ALBERT

Notes: Acoustic reverse-time finite-difference migration for zero-offset data is extended from two- to three-dimensional media. The formulation is based on the full three-dimensional acoustic wave equation and so has no dip restrictions and it involves extrapolation in a velocity distribution variable in three dimensions. The algorithm is demonstrated by successful migration of synthetic data sets for three models: a point diffractor, an oblique pinch-out, and a dome overlying a planar reflector.

Notes: Seismic attenuation introduces modifications in the wavelet shape in vertical seismic profiles. These modifications can be quantified by measuring particular signal attributes such as rise-time, period and shape index. Use of signal attributes leads to estimations of a seismic-attenuation log (Q-log).To obtain accurate signal attributes it is important to minimize noise influence and eliminate local interference between upgoing and downgoing waves at each probe location. When tube waves are present it is necessary to eliminate them before performing separation of upgoing and downgoing events. We used a trace-by-trace Wiener filter to minimize the influence of tube waves. The separation of upgoing and downgoing waves was then performed in the frequency domain using a trace-pair filter.We used three possible methods based on signal attribute measurements to obtain g-log from the extracted downgoing wavefield. The first one uses a minimum phasing filter and the arrival time of the first extremum. The two other methods determine the Q-factor from simple relations between the amplitudes of the first extrema and the pseudo-periods of the down-going wavelet.The relations determined between a signal attribute and traveltime over quality factor were then calibrated using field source signature and constant-Q models computed by Ganley's method. Q-logs thus obtained from real data are discussed and compared with geological information, specifically at reservoir level.Analysis of the tube wave arrivals at the level of the reservoir showed a tube wave attenuation that could not be explained by simple transmission effects. There was also a loss of signal coherence. This could be interpreted as tube wave diffusion in the porous reservoir, followed by dispersion. If this interpretation can be verified, tube wave analysis could lead to further characterization of porous permeable zones.

Notes: During the last couple of years there has been much research in the area of wavefield separation of borehole seismic data, and several articles have been published on various separation techniques. Methods involving the application of two-dimensional Fourier transformation, the Radon transformation, multi-level median filters or optimal filters, are all suggested as possible approaches to the wavefield separation problem.This paper compares some of these methods commonly used in the industry.The theories of the chosen methods are described to see how they are related. Using the different methods on synthetic and real data, we show how this theoretical relation is reflected in the relatively similar results obtained. We also show how the different filters treat coherent and random noise.

Notes: Matrix equations are derived to transform the resistivity sounding data obtained in one type of a four-electrode array to the corresponding resistivity sounding data that would be obtained using a different four-electrode array. These expressions are based primarily on recent work in which we have established a linear relation between the apparent resistivity and the kernel function by using a powerful exponential approximation for the kernel function. It is shown that the resistivity sounding data of two different four-electrode arrays have a linear relation through an essentially non-singular matrix operator and, as such, one is derivable from the other for a one-dimensional model and it can also be extended to two-dimensions.Some numerical examples considering synthetic data are presented which demonstrates the efficiency of the method in such transformations. Two published field examples are also considered for transformation giving a reliable interpretation.

Notes: Underground gravity observations in deep coal mines using the conventional gravity meters Worden (type Master) and LaCoste-Romberg (model D), both of which have been adapted to the fire damp regulations, can be accurate to ± 10 and ± 3 μgal, respectively. For underground determination of the vertical gradient of gravity the LaCoste-Romberg meter is used together with a specially designed measuring tower. Using this euipment an accuracy in tower gradient observations of ± 30 E was obtained.To apply the equipment to precision gravity observations in underground situations an additional correction, i.e. a gallery correction, is needed. High accuracy in correction is achieved by a new method of three-dimensional modelling. The gravity effect is computed for bodies with a surface approximated by triangular elements, which are generated from corner points of the body. The combination of gallery correction with tower gradient data leads to a new method for in situ density determination. It offers the possibility of horizontal instead of vertical density profiling.To demonstrate the effectiveness of the developments in underground observations the localization of a pump room is presented. Microgravity and tower gradient observations were carried out to detect the cavity. The horizontal gradient was also calculated to give a more reliable location.

Notes: A new time-domain method is introduced for the calculation of theoretical seismograms which include frequency dependent effects like absorption. To incorporate these effects the reflection and transmission coefficients become convolutionary operators. The method is based on the communication theory approach and is applicable to non-normal incidence plane waves in flat layered elastic media. Wave propagation is simulated by tracking the wave amplitudes through a storage vector inside the computer memory representing a Goupillaud earth model discretized by equal vertical transit times. Arbitrary numbers of sources and receivers can be placed at arbitrary depth positions, while the computational effort is independent of that number. Therefore, the computation of a whole plane-wave vertical seismic profile is possible with no extra effort compared to the computation of the surface seismogram. The new method can be used as an aid to the interpretation of plane-wave decomposed reflection data where the whole synthetic vertical seismic profile readily gives the interpreter the correct depth position of reflection events.

Notes: A parameter estimation or inversion procedure is incomplete without an analysis of uncertainties in the results. In the fundamental approach of Bayesian parameter estimation, discussed in Part I of this paper, the a posteriori probability density function (pdf) is the solution to the inverse problem. It is the product of the a priori pdf, containing a priori information on the parameters, and the likelihood function, which represents the information from the data. The maximum of the a posteriori pdf is usually taken as a point estimate of the parameters. The shape of this pdf, however, gives the full picture of uncertainty in the parameters. Uncertainty analysis is strictly a problem of information reduction. This can be achieved in several stages. Standard deviations can be computed as overall uncertainty measures of the parameters, when the shape of the a posteriori pdf is not too far from Gaussian. Covariance and related matrices give more detailed information. An eigenvalue or principle component analysis allows the inspection of essential linear combinations of the parameters.The relative contributions of a priori information and data to the solution can be elegantly studied. Results in this paper are especially worked out for the non-linear Gaussian case. Comparisons with other approaches are given. The procedures are illustrated with a simple two-parameter inverse problem.

Notes: For converted waves stacking requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. We consider converted waves of the PS- and SP-type in a stack of horizontal layers.The coordinates of the conversion points for waves of PS- or SP-type, respectively, in a single homogeneous layer are calculated as a function of the offset, the reflector depth and the velocity ratio vp/vs. Knowledge of the conversion points enables us to gather the seismic traces in a common conversion point (CCP) record. Numerical tests show that the CCP coordinates in a multilayered medium can be approximated by the equations given for a single layer. In practical applications, an a priori estimate of vp/vs is required to obtain the CCP for a given reflector depth.A series expansion for the traveltime of converted waves as a function of the offset is presented. Numerical examples have been calculated for several truncations. For small offsets, a hyperbolic approximation can be used. For this, the rms velocity of converted waves is defined. A Dix-type formula, relating the product of the interval velocities of compressional and shear waves to the rms velocity of the converted waves, is presented.

Notes: An increase in the grain/pore size can cause the received echo signal to be distorted due to the preferential attenuation of the high-frequency components of the transmitted acoustic signal. Therefore, a rock acts as a low-pass filter and the property of the filter has a linear relation to the grain/pore size. The results have shown that P- and S-wave attenuations can be used to characterize selected internal characteristics of a rock. For example, an increase in the differential stress can cause an increase in the attenuation, due to the sensitivity of the S-wave to microcracks.

Notes: Three-component recordings permit the construction of particle trajectories. These three-dimensional pictures of particle motion show successive predominant directions of polarization and allow wave modes with distinct polarization directions to be recognized. A polarization selection, called ‘spatial directional filtering’, can be accomplished by several methods; four techniques are described. The application of these polarization filters to a noise shot, offset VSPs and CDP stack are also presented. This type of filtering is shown to cancel waves with undue polarization and to enhance the signal-to-noise ratio.

