynamite sources make additional improvements possible where high source multiplicity is advantageous. Excellent dynamic correlations yield accurate velocity control as well as definitions of apparent velocities attributable to multiples and primary-to-multiple amplitude relationships.Non-dynamite sources are being used more and more extensively in offshore exploration. The advent of digital recording and processing provides a means for improving depth of penetration and resolution of many non-dynamite sources.

Notes: The electromagnetic field radiated from a magnetic dipole lying on the ground is considered, in the extremely low frequency range (DC to 20 000 Hertz).Theoretical and experimental data are given on the characteristics of the surface wave (vanishing wave) generated at the air-ground interface, in the case of an homogeneous subsurface.The case of a subsurface with electrical resistivity varying with depth is considered.It is shown how the above-mentioned characteristics may be applied in the quantitative investigation of the electrical resistivity of the subsurface as a function of depth, in a method using the measurements on the ground of all the components of the radiated field: horizontal electrical components, vertical and horizontal magnetic components.

Notes: Book review in this articleHandbuch der Physik/Encyclopedia of Physics, Ed.: S. FlüggeThe Aurora. By S.-I. Akasofu, S. Chapman and A. B. Meinel.Time-Variations of Cosmic Rays. By S. E. Forbush.Magnetic Properties of Rocks and Minerals. By T. Nagata.

Notes: A theory is developed to predict the amplitude and velocity of the first arrival produced by a thin solid refractor embedded in a solid environment. Laboratory experiments on a three dimensional model substantially confirm the theory. The essential conclusion may be found in Figure 8 where it is shown that for a constant wavelength, and for thicknesses up to about one half a wavelength, the attenuation per unit distance decreases monotonically with increase of refractor thickness.The assumption is made that the amplitude, A, attenuates as (x)-n exp(-βx), where x is horizontal distance and n and β are constants. It is emphasised that it is difficult to obtain reliable values for n and β from the initial amplitude measurements.

Notes: Book reviewed in this article: State of Stress in the Earth's Crust, Proceedings of the International ConferenceF. A. Vening Meinesz, The Earth's Crust and Mantle (Development in Solid Earth Geophysics)

Notes: A formula is developed for the vertical magnetic field due to an alternating current passing through a long horizontal cable placed on a two-layer ground. The variations of the phase and amplitude ratio of the vertical field, along profiles perpendicular to the cable line are investigated. Within the limits encountered in practice, it is found that if the upper layer is conductive, as compared to the lower layer, the phase may vary appreciably whereas the amplitude ratio changes as in the case of vacuum.

Notes: Book review in this articleN. A. Ogil'vi, D. I. Fedorovich, Groundwater Seepage Rates. English translation by N. H. Choksy, Consultants Bureau, New York 1966, 33 pp., 12 fig.

Notes: Mapping of fault patterns is an important part of geophysical exploration. A computerized digital template analysis method is described which tests gravity maps for the effects of faults by comparing measured gravity data with calculated master curves. The interpreted gravity data are incorporated in a tectonic map using geological symbols and units, for ready use by the geologists.Tectonics can be investigated by gravity detailing if the smallest undulations on the Bouguer map are taken into consideration. Up to now, residual and derivative gravity maps have explained gravity effects by assuming spherical bodies which are almost unknown in geology. The method discussed here uses tectonic elements, such as fault-blocks and dikes as a basis of interpretation instead of the spherical bodies of the conventional interpretation methods.Gravity data can be easily and relatively cheaply obtained in the early phases of exploration by area wide spot coverage following lines of easy access such as roads, etc. Seismic studies, by contrast, have the disadvantage of being executed along predetermined profile lines. Only after sufficient detailing do seismic profiles permit-if at all -an areal mapping of faults. Thus a tectonic map is obtained only at the end of a geophysical survey instead of being available prior to the planning of costly seismic profiles. The use of gravimetric data and their interpretation by the suggested method provides tectonic detail maps in the early phases of geophysical studies.In addition, this article discusses a general geophysical interpretation method, using the investigation of faults by gravity as an example. Applications of this method for different gravity and magnetics problems as well as for combined interpretations are outlined. Detailed case histories will be published in later articles.