Notes: Gold, as a trace element, is not directly detectable by geophysical borehole logging techniques. Geophysical logging methods have therefore been used to infer the presence of structural features and alteration processes associated with gold. Since these features and processes differ with the style of gold mineralization, a unique relation between geophysical anomalies and gold cannot be established. However, in a particular environment, such an association can be established. We examined geophysical log data (self potential, induced polarization, resistivity, gamma, temperature, and temperature gradient) and drill core from the Barber-Larder property in NE Ontario. The geophysically detectable alteration processes associated with gold were identified as sericitization and pyritization, by means of factor analysis. A linear discriminant function was constructed which allowed the zones of economic mineralization (nominally 0.05 oz/ton or 1.5 ppm) to be identified with a 75% success rate based on geophysical log data alone. This rate was achieved without sophisticated non-linear data transformations.

Notes: A model of parallel slip interfaces simulates the behaviour of a fracture system composed of large, closely spaced, aligned joints. The model admits any fracture system anisotropy: triclinic (the most general), monoclinic, orthorhombic or transversely isotropic, and this is specified by the form of the 3 × 3 fracture system compliance matrix. The fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy. To compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 × 3 matrices. When the fractures are assumed on average to have rotational symmetry (transversely isotropic fracture system behaviour) and the background is assumed isotropic, the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters (in addition to the two isotropic parameters of the isotropic background). Dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints, i.e. there are two additional parameters due to the presence of the microcracks which play roles in the stress-strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints. Thus, knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation. As the aligned microcracks, which were assumed to be ellipsoidal, with very small aspect ratio are allowed to become non-fiat, i.e. have a growing aspect ratio, the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks. The divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0.3.

Notes: Ray theories are a class of methods often chosen to compute synthetic seismograms due to their efficiency and ability to deal with complex, three-dimensional inhomogeneous media. To deal with the large number of rays needed to compute synthetic seismograms, a ray generation algorithm is given which is capable of generating a numerical code describing each ray. The code describes a subset of all possible rays by considering only pre-critical reflections. In a horizontally plane-layered medium the generation of rays and computation of amplitudes and traveltimes can be efficiently accomplished by grouping the rays into reflection order and dynamic analogue groups. Expressions summing all unconverted rays and rays with a single mode conversion are given for source and receiver located at arbitrary positions within the medium. Examples of zero-offset synthetic VSPs obtained by this method are given.

Notes: The cross-correlation technique for increasing the anomaly-to-noise ratio is applied to the interpretation of resistivity profiles.To verify the method theoretically, resistivity profiles above a body having the shape of a parallelepiped were simulated with correlated and uncorrelated noise. Seven different electrode geometries are discussed. As a practical test, we considered profiles of a geoelectrical survey to locate tombs at a site of archaeological interest.When the shape and dimensions of the anomaly can be foreseen, the cross-correlation method can be applied and it gives a substantial improvement in the signal-to-noise ratio.

Notes: In the quantitative data interpretation for HLEM induction prospecting, a vertical half-plane model in an insulating medium is widely employed. For this assumption to be valid, the steeply dipping massive sulphide dykes must have large strike lengths and depth extents, but small thickness.We report investigations, using the laboratory scale-modelling method, on the response variation of large vertical conductors as the thickness is varied. We conclude that a steeply dipping large dyke can be approximated by a half-plane model only if its thickness is less than half the skin depth. An inductively thick conductor produces larger amplitudes and relatively higher quadrature compared to a thin conductor, even if both have the same induction number.

Notes: A model has been developed to relate the velocities of acoustic waves Vp and Vs in unconsolidated permafrost to the porosity and extent of freezing of the interstitial water. The permafrost is idealized as an assemblage of spherical quartz grains embedded in a matrix composed of spherical inclusions of water in ice. The wave-scattering theory of Kuster and Toksoz is used to determine the effective elastic moduli, and hence the acoustic velocities. The model predicts Vp and Vs to be decreasing functions of both the porosity and the water-to-ice ratio. The theory has been applied to laboratory measurements of Vp and Vs in 31 permafrost samples from the North American Arctic. Although no direct measurements were made of the extent of freezing in these samples, the data are consistent with the predictions of the model. Electrical resistivity measurements on the permafrost samples have demonstrated their essentially resistive behaviour. The ratio of resistivity of permafrost in its frozen state to that in its unfrozen state has been related to the extent of freezing in the samples.Electromagnetic and seismic reflection surveys can be used together in areas of permafrost: firstly an EM survey to determine the extent of freezing and then the acoustic velocity model to predict the velocities in the permafrost. The necessary transit time corrections can thus be made on seismic reflection records to compensate for the presence of permafrost.

Notes: The classical aim of non-linear inversion of seismograms is to obtain the earth model which, for null initial conditions and given sources, best predicts the observed seismograms. This problem is currently solved by an iterative method: each iteration involves the resolution of the wave equation with the actual sources in the current medium, the resolution of the wave equation, backwards in time, with the current residuals as sources; and the correlation, at each point of space, of the two wavefields thus obtained.Our view of inversion is more general: we want to obtain a whole set of earth model, initial conditions, source functions, and predicted seismograms, which are the closest to some a priori values, and which are related through the wave equation. It allows us to justify the previous method, but it also allows us to set the same inverse problem in a different way: what is now searched for is the best fit between calculated and a priori initial conditions, for given sources and observed surface displacements. This leads to a completely different iterative method, in which each iteration involves the downward extrapolation of given surface displacements and tractions, down to a given depth (the‘bottom’), the upward extrapolation of null displacements and tractions at the bottom, using as sources the initial time conditions of the previous field, and a correlation, at each point of the space, of the two wavefields thus obtained. Besides the theoretical interest of the result, it opens the way to alternative numerical methods of resolution of the inverse problem. If the non-linear inversion using forward-backward time propagations now works, this non-linear inversion using downward-upward extrapolations will give the same results but more economically, because of some tricks which may be used in depth extrapolation (calculation frequency by frequency, inversion of the top layers before the bottom layers, etc.).

Notes: Two particular sources of distortion, which may be encountered when applying tomographic imaging techniques to crosshole seismic data, have been investigated.Errors in survey locations of the shots and receivers can produce significant distortions in the images obtained. A simple method for solving simultaneously for the velocity field and shot and receiver location errors is presented and applied to synthetic and real data.Reflection and refraction of rays at velocity interfaces may produce poor density and angular coverage of the rays within the region of interest. It is shown that the effect of the velocity field on the ray coverage can significantly affect the resolution in the velocity image, even if ray bending is taken into account. One consequence of this effect is that, in some cases, little improvement in image quality is achieved by using curvi-ray rather than straight-ray inversion techniques, despite the occurrence of pronounced ray bending.

Notes: The WKB-method is used for the derivation of both the complex dispersion relation and displacement functions for Love channel-waves that propagate in a coal seam of varying thickness. The constant Q-model is used to describe the anelastic friction. With numerical solutions of the absorption-dispersion relation, the influence of thickness changes on the phase velocity and absorption coefficient of Love seam-waves is analysed at various frequencies. It is shown that the changes in the seam thickness can be optimally detected around the average Airy-phase frequency. An equivalence is pointed out between the wave guide structures: homogeneous with varying seam thickness and horizontally inhomogeneous with constant seam thickness.

Notes: Methods of minimum entropy deconvolution (MED) try to take advantage of the non-Gaussian distribution of primary reflectivities in the design of deconvolution operators. Of these, Wiggins’(1978) original method performs as well as any in practice. However, we present examples to show that it does not provide a reliable means of deconvolving seismic data: its operators are not stable and, instead of whitening the data, they often band-pass filter it severely. The method could be more appropriately called maximum kurtosis deconvolution since the varimax norm it employs is really an estimate of kurtosis. Its poor performance is explained in terms of the relation between the kurtosis of a noisy band-limited seismic trace and the kurtosis of the underlying reflectivity sequence, and between the estimation errors in a maximum kurtosis operator and the data and design parameters.The scheme put forward by Fourmann in 1984, whereby the data are corrected by the phase rotation that maximizes their kurtosis, is a more practical method. This preserves the main attraction of MED, its potential for phase control, and leaves trace whitening and noise control to proven conventional methods. The correction can be determined without actually applying a whole series of phase shifts to the data. The application of the method is illustrated by means of practical and synthetic examples, and summarized by rules derived from theory. In particular, the signal-dominated bandwidth must exceed a threshold for the method to work at all and estimation of the phase correction requires a considerable amount of data.Kurtosis can estimate phase better than other norms that are misleadingly declared to be more efficient by theory based on full-band, noise-free data.

Notes: The Offset Wenner resistivity sounding system provides for the extrapolation of the Wenner resistivity curve. The extrapolation technique was applied to data measured in the Solomon Islands and it is shown to be unreliable. An accurate method of predicting the reliability of extrapolation using measured resistances could not be found.

Notes: The concept of multifrequency induction logging simulations in the frequency range of 10 kHz to 1 MHz, applied to two-dimensional, axial symmetric model geometries, is presented. The scalar Helmholtz equation has been solved by a finite-element procedure. The model domain has been discretisized under the condition that the discontinuities in conductivity are represented by the nodes of the adjacent triangular elements. The modification of the signal distribution by the skin effect is illustrated for several models. Several sets of induction logs have been calculated with particular consideration of the frequency-dependent conductivities and permittivities.The improvement of a multifrequency inversion technique, based on standard least-squares methods, is shown for a two-layer model including borehole and invasion zones. Using this improved inversion technique we can state, as an additional inversion parameter, the frequency dependence of each inverted rock conductivity.

Notes: The wavefield in, and at the surface of, a homogeneous, isotropic, perfectly elastic half-space, excited by a traction distribution at the surface of the medium is investigated. The emitted wavefield is a spatial convolution of the surface tractions and the spatial impulse response. The properties of the wavefield in the far-field of the medium are derived and it is shown that the far-field particle velocity is essentially equal to a weighted sum of the time derivative of the integrated surface tractions, that is, of the components of the ‘ground force’. The theory is valid for an arbitrary geometry and orientation of the surface tractions, and is independent of the boundary conditions at the surface of the medium.The surface tractions are related to a source that consists of a mass distribution with an arbitrary force distribution imposed upon it. A boundary condition is introduced that accounts for the mass load and the forces applied to it but neglects vibrations within the mass. The boundary condition follows from the equation of motion of the surface mass load.The theory is applied to the Vibroseis configuration, using a P-wave vibrator model with a uniformly distributed force imposed on top of the baseplate, and assuming that horizontal surface traction components are absent. The distribution of displacement and stress directly underneath the baseplate of a single vibrator and an array of vibrators is investigated. Three different boundary conditions are used: (1) assuming uniform pressure, (2) assuming uniform displacement, (3) using the equation of motion of the baseplate as a boundary condition. The calculations of the distribution of stress and displacement over the plate for different elastic media and several frequencies of operation show that only the results obtained with the mixed boundary condition agree with measurements made in the field.The accuracy of three different phase-feedback signals is compared using synthetic data. Baseplate velocity phase-feedback leads to huge deviations in the determination of the far-field wavelet; reaction mass acceleration phase-feedback looks stable but neglects the differentiating earth filter; and phase-feedback to a weighted sum of baseplate and reaction mass accelerations becomes unstable with increasing frequency. The instability can be overcome using measurements over the whole baseplate.The model can be extended to a lossy layered earth.

Notes: This paper describes a method of generating pseudovelocity logs using measurements of electrical resistivity. A theoretical relation between electrical resistivity and transit time, which is applicable to a wide range of lithologies, has been developed. The application of this relation using a method which defines lithoresistivity zones as lithological intervals related to the same formation and showing small resistivity variations, has been tested in the Recôncavo sedimentary basin in Bahia, Brazil. A comparison of derived pseudovelocity logs with actual sonic logs for five wells whows the validity of the present approach.

Notes: In mapping the topography of the basement of deep sedimentary basins by gravity modelling, the accuracy can be improved by incorporating an exponential increase in density with depth. For calculating the gravity effect of a three-dimensional (3D) structure with such an exponential density-depth relation a frequency-domain forward algorithm based on series expansion is presented, the numerical evaluation of which can be performed efficiently by fast Fourier transform. The algorithm can be applied in a recursive procedure to give the inverse solution in terms of basement relief.The inversion procedure is satisfactorily tested on a 2D synthetic example and a 3D field example of gravity data from the western margin of the Pannonian Basin in eastern Austria, where up to 2.2 km of Tertiary sediments overlie an igneous or metamorphic basement. The results are confirmed by basement intersections in several wells.

Notes: The usual description of electric field measurements in terms of potential differences is not entirely adequate at high frequencies. In general, the telluric electric field is non-conservative and voltage measurements depend on the contour described by the cable. A simple error analysis helps to recognize those situations where systematic errors may be significant for present day standards.

Notes: A complete mathematical analysis is proposed for direct current resistivity prospecting over the surface of a layered paraboloid. The analysis evaluates the Green's function in parabolic coordinates for a current source at the vertex. The general solution is obtained as a Fourier-Bessel integral involving those curvilinear coordinates that have a kernel function which is similar to that of a half-plane containing inhomogeneous layers. This similarity permits the computation of a class of sounding curves over such an oval surface providing a way to analyse field data over hilly terrain.

Notes: A method of detection of diffracted waves on common-offset sections is proposed. The method utilizes the main kinematic and dynamic properties of the diffracted waves. The detection algorithm is defined by an automatic procedure including phase correlation of the diffracted waves and the application of certain statistical criteria. This procedure enables us to make decisions with regard to the presence of the diffracted waves and also to estimate parameters of the scattering objects. The method is applied to synthetic and field data and, even for a relatively low signal-to-noise ratio, it gives reliable results.

Notes: The Kunetz-Claerbout equation for the acoustic transmission problem in a layered medium in its original form establishes the relation between the transmission and the reflec tion response for P-waves in an horizontally layered medium and with vertical incidence. It states that the reflection seismogram due to an impulsive source at the surface, is one side of the autocorrelation of the seismogram due to an impulsive source at depth and a surface receiver.By adapting Claerbout's formulation to the transmission of SH-waves, the Kunetz-Claerbout equation also holds for reflection and transmission coefficients dependent on the incident angle. Thus, earthquake geometry SH-transmission seismograms can be used to caculate corresponding pseudoreflection seismograms which, in turn, can be inverted for the impedance structure using the Levinson algorithm. If the average incidence angle is known, a geometrical correction on the resulting impedance model can improve the resolution of layer thicknesses.In contrast to the inversion of reflection seismograms, the Levinson algorithm is shown to yield stable results for the inversion of transmission seismograms even in the presence of additive noise. This noise stabilization is inherent to the Kunetz-Claerbout equation.Results of inverted SH-wave microearthquake seismograms from the Swabian Jura, SW Germany, seismic zone obtained at recording site Hausen im Tal have been compared with sonic-log data from nearby exploration drilling at Trochtelfingen. The agreement of the main structural elements is fair to a depth of several hundred metres.

Notes: Inverse Q-filtering (IQF) is a technique designed to correct for transmission losses due to inelastic attenuation. It is based on the constant-Q model and is derived from a Taylor series solution of a standard convolutional-trace model (primaries only). To avoid a non-causal solution, the attenuation is assumed to be minimum-phase. Band limitation is introduced to make IQF a stable process in the presence of noise. The main features of IQF are demonstrated using both synthetic and field data.

Notes: Two techniques for the measurement of attenuation–spectral ratio and rise time techniques–were tested and compared in the laboratory. The spectral ratio technique proved to be reliable and easy to implement for intermediate values (5 〈 Q 〈 50) of attenuation. For low (Q 〉 50) and high attenuations, the spectral ratio technique is inaccurate. Calculating the rise time on simulated signals, we found a relation between rise time τ and the ratio travel-time to quality factor T/Q which could be approximated in intervals by the linear relation τ=τ+C*T/Q. The constants τ and C depend on the absolute value of T/Q and on the initial source signal. The rise time technique, performed on the first quarter period of the signal, enables high attenuations (Q 〈 5) to be measured. The determination of the relation between τ and T/Q is possible if one knows the initial source. We theoretically approximate this relation through a simulation using a realistic propagation model. With laboratory measurements made on Fontainebleau sandstone, we show that the rise time technique using the theoretical relation τ=τ(T/Q) gives comparable values of Q to those obtained from the spectral ratio technique. In borehole seismics, where it is often difficult to remove undesired signals, the rise time technique applied with the right (τ, T/Q) relation is the best method to use.