Notes: To be able to make use of all existing probe interpretation techniques, it is desirable that field resistivity observations be conducted in such a way that it is possible to construct an equivalent curve for the surface variation of potential about a point source. Further, the usual parallel layer interpretation will only be justified in as much as the observed potential curve is compatible with such a subsurface geometry. Thus, whilst a potential curve may be constructed from suitable finite potential differences obtained using a Wenner configuration of electrodes, it can be shown, using the tri-potential technique of measurements, that these potential differences may arise partly from lateral resistivity variations.In this paper, a ladder network technique is employed to display these lateral effects and an adjustment method proposed to reduce them. The adjusted potential differences obtained form a consecutive series suitable for summation to give the potential function. These values are subject to further minimum adjustments required for them to comply with slope and curvature conditions for a layered medium. After forming the potential curve by summation, a final numerical smoothing process is carried out. From this smoothed potential curve, corresponding Wenner and Schlumberger curves can readily be derived for interpretation.The method proposed thus attempts to extract from the observed data the maximum part which can be reconciled with a purely depth variation of resistivity. A method is also proposed for compounding the ‘errors of closure’ of the network to provide a Lateral Inhomogeneity Index which gives a measure of the departure of the observed data from the basic interpretation requirements.The method involves no great labour, but can readily be programmed for a computer if desired. Examples are given of the application of the method to field observations. In the interest of objectivity, the final smoothing has been confined to a single stage but in certain very extreme examples a further stage may prove desirable.

Notes: Book reviewed in this article:M. R. J. Wyllie, The Fundamentals of Well Log Interpretation.

Notes: Proton precession magnetometers usually operate discontinuously since thy rely one intermittent impulses. The aerial versions of these magnetometers suffer from relatively high background noise. The type of magnetometer discussed in this paper has solved the two problems of discontinuity of measurements and reduced sensitivity due to background noise.Comparative texts with an established flux-gate apparatus have given significant and convincing results.

Notes: Book reviewed in this article:S. I. Kuznetsov, M. V. Ivanov and N. N. Lyalikova, Introduction to Geological Microbiology Organic Geochemistry, Editor I. A. Breger

Notes: The formula for the Bouguer anomaly contains the density of the masses above the datum plane. If we use a wrong value for the density we obtain on the Bouguer map additional anomalies which coincide with the topographic features.If we do not know the Bouguer density we can compute several Bouguer maps based on different arbitrary densities. Then we select that map which shows the least correlation with the topography and obtain in this way a reasonable value for the density. This method has been found by Nettleton.Several authors have formulated this process mathematically and have elaborated numerical methods. This paper will present such a method. It differs from the former methods by the following:〈list xml:id="l1" style="custom"〉1A general formula for the Bouguer density is presented, using a non-specified linear operator. By choosing special definition for this operator, we can obtain the formulae of several of the known methods.2It is shown that the determination of the density by “Nettleton Profiles” gives less reliable results than the statistical investigation of the whole area covered by the gravity survey.3The known methods do not consider the variations of the vertical gradient. It is shown that in areas with a regional gravity anomaly or an extended topographic feature the known methods yield poor results.4It is shown that the vertical gradient of gravity used as operator gives a most exact and simple formula.5It is shown how the electronic computer—after reading the Bouguer values based on an arbitrary initial density—can compute the residuals, derivatives etc., which are based on the corrected Bouguer density.

Notes: An electronic analogue was used to obtain geophone distortion of typical seismic pulses. Some of the results were checked by computation and in all cases agreement was extremely close. For late arrival events estimates of attenuation and phase shift may be made from the steady-state response curves. It is explained why these curves are not applicable to the first peak, for which one must use the results in Table III.Ground-geophone coupling introduces the same distortion as a very lightly damped galvanometer with a natural frequency usually in the range 100c/s—200c/s. In swampy terrain this frequency may reduce to 30c/s—40c/s and coupling effects may be severe.An electronic unit whose characteristics are the inverse of those of a geophone has been used to improve the first peak amplitude of a seismic refraction record. Since 1c/s geophones are often desirable in refraction survey it may well be more economic to use higher frequency geophones followed by their inverse filter.

Notes: The paper describes a new method for the calculation of standard-graphs i.e. resistivity-curves for assumed resistivity profiles. It starts from the integral of Stefanesco and arrives at a system of image poles, similar to, but simpler than earlier developed systems. The advantages of the new method are described, the accuracy is discussed and it is indicated how the accuracy can be improved by a simple artifice.

Notes: In the present study an attempt is made to relate the general pattern of reflection seismograms obtained over a coal basin to the acoustical properties peculiar to the Coal Measures. The Carboniferous is characterized by a very rapid succession of distinct lithological units, resulting in a surprising variability in their physical properties. Coal seams in particular are conspicuous by their low density and velocity and they produce acoustical contrasts of 35–50 % with respect to country rock. The resulting heavy shielding action prevents the seismic energy from penetrating deeply into this type of formation.With the aid of synthetic seismograms, arranged into synthetic profiles, it is shown that only a minor part of the Coal Measures reflections is of primary origin. The majority has a secondary character brought about by reverberations inside the weathering zone. Thus the conclusion is reached that reflection shooting allows of mapping only the structure of the top section of the Carboniferous, which is sufficient for the purposes of the coalmining industry.

Notes: Biot's poroelastic differential equations are modified for including matrix–fluid interaction mechanisms. The description is phenomenological and assumes a solid–fluid relaxation function coupling coefficient. The model satisfies basic physical properties such as, for instance, that P-wave velocities at low frequencies are lower than those predicted by Biot's theory. In many cases, the results obtained with the Biot (two-phase) modelling are equal to those obtained with single-phase elastic modelling, mainly at seismic frequencies. However, a correct equivalence is obtained with a viscoelastic rheology, which requires one relaxation peak for each Biot (P and S) mechanism. The standard viscoelastic model, which generalizes compressibility and shear modulus to relaxation functions, is not appropriate for modelling the Biot complex moduli, since Biot's attenuation is of a kinetic nature (i.e. it is not related to bulk deformations). The problem is solved by associating relaxation functions with each wave modulus. The equivalence between the two modelling approaches is investigated for a homogeneous water-filled sandstone and a periodically layered poroelastic medium, alternately filled with gas and water. The simulations indicate that, in the homogeneous case, particle velocities in the solid skeleton, caused by a source applied to the matrix, are equivalent to viscoelastic particle velocities. In a finely layered medium, viscoelastic modelling is not, in principle, equivalent to porous modelling, due to substantial mode conversion from fast wave to slow static mode. However, this effect, caused by local fluid-flow motion, can be simulated by including an additional relaxation mechanism similar to the squirt-flow.

Notes: An algorithm for modelling and migrating ground penetrating radar (GPR) data in moderately heterogeneous dispersive media is presented. The method is based on wavefield extrapolation in the frequency–wavenumber (f–k) domain, from the solution of the 2D Maxwell's equations. The wavefield is extrapolated by a phase-shift technique using a constant relative permittivity K and a quality factor Q. It is then modified by a correction term to handle the lateral K and Q variations. The spatial distribution of the K and Q-factor values, representing the given model parameters, is introduced into the algorithm by a regular grid parametrization. The radar wave dispersion and attenuation, induced by relaxation processes, are taken into account by a linear frequency-dependent Q model, and expressed by a complex wavenumber in the propagation equation.A synthetic case and a field data set illustrate the potential of the method for frequencies of 300, 500 and 900 MHz. In the first case, a typical civil engineering problem is considered. The frequency dependence of the wave velocity and attenuation is well illustrated. The synthetic data are afterwards migrated using the initial model parameters. The results show the importance of using spatially varying model parameters in the migration processes. The second case concerns an application of the method to a real data set. In order to adjust the model parameters, a forward modelling sequence is performed until the best match between the measured and the synthetic data is achieved. A depth migration is then applied to the data, and the result is compared with the initial model parameters.In conclusion, we assess the contributions of the method to industrial applications, by discussing the performance of the algorithm compared with its limitations.