Notes: A technique to evaluate an ideal performance of a deconvolution operator has been obtained by dividing the input trace into a number of sections. The error energy is seen to decrease with an increase in the number of sections. Numerical examples show that the error energy becomes zero following a relation between the number of sections, the length of input and the length of the filter.

Notes: We propose a wave scattering approach to the problem of deconvolution by the inversion of the reflection seismogram. Rather than using the least-squares approach, we study the full wave solution of the one-dimensional wave equation for deconvolution. Randomness of the reflectivity is not a necessary assumption in this method. Both the reflectivity and the section multiple train can be predicted from the boundary data (the reflection seismogram). This is in contrast to the usual statistical approach in which reflectivity is unpredictable and random, and the section multiple train is the only predictable component of the seismogram. The proposed scattering approach also differs from Claerbout's method based on the Kunetz equation.The coupled first-order hyperbolic wave equations have been obtained from the equation of motion and the law of elasticity. These equations have been transformed in terms of characteristics. A finite-difference numerical scheme for the downward continuation of the free-surface reflection seismogram has been developed. The discrete causal solutions for forward and inverse problems have been obtained. The computer algorithm recursively solves for the pressure and particle velocity response and the impedance log. The method accomplishes deconvolution and impedance log reconstruction. We have tested the method by computer model experiments and obtained satisfactory results using noise-free synthetic data. Further study is recommended for the method's application to real data.

Notes: A simple unified equation of apparent resistivity for a general four-electrode array is developed. The main idea is the analytical integration of the Stefanescu expression for potential over a layered earth by writing an exponential approximation for the kernel function. Finally a matrix equation is developed to estimate the kernel function from observed apparent resistivity values. The general equation automatically reduces to the particular configuration once the electrode separations are modified suitably. Examples for Schlumberger and Wenner configurations are numerically calculated to estimate the precision of the method. Good results in a short execution time are obtained, irrespective of the shape of the apparent resistivity curve. Finally, the full interpretation of one theoretical resistivity curve and two field resistivity curves is demonstrated. The more stable ridge-regression estimation method is used in the identification of layer parameters from the kernel function.

Notes: Seismic reflection data always exhibit a progressive loss of high-frequency energy with time. This effect is partly attributable to irreversible processes such as the conversion of elastic energy into heat (commonly known as absorption), and partly to reversible processes associated with interference between reflected waves arriving at different times. This paper looks only at reversible linear elastic effects at normal incidence and asks the following question: if there were no such absorption, would there still be a progressive loss of high-frequency energy?Using normal incidence and a layered elastic earth model we prove the following results.1. The normal incidence response of a sequence of plane parallel elastic layers is non-white.2. The pressure wave reflected by a layer that is thin compared with a wavelength is differentiated with respect to the incident wave.3. The transmission response of a thin layer is consequently low-pass and the transmission response of a sequence containing many thin layers is very low-pass.4. The well-known effect of the transport of acoustic energy by peg-leg multiples within thin layers is identical with this low-pass transmission response.5. It follows that the high frequency energy is reflected back early in the seismogram.6. By comparison, very low-frequencies are transmitted through the layered sequence easily and are reflected with difficulty. There is probably a lack of low-frequency energy in the reflection seismogram, by comparison with the spectrum of the incident plane wave.It follows that any meaningful evaluation of frequency-dependent absorption in seismic data cannot take place unless the frequency-dependent linear elastic effects are taken into account first.

Notes: A new integral-equation program for calculation of the E-polarization response allows modeling of VLF for plane wave or line source input, e.g., magnetotellurics and Turam responses. The anomalous conducting body is modeled by a number of square cells, each of individual size and resistivity, and with arbitrary position in the host medium. This provides a high degree of flexibility and allows for simulation of rather complex conductivity structures. The computation time has been drastically reduced by using techniques such as digital filtering and fast Fourier transformation.The interpretation of a measured Turam profile and the influence of galvanically channelled currents in the conducting body is discussed.

Notes: Examples show that the sampling operation–i.e., the change from the continuous time domain to the discrete time domain–does not necessarily preserve the minimum-phase property. Further examples can be constructed to show that the resampling operation on the discrete time domain does not necessarily preserve the minimum-phase property. Finally it can be shown that the minimum-phase property can be either created or destroyed by sampling or resampling.

Notes: An integral equation method is described for solving the potential problem of a stationary electric current in a medium that is linear, isotropic and piecewise homogeneous in terms of electrical conductivity. The integral equations are Fredholm's equations of the ‘second kind’ developed for the potential of the electric field. In this method the discontinuity-surfaces of electrical conductivity are divided into ‘sub-areas’ that are so small that the value of their potential can be regarded as constant.The equations are applied to 3-D galvanic modeling. In the numerical examples the convergence is examined. The results are also compared with solutions derived with other integral equations. Examples are given of anomalies of apparent resistivity and mise-a-la-masse methods, assuming finite conductivity contrast. We show that the numerical solutions converge more rapidly than compared to solutions published earlier for the electric field. This results from the fact that the potential (as a function of the location coordinate) behaves more regularly than the electric field. The equations are applicable to all cases where conductivity contrast is finite.

Notes: A seismic survey was carried out on a tidal flat in the SW-Netherlands in order to determine shear-wave velocities in sediments by means of higher-mode Rayleigh waves. The dispersion properties of these Rayleigh waves were measured in the 2-D amplitude spectrum–or f, k-spectrum–and resulted in phase velocities for six different modes as a function of frequency (5–30 Hz). These observed phase velocities were inverted for a nine-layer model for the shear-wave velocity to a depth of 50 m.

Notes: The space-time acoustic wave motion generated by an impulsive monopole source is calculated with the aid of the Cagniard-de Hoop technique. Two configurations with plane interfaces are discussed: an air/fluid/solid configuration with the source and the receiver located in the fluid layer; and a stack of n fluid layers between two acoustic half-spaces where the source and the receiver are located in the upper half-space. Synthetic seismograms are generated for the pressure of the reflected wavefield, using the source signature of an airgun.

Notes: In total 77 direct current resistivity soundings were carried out during a geothermal exploration survey of the Genisea, NE Greece, geothermal field. The data revealed a high electrical conductivity zone at the center of the investigated area and suggested that an anomalous heat source lay beneath the study area.This was confirmed by subsequent drilling data. Temperature measurements, from 11 boreholes, were used for the construction of isotherms that correlated very closely with the geoelectric data.

Notes: Many ground TEM systems use an on-off type of primary field waveform and measure the secondary field only in the transmitter off-time, so as to realize the pure secondary field measurement. The width of the trailing edge of the primary pulses and the duration of the transmitter on-time form a time-constant (Tc) window. Most effective excitation is achieved if the target conductor has a Tc falling into this window.To be able to measure in the transmitter on-time, two primary field waveforms are proposed. The first is a series of unipolar pulses with identical steep ramps at both leading and trailing edges. Measurements made in the on-time after the leading edges simply reduce the stacking time needed and power consumption by half. Also, long- Tc conductors are better excited. The second is a series of bipolar pulses with long ramps as the leading edges and short ramps as the trailing edges. This waveform presents two different Tc-windows at the same time and helps to improve the detection of long-Tc conductors in the presence of short- Tc ones.

Notes: Recent work by Räder, Schott, Dresen and Rüter has provided a means of calculating dispersion and amplitude distribution curves for SH channel waves in multilayered media. An alternative calculation procedure is presented and the P-SV wave type is also included. Numerical results are given for a coal seam containing a band of dirt of either higher or lower seismic velocities than the coal itself.

Notes: A horizontal transmitter loop (vertical magnetic dipole) is used for frequency electromagnetic (FEM) soundings. The frequency ranges from approximately 6 Hz to about 4000 Hz. The vertical and radial magnetic field components are measured for 20 frequencies per decade several hundred meters from the transmitter loop. A very small bandwidth is selected for amplification using a reference signal. An Apple computer is used for data acquisition.A computer program for Marquardt inversion optimizes the parameters for the n-layer case: the resistivities and thicknesses of individual beds and a correction factor for the primary magnetic field. Interpretation of each component individually yields practically the same parameters. Examples from the field are given with interpretation; comparison with dc resistivity measurements is provided.The ratio of vertical/radial magnetic field components vs. frequency can be transformed simply into apparent resistivity vs. apparent depth. This can be done in the field to obtain an estimation of the depth of the layer boundaries. FEM results are compared with Schlumberger d.c. sounding obtained at the same site.

Notes: The propagation of Love seam-waves across washouts of coal seams was studied by calculating synthetic seismograms with a finite-difference method. Seam interruption, seam end and seam thinning models were investigated. The horizontal offset, the dip of the discontinuities and the degree of erosion served as variable parameters. Maximum displacement amplitudes, relative spectral amplitudes and phase and group slowness curves were extracted from the synthetic seismograms.Both seam interruption and seam thinning reduce the maximum displacement amplitudes of the transmitted Love seam-waves. The degree of amplitude reduction depends on the horizontal offset and the degree of erosion. It is four times greater for a total seam interruption than for an equivalent seam thinning with a horizontal offset of four times the seam thickness. In a seam cut vertically, the impedance contrast between the coal and the washout filling determines the maximum displacement amplitudes of the reflected Love seam-waves. They diminish by a maximum factor of four in oblique interruption zone discontinuities with a dip of maximum 27°, and by a maximum factor of ten in a seam thinning with a degree of erosion of at least 22%.The analysis of the relative spectral amplitudes indicates a preferential transmission of those phases with frequencies below, and a preferential reflection of those phases with frequencies above the first mode Airy-phase. The relative spectral amplitudes of the reflected Love seam-waves show a distinct interference pattern of the waves reflected at both interruption zone discontinuities.The dispersion analysis reveals a flattening of the phase and group slowness curves with increasing frequencies, horizontal offset and degrees of erosion.These results imply that a detection of washouts in-mine will be possible in a frequency range including at least the first mode Airy-phase. An interference pattern and a flattening of the dispersion curve indicate a washout rather than other seam obstructions and leads to an estimate of the washout dimension.

Notes: Investigations show that the depth range of the gravity method for detecting cavities is considerably greater than expected on the basis of theoretical calculations that consider only the depth and shape of the cavity.The cavity generates its own gravity field that is the sum of the activity of the cavity itself and the density changes caused in the surrounding rocks by the process of their destruction as a result of the cavity's expansion. The latter factor is decisive for the cavity's detection by the gravity method in several cases.The extent of the zones of change density in the surrounding rocks and their actual shape depend on many parameters. Thus, the determination of the depth of the cavity cannot be made by comparing measured and theoretical curves of gravity anomalies. The location of the center of gravity of the area disturbed by the cavity or upper boundary of its development towards the ground surface can be determined by denoting the singular point of gravity as a result of the downward analytical continuation of Ag.The Strakhov-Grigorieva-Lapina (1977) method fulfils the necessary conditions in the field.

Notes: Short filters for calculating Hankel-transformations, with special attention to the d.c.-sounding problem, have been published in recent years. These filters, with a typical length of less than 25 coefficients, have made it possible to implement, e.g., VES-interpretation programs on microcomputers and 3-D electric and electromagnetic modeling programs on minicomputers. Initially the performance of the short filters was rather poor, but with the introduction of short optimized filters there has been a considerable improvement in the accuracy.An optimization procedure is applied to design a 20-point filter for the Fourier sine-transformation. This filter may be useful in electromagnetic prospecting theory, e.g., in the calculation of the electric and magnetic field from a line source.

Notes: This paper reviews computer techniques used in the automatic zoning and correlation of well-logs. Prior to correlating, well-logs are to be segmented–or ‘zoned’–so as to delineate sections that have similar properties. Techniques discussed include statistical methods such as variance tests and Student's t-test, linguistic analysis, the use of Walsh functions and spectral analysis.Well-log correlation, which may be between traces from different wells or between traces from the same hole (as in dip logs), is used in basin studies and the determination of structural dip. A variety of methods are reviewed including conventional time and frequency correlation, sequence slotting, pattern recognition and frequency analysis. Future directions for investigation are proposed.

Notes: A portable low-power Very Low Frequency (VLF) transmitter using a large square loop antenna has been designed, assembled and tested by the Geological Survey of Canada (GSC) for geological studies of fracture patterns in igneous rock masses. Standard laboratory equipment, consisting of a signal generator, a 1100-W power amplifier and several high-power tuning capacitors, was used for the purpose.Field tests at the Chalk River facilities of Atomic Energy of Canada Limited have demonstrated a remarkable similarity between survey results obtained using the VLF signals from the local loop transmitter and from distant US Navy VLF transmitters. The local loop was used to simulate the fields from navy stations NAA in Cutler, Maine and NSS in Annapolis, Maryland. Conductor axes, mapped by using these navy stations, and by using the loop antenna yielded almost identical results. A survey was also done in the same area with the local loop placed in such a manner that the direction of the VLF field was at 45° to the field directions from NAA and NSS. In this case, the same conductor axes were located with only minor shifts in position, indicating that conductors whose axes lie within 45° of the direction of the primary horizontal magnetic field are mapped. Thus, it is probably sufficient to have two sources with orthogonal VLF fields to map all VLF conductors in an area. Since in most areas at least one navy VLF station can be used, the local loop transmitter can be used to generate a signal at right angles to the direction from the navy transmitter to allow a more complete VLF survey coverage.

Notes: The article provides a theoretical basis for the extension of the method of scaling law deconvolution to three dimensions using airgun arrays as a sound source.Earlier papers by the author required the dimensions of the scaled sources to be different while the depths and firing pressures were maintained the same in order to preserve the same dynamics of the scaled sources at scaled time. However, this forces the source ghost to be considered as part of the impulse response of the earth rather than as part of the downgoing source wave. And, in fact, the dynamics of the scaled sources are not the same at the same depth because the ghost reflection modulates the behaviour of the oscillating bubbles generated by the airguns, and this modulation does not scale.To force the sources to scale properly, including the ghost interaction, the larger source must be put at greater depth, where hydrostatic pressure is greater, and the initial firing pressure must be adjusted accordingly. Thus, the depth, initial firing pressure and gun volume are all variables. The interaction among guns in scaled airgun arrays also scales exactly if the geometry of an array and the depth of its deployment are scaled by the same factor.

Notes: Wave field extrapolation including critical angle events in modeling, migration and inversion can be handled with algorithms based on both the one-way wave equations and the two-way wave equation. It is shown that for 1-D inhomogeneous media, critical angle events as well as multiple reflections may elegantly be included in pre-stack modeling, pre-stack migration and velocity inversion. For 2-D and 3-D inhomogeneous media a powerful pre-stack migration scheme can be developed which includes critical angle events as well as multiple reflections. Finally, suggestions for practical applications are given.

Notes: Bayesian statistics are applied to the problem of signal-to-noise ratio enhancement from a common-midpoint gather. By maximizing the a posteriori probability distribution of the gather with respect to the minimum-offset trace and suppressing multiples via a semblance criterion, a statistically biased stack is formed with signal-to-noise ratio comparable to that of the usual stack while preserving the resolution and registration of the original noisy trace.Application of the algorithm to real data reveals geologically significant features which are indistinct in the standard stacked section.

Notes: The increase in the number of geophone groups in production records during recent years and the requirement for accurate basic static corrections for high resolution records have made it necessary to develop sufficiently accurate automatic techniques for the determination of static corrections.A fully automatic method is presented which makes use of the delay-time method in order to compute static corrections at each shot position. Delay times, weathering and subweathering velocities are determined from automatic picks of the first arrivals on common-offset trace collections.It is assumed that the weathering is a single layer and that the dip of the subweathering layer under the geophone groups is small.The picking routine is fully automatic and successful in most cases, provided the signal-to-noise ratio is sufficiently high.The subsequent filtering of erroneous values for picked times is performed by means of statistical techniques, using curves of picked times on common-offset trace collections. If the distance between receivers and shot-points on the profile is sufficiently short, one can expect only little change in the picked times of two contiguous traces.The method is well adapted to end-on spreads with a great number of traces, where distances between geophone groups are short.Examples are presented showing the possibilities of the method for the determination of long wavelength as well as short wavelength components of static corrections.