Notes: Vibroseis data recorded at short source–receiver offsets can be swamped by direct waves from the source. The signal-to-noise ratio, where primary reflections are the signal and correlation side lobes are the noise, decreases with time and late reflection events are overwhelmed. This leads to low seismic resolution on the vibroseis correlogram. A new precorrelation filtering approach is proposed to suppress correlation noise. It is the ‘squeeze-filter-unsqueeze’ (SFU) process, a combination of ‘squeeze’ and ‘unsqueeze’ (S and U) transformations, together with the application of either an optimum least-squares filter or a linear recursive notch filter. SFU processing provides excellent direct wave removal if the onset time of the direct wave is known precisely, but when the correlation recognition method used to search for the first arrival fails, the SFU filtering will also fail. If the tapers of the source sweeps are badly distorted, a harmonic distortion will be introduced into the SFU-filtered trace. SFU appears to be more suitable for low-noise vibroseis data, and more effective when we know the sweep tapers exactly. SFU requires uncorrelated data, and is thus cpu intensive, but since it is automatic, it is not labour intensive.  With non-linear sweeps, there are two approaches to the S,U transformations in SFU. The first requires the non-linear analytical sweep formula, and the second is to search and pick the zero nodes on the recorded pilot trace and then carry out the S,U transformations directly without requiring the algorithm or formula by which the sweep was generated. The latter method is also valid for vibroseis data with a linear sweep. SFU may be applied to the removal of any undesired signal, as long as the exact onset time of the unwanted signal in the precorrelation domain is known or determinable.

Notes: Accurate well ties are essential to practical seismic lithological interpretation. As long as the geology in the vicinity of the reservoir is not unduly complex, the main factors controlling this accuracy are the processing of the seismic data and the construction of the seismic model from well logs. This case study illustrates how seismic data processing to a near-offset stack, quality control of logs and petrophysical modelling improved a well tie at an oil reservoir. We demonstrate the application of a predictive petrophysical model in the preparation and integration of the logs before building the seismic model and we quantify our improvements in well-tie accuracy. The data for the study consisted of seismic field data from a 3D sail line through a well in a North Sea oilfield and a suite of standard logs at the well. A swathe of fully processed 3D data through the well was available for comparison. The well tie in the shallow section from first-pass seismic data processing and a routinely edited sonic log was excellent. The tie in a deeper interval containing the reservoir was less satisfactory: the phase errors within the bandwidth of the seismic wavelet were of the order of 20°, which we consider too large for subsequent transformation of the data to seismic impedance. Reprocessing the seismic data and revision of the well-log model reduced these phase errors to less than 10° and improved the consistency of the deep and shallow well ties. The reprocessing included densely picked iterative velocity analysis, prestack migration, beam-forming multiple attenuation, stacking the near-offset traces and demigration and remigration of the near-offset data. The petrophysical model was used to monitor and, where necessary, replace the P-wave sonic log with predictions consistent with other logs and to correct the sonic log for mud-filtrate invasion in the hydrocarbon-bearing sand. This editing and correction of the P-wave transit times improved the normal-incidence well tie significantly. The recordings from a monopole source severely underestimated the S-wave transit times in soft shale formations, including the reservoir seal, where the S-wave velocity was lower than the P-wave velocity in the drilling mud. The petrophysical model predicted an S-wave log that matched the valid recordings and interpolated between them. The subsequent seismic modelling from the predicted S-wave log produced a class II AVO anomaly seen on the CDP gathers around the well.

Notes: We design a velocity–porosity model for sand-shale environments with the emphasis on its application to petrophysical interpretation of compressional and shear velocities. In order to achieve this objective, we extend the velocity–porosity model proposed by Krief et al., to account for the effect of clay content in sandstones, using the published laboratory experiments on rocks and well log data in a wide range of porosities and clay contents.The model of Krief et al. works well for clean compacted rocks. It assumes that compressional and shear velocities in a porous fluid-saturated rock obey Gassmann formulae with the Biot compliance coefficient. In order to use this model for clay-rich rocks, we assume that the bulk and shear moduli of the grain material, and the dependence of the compliance on porosity, are functions of the clay content.Statistical analysis of published laboratory data shows that the moduli of the matrix grain material are best defined by low Hashin–Shtrikman bounds. The parameters of the model include the bulk and shear moduli of the sand and clay mineral components as well as coefficients which define the dependence of the bulk and shear compliance on porosity and clay content. The constants of the model are determined by a multivariate non-linear regression fit for P- and S-velocities as functions of porosity and clay content using the data acquired in the area of interest.In order to demonstrate the potential application of the proposed model to petrophysical interpretation, we design an inversion procedure, which allows us to estimate porosity, saturation and/or clay content from compressional and shear velocities.Testing of the model on laboratory data and a set of well logs from Carnarvon Basin, Australia, shows good agreement between predictions and measurements. This simple velocity-porosity-clay semi-empirical model could be used for more reliable petrophysical interpretation of compressional and shear velocities obtained from well logs or surface seismic data.