Notes: A new deterministic technique for estimating a wavelet suggested by Loewenthal and Jakubowicz requires measurement of both pressure and vertical particle velocity. Through construction of the impedance function a deterministic estimation of the wavelet and the reflectivity can be obtained.This idea is tested for a one-dimensional model. The test is carried out by forming a synthetic seismogram of both pressure and particle velocity and checking the formulas for obtaining the estimated wavelet under noisy conditions.

Notes: Four methods for the determination of Q in marine sediments are compared: two traditional methods, i.e. the risetime and the spectral ratio method, and two newly established ones, the spectrum modeling and the wavelet modeling method. In the latter one Q and the reflection time T are determined simultaneously, which gives a much better accuracy for T than reading it from the seismogram. The risetime and the spectral ratio methods are used for obtaining Q directly from the data. The principle of the modeling methods is to calculate the effect of absorption and dispersion on a reference wavelet or its spectrum for various values of Q, and the best fit between the observed and the calculated data leads to the optimum result. Numerical tests on synthetic data show that a precision of more than 25% for data containing noise or superposed arrivals can hardly be achieved; in any case, wavelet modeling is the superior method. Application to data from a vertical reflection profile in the Baltic Sea yields Q in the range of 15–100 for different layers, which is to be expected in the sedimentary environment of this area.The computations were performed in the Computer Center of Kiel University. The authors thank R. Meissner for his comments on the manuscript.

Notes: Small offsets in hard coal seams can be detected with the aid of seam (channel) waves. Transmission and reflection of seam waves depend, among other parameters, upon the symmetry properties of the sequence rock/coal/rock. Two typical unsymmetrical sequences are found in European coal deposits: (i) coal seams with roof and floor of differing acoustic impedance and (ii) coal seams interlayered with rock and soil.Two-dimensional analog models with appropriate impedance contrasts are used to study the effect of the unsymmetrical layers upon the propagation of Rayleigh seam waves. Data analysis is based upon amplitude measurements both parallel and perpendicular to the layers and dispersion curves.The effect of unsymmetrical roof (rock 1) and floor (rock 2) was studied with models containing homogeneous coal seams. Leaky mode wave groups with phase velocities (cR) in the range between the SV-wave velocities (βr1, 2) of the two rock materials, i.e. βr1≥cR 〉 βr2, form a characteristic part of the Rayleigh seam wave signal. Using Knott's energy coefficient calculations it is shown that in that range energy leakage into the surrounding rock by refracted SV-waves is restricted to only one of the two interfaces, namely coal/rock 2. At the other interface, coal/rock 1, all waves are totally reflected. Thus, the high amplitudes of these leaky mode wave groups are explained by “quasi-normal mode” features.The influence of a dirt bed on wave propagation was studied in models where the roof and the floor have the same elastic properties. The maximum thickness of the dirt bed did not exceed 20% of the total seam thickness. The effect of the bed's location within the seam was also investigated.For all recorded normal-mode wave groups either the total seam or the coal layers could be regarded as wave guides. This was shown by the fact that the phases could be associated with the phase velocity dispersion curves calculated for the symmetrical sequence rock/coal/rock. These curves are relevant under the condition that the thickness of the coal layer assumed under the calculation coincides with the thickness of the effective wave guide of the respective wave groups.Wave groups guided in the total seam are not influenced by either the thickness or the position of the dirt bed. On the other hand, for wave groups guided in the coal layers, the quotient of signal amplitudes in the coal layers is influenced by the position of the dirt bed.

Notes: Shotpoint gathers from conventional reflection seismic surveys contain both reflected and refracted waves. In this study shot records were processed and analyzed, and the data were modeled with reflected, refracted, and reflected-refracted waves to fit the recorded data. The result is a detailed velocity model. The inverse problem for refracted waves was solved by using the Wiechert-Herglotz inversion.A 500-km-long 26-fold reflection seismic line from the Barents Sea, north of Norway, has been investigated. The data show high velocities, multiple reflections, and various types of noise. To test the method a total of 34 shot gathers were analyzed along this line. The aim of the interpretation was to determine the velocity in the seafloor and the near-surface sediments. It is possible to map the vertical as well as the lateral velocity distribution in detail. Depending on the length of the streamer and the velocity gradient in the sediments, the calculated depth varies between 300 and 500 m below the seafloor. These velocities were also compared to the stacking velocities obtained from the reflection seismic data to see how the velocities determined by different methods were related.The velocity distribution in the sediments is one of the key factors in seismic interpretation. The technique discussed in this paper can contribute to velocity information both in the processing and interpretation of seismic data.

Notes: In the course of investigations concerning disposal of radioactive waste, DC-geoelectric soundings were performed in the salt mine Asse in 1982. The survey resulted in the determination of resistivities of various salt formations. A comparison of various resistivities obtained in salt formations in the mine shows that it is possible to estimate the content of free water in salt using Archie's equation.The significant result of this survey is that salt formations in the mine can be divided into two categories according to their resistivities:1. Salt with resistivity between 107 and 108Ωm (particularly Na2Sp and Na3β). The particularly pure halitic formations are to be found within this resistivity range.2. Salt with resistivity between 103 and 105Ωm (Na2Tl, K2, transition salt). The salt formations with thin layers of anhydrite and a high content of hygroscopic salts are classified in the paper.

Notes: Various exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane-wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately.Rather than invert each plane-wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane-wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time-domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process.

Notes: The geophysical data processor today has on offer a great variety of tools for the inversion of seismic reflection data to estimate geological structure. The major subset of these comprises migration procedures, which span a wide range of sophistication and cost in terms both of computation time and manual effort on the part of interpreters and processing staff. The choice of an over-powerful process can be very wasteful, but on the other hand too naive a migration procedure can lead to wrong interpretations which are much more costly still.Complete inversion procedures which aim to delineate all changes in rock densities and elastic properties in the subsurface are still in the imaginative stages of research. Not even the most sophisticated migration procedure in current use with real data, however, provides a complete inversion, but all depend in some measure on prior knowledge of the velocity structure of the section of the earth traversed by the seismic energy. Such knowledge may be very approximate at first, but each inversion should, through the skill of the interpreter, allow him to revise his velocity model and, up to some limit imposed by the quality and ambiguity of the original data, to improve the next inversion. Paradoxically, he can often be helped by using forward modeling procedures to check the implications of his ideas in the data domain, both in deciding how to update the velocity model and in selecting the most appropriate migration process to use next.We review here the currently available toolkit of migration and modeling processes and make suggestions as to how each process can fit into a learning strategy which can improve the interpretation as economically as possible and in as many iterative steps as the complexity of the earth's velocity structure makes necessary. An example is shown of the strategy being used in a complex overthrust region.The authors wish to thank the Chairman and Board of Directors of BP Exploration Co. for permission to publish this paper, and also make acknowledgment to our colleagues whose labours in research and development have made available to our use many of the essential tools required to implement the strategies we describe.

Notes: The time-domain induced polarization (IP) of saturated Sherwood Sandstone correlates significantly with the intergranular permeability and the matrix conductivity but only at low electrolyte concentrations (〈 500 p.p.m. NaCl). An increase in the magnitude of sandstone IP with increase in the valence of the electrolyte cation is pronounced but occurs only at intermediate concentrations, i.e., between 100 and 2500 p.p.m. Surface IP and resistivity depth sounding measurements, supplemented by data from laboratory measurements, can be used to estimate the groundwater conductivity and hence the salinity in a moderate to strongly saline sandstone aquifer.

Notes: When a rather extensive network of short distance refraction profiles was shot the following two observations were made. Firstly, the wave velocity in the weathered layer showed a quite considerable fluctuation in horizontal direction, the extreme values being of the order of 300 and 700 m/sec. A practical result of this scattering of the velocities is that an uncertainty of about 10% is introduced in the computation of the weathering corrections. The second observation is that, in the majority of cases, the travel time curve does not pass through the origin. It could be ascertained that this observation was not caused by errors in the method of observation. A probable explanation of the phenomenon is found in a theory that has been developed by Gassmann, who derived the velocity distribution for a hexagonal packing of spherical solid bodies. According to this theory extremely low velocities would occur in the first few centimeters of the crust of the earth. Qualitatively, our observations are in agreement with the theory of Gassmann.

Notes: The geophysicists who attempted to evaluate elastic anisotropy of some bedded formations most often gave but little information about recording and interpretating the measurements.May be they did not lay enough stress on the fact that any determination of the anisotropy factor is a critical operation and that, to have some certainty. it must be made under good conditions and then discussed.Due to the very favourable conditions offered: undisturbed tectonics and topography, relatively regular series the Berriane district in Northern Sahara, is rather well suited to accurate measurements and to an anisotropy study down to 1,250 meters. Since measurements have been carried out in the wildcat drilled at Berriane by S. N. Repal, it seems interesting to communicate the results obtained and to discuss them according to the influence of high velocity layers.It can be noted that in the clay and sand series which have been investigated, anisotropy coefficient amounts to 1.09 or so.To conclude, it seems desirable that determinations made by numerous operators should allow a more accurate knowledge of the anisotropy factor in the main types of rocks.

Notes: The aim of the present investigation is to examine the significance of the second derivative for the purpose of the prospective determination of the geological properties of the district of Offenburg, which are relatively wellknown as a result of both reflection seismic and bore profile findings.The calculation of the second derivative is carried out by means of three approximation formulae, which are compared with each other. In contrast to the isogam map the second derivative shows some additional characteristics, whose structural significance illuminates the comparison with the results of reflection seismics.A geological profile constructed on the basis of 6 wells completely confirms the geophysical findings.

Notes: Using a comprehensive theory of the vertical force variometer, it is shown that the mean of the two readings taken in azimuths 180 degrees apart only eliminates the error of misorientation and of inclination of the knife edge if these factors are sufficiently small. The necessary accuracy in the 180 degree rotation and in the readjustment of the levels are investigated and a practical test is developed to allow the initial adjustments to be determined. Finally, a brief description of a new variometer tripod is given.

Notes: It is known that good use can be made of calculating the second vertical derivative of gravitational and magnetic fields. The first derivative, or Vertical Gradient, has the same properties, Like the second derivative, it does not depend on the locally linear regional anomaly. Moreover, the gradient is less affected by experimental errors.The report gives a practical method of calculating the vertical gradient. Its application is identical to that in general use for calculating the second derivative, except that the numerical coefficients are different. The method also allows the establishment of formulae for downward extension of the field and its derivatives.

Notes: In the region covered by the paper, electrical methods have been applied in four different zones:〈list xml:id="l1" style="custom"〉a) Ales-Maruejols Basin (resistive lower Oligocene blanketed by conductive Upper Oligocene);b) Ledignan and Vaunage-Lunel anticlines (faulted structures in the marly and limy Cretaceous, with different resistivities;c) Camargue (thick series of conductive sediments);d) Beziers Basin (highly complicated structures in the Mesozoic, widely blanketed by conductive Miocene).It may be assumed that electrical methods can yield valuable information enabling one to define the rugged subsurface topography of resistive strata burried under a reasonably thick cover of conductive sediments especially when a part of the lower formation outcrops even if the part exposed be small. Faults may be delineated and much, more information is obtainable than can be expected from gravity meter survey at a price not very much higher.

Notes: For the treatment of the problems involved in the interpretation of gravity pictures this paper gives a formula that holds generally for any potential function. It provides an extended applicability of the relation used by Elkins for the computation of the second derivative, and also yields an analogous relation to derivatives of higher order of the gravity field.This relation has not been utilized to determine in details the course of the derivatives of higher order in a plane, but is merely applied to points of comparatively extreme curvature of the isogams where the differential values present a ratio favourable to the “noise level”. By this method the values of the derivatives of higher order will not be determined themselves but only the ratio's responsible for the depth of divergence in comparison with the course of an anomaly of masses replaced by points.It is shown by examples of intercalated masses that the divergence points are important and by law related to the form and position of the density contrasts themselves.An analysis of the total gravity picture is made possible by progressing from elements close to the surface to deeper ones. In this way the fundamental features of the earth's crust will be obtained. The application of the analysis process to a gravity anomaly actually measured in Northwest Germany is given.

Notes: When refraction time signals are transmitted over a radio link between shooter and observer there is a serious risk of interference from electrical storms. This risk can be minimised by sending a series of signals at fixed time intervals and the paper describes a simple device which will do this with the required accuracy.

Notes: Seismic reflection, telluric and gravity results are given for the lifted area of Ferrara, in Northern Italy. The agreement is shown between the available shallow seismic data and the gravity evidences. For a portion of the above area where seismic results are particularly poor the vertical gradients method gives a resolution of a gravity anomaly and confirms the telluric information. The residual gravity values, the vertical gradients and the telluric data along a seismic line crossing the zone are compared with seismic results and with evidences from adjacent wells.

Notes: Investigations into reflection seismic on the salt structure of Heide raised the following questions:〈list xml:id="l1" style="custom"〉1) How can the different directions of trend of a series of layers be established?2) How are the contour maps of reflecting horizons to be constructed if there is no general trend of the layers?To answer these questions, the case of the subsoil consisting of a series of layers with plane reflecting beds and constant layer-velocities is treated strictly. The strike lines of the reflecting planes may be at any angle whatever. However, formulas for constructing contour maps of the reflecting planes have been derived. With these formulas, the problem quoted under 1) has also been solved.The construction of contour maps is given.For special cases, formulas are obtained which have already been proved by others.

Notes: The triple integral for the attraction of a mass on a point is transformed in a double sum. This double sum serves to construct a graph for the rapid determination of the gravimetric influence of structures given by depth contours. The influence of topography can also be computed with this graph.

Notes: Power spectrum analysis of the Bouger gravity values in the Eastern Alps suggests that the gravity field may be separated into long and short wavelength components. The long wavelength component is assumed to be caused by Alpine crustal thickening. This long wavelength component was subjected to a gravimetric single density-interface inversion procedure, giving a gravimetric Mohorovičić model which is generally in good agreement with Moho-depths derived by refraction and reflection seismology.The residual high-frequency gravity component correlates well with the main surface geological units in the Eastern Alps.Apparent density mapping by applying an inverse density deconvolution filter to the short wavelength gravity component gives density values for the upper crust which correspond well with averaged density values from rock samples.

Notes: Hydrogeological problems which involve the determination of lateral variations in structures or physical properties may be solved with electrical resistivity gradient profiling if there are significant variations in electrical resistivity, spatially or temporally. The method is explained, evaluated for sensitivity, compared with other methods, and applied to the location of volcanic dike zones that are impounding an anomalous water body near Schofield, Oahu, Hawaii. From the electrical soundings and other independent data, the lateral positions of the boundaries have been refined and their nature estimated.

Notes: 3D Kirchhoff migration and acoustic Born inversion of zero-offset seismic data in a constant-velocity medium can be uniformly factored as a cascade of two 2D diffraction integrals. The formal argument is based on a straightforward implementation of the original time-domain approach of Gibson, Larner and Levin. The factorization differs from the factorization described by Jakubowicz and Levin in omitting all time-dependent filters from the 2D operators in favour of ID filtrations performed as a preprocess and a postprocess.

Notes: Effective noise reduction of single-sweep recorded data is achieved by application of a velocity filter process on a decomposed vibrator pattern. This technique promises high resolution results with a minimum effect on signal characteristic. A comparison of the stacked section of records vertically stacked in the field with the stacked section of velocity-filtered receiver gathers shows a significant increase in resolution and signal-to-noise ratio.