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: Sedimentary rocks beneath the Columbia River Basalt Group are recognized as having potential for oil and gas production, but the overlying layered basalts effectively mask seismic reflections from the underlying sediments. Four electromagnetic (EM) methods have been applied on profiles crossing Boylston Ridge, a typical east–west trending anticline of the Yakima Fold Belt, in an attempt to map the resistivity interface between the basalts and the sediments and to map variations in structure and resistivity within the sediments. The EM surveys detected strong variations in resistivity within the basalts, and in particular the continuous magnetotelluric array profiling (EMAP) revealed resistivity lows beneath the surface anticlines. These low resistivity zones probably coincide with fracturing in the core of the anticlines and they appear to correlate well with similar zones of low seismic velocity observed on a nearby seismic profile.The controlled-source EM surveys (in-loop transient, long-offset transient, and variable-offset frequency-domain) were designed in anticipation of relatively uniform high resistivity basalts, and were found to have been seriously distorted by the intrabasalt conductors discovered in the field. In particular, the resistivity sections derived from 1D inversions were found to be inconsistent and misleading. The EMAP survey provided the most information about the subsurface resistivity distribution, and was certainly the most cost-effective. However, both controlled-source and EMAP surveys call for accurate 2D or 3D inversion to accommodate the geological objectives of this project.

Notes: Five examples, obtained during exploration for hydrocarbons in the Pannonian Basin of Hungary, are used to show how the interpretation of seismic sections can be usefully complemented by results from MT surveys.Selection of the most appropriate MT quantities, considered to be proper ‘MT attributes’ for the purpose of visualization as well as recognition of the subsurface structures and the different inversions of MT data is essential for practical integration of seismic and MT surveys.A new technique providing a semiquantitive MT-attribute pseudosection for the purpose of visualization of the subsurface structures is proposed. The procedure utilizes derivative functions of the phase of MT impedance for visualization and derives estimated depths from the Bostick transformation of Cagniard apparent resistivities.On the basis of the MT-attribute pseudosections, constructed from the phase derivatives and transformed resistivity data, depths are estimated for interfaces between geological formations with significant resistivity contrast. In particular examples, the interface between the Tertiary sediments and the older basement rocks as well as tectonic fracture zones with decreased resistivity can be resolved.

Notes: A new 3D wavefield modelling approach based on dynamic ray tracing is presented. This approach is called wavefront construction, and it can be used in 3D models with constant or smoothly varying material properties (S- and P-velocity and density) separated by smooth interfaces. Wavefronts consisting of rays arranged in a triangular network are propagated stepwise through the model. At each time step, the differences in a number of parameters are checked between each pair of rays on the wavefront. New rays are interpolated whenever this difference between pairs of rays exceeds some predefined maximum value. A controlled sampling of the wavefront at all time steps is thus obtained. Receivers are given multiple-event values by interpolation when the wavefronts pass them. The strength of the wavefront construction method is that it is robust and efficient.

Notes: This work presents a new modelling scheme for the simulation of electromagnetic radio waves, based on a full-field simulator. Maxwell's equations are modified in order to include dielectric attenuation processes, such as bound- and free-water relaxation, ice relaxation and the Maxwell–Wagner effect. The new equations are obtained by assuming a permittivity relaxation function represented by a generalized Zener model. The convolution integral introduced by the relaxation formulation is circumvented by defining new hidden field variables, each corresponding to a different dielectric relaxation. The equations are solved numerically by using the Fourier pseudospectral operator for computing the spatial derivatives and a new time-splitting integration algorithm that circumvents the stiffness of the differential equations. The program is used to evaluate the georadar electromagnetic response of a Japanese burial site, in particular, a stone coffin-like structure.

Notes: The clay-sand mixture model of Xu and White is shown to simulate observed relationships between S-wave velocity (or transit time), porosity and clay content. In general, neither S-wave velocity nor S-wave transit time is a linear function of porosity and clay content. For practical purposes, clay content is approximated by shale volume in well-log applications. In principle, the model can predict S-wave velocity from lithology and any pair of P-wave velocity, porosity and shale volume. Although the predictions should be the same if all measurements are error free, comparison of predictions with laboratory and logging measurements show that predictions using P-wave velocity are the most reliable. The robust relationship between S- and P-wave velocities is due to the fact that both are similarly affected by porosity, clay content and lithology. Moreover, errors in the measured P-wave velocity are normally smaller than those in porosity and shale volume, both of which are subject to errors introduced by imperfect models and imperfect parameters when estimated from logs.Because the model evaluates the bulk and shear moduli of the dry rock frame by a combination of Kuster and Toksöz’ theory and differential effective medium theory, using pore aspect ratios to characterize the compliances of the sand and clay components, the relationship between P- and S-wave velocities is explicit and consistent. Consequently the model sidesteps problems and assumptions that arise from the lack of knowledge of these moduli when applying Gassmann's theory to this relationship, making it a very flexible tool for investigating how the vP-vs relationship is affected by lithology, porosity, clay content and water saturation. Numerical results from the model are confirmed by laboratory and logging data and demonstrate, for example, how the presence of gas has a more pronounced effect on P-wave velocity in shaly sands than in less compliant cleaner sandstones.

Notes: A publicly available and maintained electromagnetic finite-difference time domain (FDTD) code has been applied to the forward modelling of the response of 1D, 2D and 3D geophysical targets to a vertical magnetic dipole excitation. The FDTD method is used to analyse target responses in the 1 MHz to 100MHz range, where either conduction or displacement currents may have the controlling role. The response of the geophysical target to the excitation is presented as changes in the magnetic field ellipticity.The results of the FDTD code compare favourably with previously published integral equation solutions of the response of 1D targets, and FDTD models calculated with different finite-difference cell sizes are compared to find the effect of model discretization on the solution. The discretization errors, calculated as absolute error in ellipticity, are presented for the different ground geometry models considered, and are, for the most part, below 10% of the integral equation solutions.Finally, the FDTD code is used to calculate the magnetic ellipticity response of a 2D survey and a 3D sounding of complicated geophysical targets. The response of these 2D and 3D targets are too complicated to be verified with integral equation solutions, but show the proper low- and high-frequency responses.

Notes: The use of MKS system units in preference to the cgs system facilitates accurate numerical calculation in magnetostatic problems in geophysics and the practice of stating the precise dimensions of every unit guards against confusion. Suggestions are made for the unique definition of quantities such as magnetic potential, etc. for which the undesirable circumstance of arbitrary alternatives still persists.

Notes: The Fourier transform formula for a two-dimensional fault truncating a horizontal bed at an arbitrary angle of inclination is derived. The amplitude spectrum of the Fourier transform is found to give information about the depth to the top of the upper part of the faulted bed and the inclination of the fault-plane. Under suitable conditions the thickness and the displacement of the bed involved can be obtained. With actual field data, these transforms can be obtained at discrete points by a Fourier analysis of the gravity anomaly. A field example from the Logan fault area near Montreal, Que., Canada, is given.

Notes: Die Interpretation magnetischer Anomalien durch Modellkörper geschieht bevorzugt nach der indirekten Methode (trial und error). Dieses von Hand aufwendige Verfahren läβt sich mit Hilfe der Ausgleichsrechnung nach der Methode der kleinsten Quadrate Rechenautomaten übertragen.Die allgemeinen Grundlagen des Verfahrens werden beschrieben. Wesentliche Voraus-setzungen sind:〈list xml:id="l1" style="custom"〉1)die Annahme bestimmter Körperformen2)das Vorhandensein von Näherungswerten der Unbekannten (Lage, Magnetisierung etc.)3)eine genügend groβe Anzahl von Meβwerten, um den Ausgleichsprozeβ durchführen zu können.Die Vorteile der Methode sind:〈list xml:id="l2" style="custom"〉1)weitgehende Automatisierung und schnelle Arbeitsweise bei Verwendung von Rechenautomaten2)Ermittlung der Fehler der UnbekanntenDie Methode wurde angewandt auf die Interpretation 2-dimensionaler ΔZ- und ΔT-Anomalien. Drei Körpertypen werden dem Rechenprogramm zugrunde gelegt, und zwar die unendliche und endliche diinne Platte und der Kreiszylinder. In die Maschine ein-gegeben werden nur die Meβwerte. Die Interpretation erfolgt im einzelnen in folgenden Schritten:〈list xml:id="l3" style="custom"〉1)Ermittlung von Näherungswerten2)Bestimmung der Körper bester Annäherung3)Iteration für den Körper bester Annäherung.Die Maschine gibt die Endwerte der Unbekannten (Lage, Einfallen, Magnetisierung etc.) mit Angabe der mittleren Fehler sowie die hierzu gehörigen Modellanomalien aus. Diese Endwerte werden einem Zeichenautomaten übergeben, der die gemessene Kurve, die theoretische Kurve und die gesuchten Modellkorper zeichnet.Interpretationsbeispiele werden vorgeführt.