Notes: In recent years, the use of wide source arrays in marine seismic surveys has been a topic of interest in the seismic industry. Although one motivation for wide arrays is to get more guns in a source array without increasing the in-line array dimension, wide arrays can also provide the benefit of suppressing side-scattered energy. Comparisons of common midpoint (CMP) stacks of data acquired offshore Washington and Alaska with wide and conventional-width source arrays, however, show only small and sometimes inconsistent differences. These data were acquired in areas where side-scattered energy is a problem. Comparisons of pre-stack data, however, show substantial differences between the wide and conventional source array data.The disparity between the stacked and prestack data is explained by analysing the effective suppression of back-scattered energy by CMP stacking. Energy reflected from scatterer positions broadside to a given CMP location has a lower stacking velocity than that of the primary reflection events. Thus, CMP stacking attenuates the side-scattered energy. In both survey areas the action of CMP stacking was so powerful in suppressing the broadside energy that the additional action of the wide array was inconsequential in the final stacked sections. In other areas, where the scattering velocity is comparable to the primary stacking velocity, wide arrays could provide considerable advantage.Even though CMP stacked data from wide and conventional-width arrays may appear similar, the reduced amount of side-scattered energy in wide-array prestack data may provide a benefit for data dependent processes such as predictive deconvolution and velocity analysis. However, wide arrays cannot be used indiscriminately because they can degrade cross-dipping primary events. They should be considered primarily as a special tool for attacking severe source-generated noise from back-scattered waves in areas where the action of CMP stacking is insufficient.

Notes: A new approximate method to calculate the space-time acoustic wave motion generated by an impulsive point source in a horizontally layered configuration is presented. The configuration consists of a stack of fluid layers between two acoustic half-spaces where the source and the receiver are located in the upper half-space. A distorted-wave Born approximation is introduced; the important feature of the method is the assumption of a background medium with vertical varying root-mean-square acoustic wave speed. A closed-form expression for the scattered field in space and time as a function of the contrast parameters is deduced. The result agrees closely with rigorously calculated synthetic seismograms. In the inverse scheme the wave speed and mass density can be reconstructed within a single trace. Results of the inversion scheme applied to synthetic data are shown.

Notes: Determination of petrography and pore fluid content is an ultimate goal of an integrated seismic-petrophysical study. For lack of a general inversion technique, forward modelling is useful in studying the relations between lithology, stratigraphy, pore fluid content and the seismic response. This report describes a study of two clastic sequences in Utah, from which 32 rock samples were analysed. A detailed petrographic study was done. Laboratory measurements were made of ultrasonic compressional- and shear-wave velocity as a function of pressure. We computed the velocities at seismic frequencies for the samples when dry, over-pressured, brine saturated, and oil saturated. The velocities were sensitive to the porosity, carbonate cementation and the depositional facies. We generated velocity profiles for hypothetical reservoirs for a range of saturation states. The velocity profiles were used to generate synthetic seismic shot gathers to study the seismic response of these clastic reservoirs. The fluid-saturation strongly affects the seismic respone, as does the presence of a coal seam. An amplitude change with offset is often observed. However, stratigraphy appears to have a stronger effect on the seismic response.

Notes: A particular methodology adapted to crystalline formations with a thin weathered zone was developed for a village hydrological project, in Benin. A combination of electrical profiles, Schlumberger and square arrays, was able to locate the most fractured zones in the basement. We present some results obtained from theoretical models as well as from field data.The suggested methodology uses both measurements of resistivity and anisotropy. Strong anisotropy and low resistivity indicate the most productive hydrogeological areas.

Notes: Two-dimensional VSP surveys are often conducted to provide structural illumination of the subsurface away from the borehole. The illumination is achieved through offsetting the source with respect to the downhole geophone. This inevitably gives rise to mode-conversions in both downgoing and upgoing wavefields.Migration of mixed-mode wavefields is complex because the velocity profile used for wavefield extrapolation is valid only for a particular propagation mode; the other mode always propagates at a different velocity. It is therefore advisable to separate the wave-types (P-wave and SV-wave) prior to migration. This may be achieved through wavemode filtering, a multichannel process which exploits the relation between propagation velocity, slowness of events at the recording array and particle motion. The necessary information about particle motion is available only if the VSP data are acquired with a three-component downhole geophone assembly.The wavemode filter partitions wave-types at the recording array; it provides no information about the various changes of propagation mode experienced by the energy as it travels from source to geophone. For the purpose of migration, the intermediate modes of propagation must be deduced.Much of the energy arriving at the receivers is P-wave which has followed the P-wave velocity profile from the source. It can therefore be imaged by conventional (Kirchhoff) migration. As an example of SV-wave imaging, a common mode-code is P-wave from source to reflector and SV-wave from reflector to geophone. Migration of such data calls for back-propagation of the geophone array wavefield, at SV-wave velocity, to the point in the subsurface where it is time-coincident with the forward propagated downwave, at P-wave velocity.

Notes: This paper gives a review of Bayesian parameter estimation. The Bayesian approach is fundamental and applicable to all kinds of inverse problems. Its basic formulation is probabilistic. Information from data is combined with a priori information on model parameters. The result is called the a posteriori probability density function and it is the solution to the inverse problem. In practice an estimate of the parameters is obtained by taking its maximum. Well-known estimation procedures like least-squares inversion or l1 norm inversion result, depending on the type of noise and a priori information given. Due to the a priori information the maximum will be unique and the estimation procedures will be stable except (in theory) for the most pathological problems which are very unlikely to occur in practice. The approach of Tarantola and Valette can be derived within classical probability theory.The Bayesian approach allows a full resolution and uncertainty analysis which is discussed in Part II of the paper.

Notes: A triple axis borehole magnetometer is described that consists of a Förster-probe (fluxgate) triplet (sensitivity 1 n T), a Förster-probe gradiometer (sensitivity 2 nT/40 cm), a gyro unit (mean angular drift approx. 0.5°/h) which is equipped with accelerometers (sensitivity 1/100°), and a data transmission unit (with multiplexer and 16-bit AD converter). The sensitive fluxgate-magnetometer can detect weakly magnetic or small source bodies. Data from the gyro and the accelerometers allow the 3-component magnetic field values to be transformed to north, east and vertical components. Since they do not rely on magnetically-determined directional data, the results are not disturbed by local anomalies of the magnetic declination. Furthermore, the magnetometer can also be used in vertical boreholes. 3-component measurements are carried out at discrete points in the neighbourhood of a source body to locate its position, and within the source body to determine the direction of magnetization. The strength of magnetization and information on magnetic classification are obtained by continuous measurement of one or more components within the source body. Calculation algorithms and computer programs are available to simplify data processing and interpretation. Survey examples are discussed.

Notes: Resistivity measurements were carried out in a survey area in the south of Germany. This area is characterized by complicated subsurface geology. Schlumberger full-arrays and their respective half-arrays were recorded simultaneously. The results obtained by the one-dimensional (1D) interpretation of the full-array measurements were incorrect because of a resistivity discontinuity. This discontinuity, under a relatively thick overburden, could only be located by the half-array soundings. Its exact location and the resistivity distribution in the subsurface were ascertained by comparing the sounding curves with 2D model curves, which are calculated by a finite-difference method.

Notes: A novel process is used to coat glass spheres with a polymerizing thermo-setting resin, only microns thick. Synthetic rocks of known grain size distribution and pore space characteristics are then made by heating the resin-coated glass spheres under compression in a special mould. The dynamic Young's moduli of these rocks are found to be affected by the percentage of resin content (cement) and the synthetic diagenesis rather than the grain size and permeability.

Notes: Broad-band ultrasonic impulses and the attenuation spectral ratio technique have been used to investigate the characteristics of synthetic rocks for different saturants, by obtaining the attenuation coefficients in the frequency range of 0.1-1.0 MHz.The general trend of the data indicates that the experimental attenuation coefficient increases with an increase in the grain/pore size. Results show that large grains/pores can increase the attenuation coefficient in all mechanisms, and water-saturated synthetic sandstone rocks result in a higher attenuation coefficient than similar oil-saturated rocks.