Notes: In one geophysical survey over a salt dome in the Gulf of Mexico, data taken from a single magnetic and seismic shipborne traverse demonstrated significantly the importance of magnetic measurements. The reduced magnetic and seismic profiles were integrated with gravity measurements from an earlier survey demonstrating the value of obtaining simultaneous geophysical data. The traverse was approximately 25 miles in length, 135 miles southeast of Galveston, Texas. The observed gradient averaged approximately 2 gammas per 1000 feet and crosses the southwest corner of a large shallow salt dome called the Way Dome. The recorded magnetic profile over the salt dome shows a negative magnetic anomaly extending for approximately 12 miles with a maximum amplitude of approximately 20 gammas. This negatively anomaly is due to the negative susceptibility contrast between the salt and cap rock that truncates the surrounding parent sediments. The shape of the negative anomaly correlates well with the continous seismic record and clearly delineates the topographical and structural features of the salt dome. The recorded analog magnetic profile was replotted, with both the regional gradient and time variations removed, which makes the observed anomaly much sharper than is noticeable on the original recorded strip chart record. A theoretical magnetic anomaly was calculated using a computer program for comparison to the observed anomaly. The results showed good correlation.

Notes: The auto-correlation function of a seismic trace contains information on all the multiple reflection activity present in the trace.The interpretation of this information is facilitated by the arrangement of autocorrelation functions in cross-sectional form, in the manner of a normal record section. This is the concept of the Sectional Auto-Correlogram.Specifically, the Sectional Auto-Correlogram will…Show if the record section does not include significant multiples, thus allowing confident picking of the primary reflections.Show if the record section does include significant multiples, giving their travel times and inclinations (and, under certain circumstances, their reflection coefficients).Indicate by what process the multiples should be treated.Yield an authoritative measure of the success of a multiple-attenuating treatment.Delineate shallow horizons, even those whose primary reflections are too early to be recorded satisfactorily.Give the true travel time of a primary reflector, and the sign of its reflection coefficient.The Sectional Auto-Correlogram allows the study of primary reflectors by consideration of the multiples generated by them, and in this sense may be said to turn multiple reflections to advantage. Thus a primary reflection at a certain time is defined if we find that every reflection on the record is followed by a multiple after this certain time. Alternatively, a primary reflection at a certain time is defined if, after that certain time, we can find a repetition of the entire record.The Sectional Auto-Correlogram also has secondary uses in fault identification, crustal studies and weathering problems.

Notes: The development of optically pumped and monitored “atomic” magnetometers has allowed the application of greater resolution in geomagnetic measurements for exploration purposes. This paper presents a survey of instrumentation in use, the variety of exploration techniques that are being used in practice, and an estimate of their state of development.Alkali metals (rubidium and cesium) and helium have been used as active elements to obtain the magnetic-field dependent Larmor frequency. Each of these instruments is capable of obtaining high resolution data (data with sensitivity numerically smaller than one-tenth gamma). They have been adapted for airborne, land, and marine usage.Such sensitivity has enabled the rapid development of geomagnetic gradiometers, high sensitivity aeromagnetics, diurnally reduced ground surveys, broad-band magneto-telluric surveys, susceptibility measurements, and convenient magnetic search and location techniques. Outlines of each procedure and an example of its application are given.

Notes: Studies made on head waves in a large number of two-dimensional horizontal and inclined layer seismic models are described. The assumption that the amplitude of head wave decreases exponentially with distance is found to be valid in horizontal layers. For the correct estimation of the head wave decay coefficient, the decrease of amplitude due to the divergence of wave energy should always be considered.The variations of head wave amplitude at large distances from the source appear to follow the theory of Heelan (1953). It is, however, concluded that the theory can only be verified from the measurements in models which have large velocity contrast and thick layer at the top.A prominent interference phenomenon between the direct and head wave has been observed near the critical distance. This is more marked for up-dip profile in the case of inclined layer models. The rate of head wave amplitude decrease with distance beyond the zone of interference is found to depend on dip angle, direction of the dip, and velocity contrast.