ALBERT

Notizen: Furness, P. 1993. Gradient Array Profiles over thin resistive veins. Geophysical Prospecting41, 113–130.Gradient array geoelectric surveys are commonly used to explore for buried sheet-like targets. It is demonstrated that under certain circumstances the responses of such features can become practically equivalent for a range of models differing considerably in resistivity and thickness. This is the dual of the familiar equivalence phenomenon associated with thin beds in geoelectric sounding operations. Hence the geoelectric response profiles over thin dipping resistive veins are conveniently studied by considering equivalent forms with vanishing thickness and infinite resistivity but with the same resistivity-thickness product. The effects of varying the dip, depth of burial, depth extent and resistivity–thickness product of such features on the gradient array response profiles are investigated by means of a series of numerical experiments. These demonstrate several effects of significance to survey design and data interpretation.In particular it is found that while the resistivity–thickness product influences the amplitude of the response profiles it has little effect on their form. A similar behaviour is found to be exhibited by veins with extended depth extent when the dip is varied.A complete quantitative interpretation of gradient array profiles over thin dipping resistive veins is thus only possible for veins of limited depth extent. For veins with an extended depth dimension, the data is ambiguous (in a practical sense) in terms of the dip and the resistivity–thickness product. Here, the interpretation can only be expected to deduce the horizontal and vertical locations of the vein apex.

Notizen: The slant-stack migration formula based on the Radon transform is studied with respect to the depth step Δz of wavefield extrapolation. It can be viewed as a generalized trace-interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz= 0 the formula yields the familiar plane-wave decomposition, while for Δz 〉 0 it provides a robust tool for migration transformation of spatially undersampled wavefields. Using the stationary phase method, it is shown that the slant-stack migration formula degenerates into the Rayleigh-Sommerfeld integral in the far-field approximation. Consequently, even a narrow slant-stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the Radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period.

Notizen: A fast algorithm is presented for numerical evaluation of forward and inverse Radon transforms. The algorithm does not perform exact one-to-one mapping as the discrete Fourier transform but, due to the use of band-limited basis functions, it is robust and sufficiently accurate for seismic applications. By rewriting the transform as a convolution, a computational speed is obtained similar to the speed of the 2D fast Fourier transform.

Notizen: Directional deconvolution of the signature from a marine seismic source array may be achieved in combination with prestack migration or dip moveout (DMO) processing. The benefit is demonstrated using an example profile from the southern North Sea. In particular, shallow, dipping reflectors have improved continuity and frequency content. The method could be extended to 3D data to remove both in-line and cross-line directivity effects.

Notizen: One application of marine seismic profiling that has an especially auspicious future is the delineation, and possible identification, of anomalously reflective material accumulated in the sediments of rivers, bays and estuaries. Analogue field data are presented which illustrate that such sediments are associated with strong sequences of multiple reflections. The rate of decay of these sequences indicates the magnitude of the reflection coefficients and the relative polarity of wavelets indicates whether they are positive or negative. If zero-offset field geometry and digital recording are used, it is possible to compare wavelets within a sequence and thereby determine acoustic impedance contrasts from which sediment density can be inferred. If the source is sufficiently broadband, it becomes possible to determine absorption characteristics as well. Two principal problems arise when analysing multiple sequences; adequate data acquisition and suitable geometric corrections. Having solved these, this type of analysis could lead to the seismic identification of sea-floor materials. Since anomalous material is often associated with effluent, the method can become an important tool in the growing effort to monitor and improve environmental quality.

Notizen: Channel waves generated in coal-seams and their reflections from discontinuities are widely used to indicate the tectonic and stratigraphic features of coal deposits, resulting in greater efficiency and safety in coal-mining. In the mining area of Ibbenbüren (F.R.G.) seam structures sometimes contain so-called mylonite zones, which are crushed coal deposits capable of binding gas. If mining hits a mylonite zone this would probably not only reduce output of the mine, but could even cause gas explosions. To investigate the influence of a mylonite zone on the propagation of channel waves, Rayleigh channel wave measurements for 2D analogue models were performed and synthetic seismograms of Love channel waves were calculated.Analogue modelling of the mylonite zone using Rayleigh seam waves within the seam was carried out using a perforation technique. Calculations were made to obtain an estimate of velocity reduction due to perforation. The results agree well with velocity values measured up to a perforation of 25% in a 2D epoxy resin model. Reflected channel wave energy was found by applying dispersion analysis in the case where the impedance reduction between the mylonite seam structure and the undisturbed seam was approximately 5%. The horizontal width of the mylonite structure was detectable from the time lag between reflected channel wave signals from both in-seam borders of the mylonite zone. Resolution of two discrete borders was possible for a width of 1.5 λ's. The influence of a vertical fault, positioned within the mylonite zone, could only poorly be resolved.Numerical model investigations of Love seam waves were concerned mainly with the variation of the horizontal width of the mylonite zone. Mylonite zones with dimensions of the order of 0.4 λ's allow definite statements about their widths from dispersion and spectral analyses. For zones with smaller widths down to 0.2 λ's, it was found that reflectivity and transmissivity analyses give a qualitative criterion for distinguishing a mylonite structure surrounding a fault from a pure fault.

Notizen: When treating the forward full waveform case, a fast and accurate algorithm for modelling seismic wave propagation in anisotropic inhomogeneous media is of considerable value in current exploration seismology. Synthetic seismograms were computed for P-SV wave propagation in transversely isotropic media. Among the various techniques available for seismic modelling, the finite-difference method possesses both the power and flexibility to model wave propagation accurately in anisotropic inhomogeneous media bounded by irregular interfaces. We have developed a fast high-order vectorized finite-difference algorithm adapted for the vector supercomputer. The algorithm is based on the fourth-order accurate MacCormack-type splitting scheme. Solving the equivalent first-order hyperbolic system of equations, instead of the second-order wave equation, avoids computation of the spatial derivatives of the medium's anisotropic elastic parameters. Examples indicate that anisotropy plays an important role in modelling the kinematic and the dynamic properties of the wave propagation and should be taken into account when necessary.

Notizen: The determination of the vertical and lateral extent of discontinuities is an important aspect of interpreting seismic reflection data. The Common Fault Point (CFP) stacking method appears to be promising in imaging discontinuities in acoustic impedance by making use of diffracted energy from a spatial array of receivers. The problems of vertical and lateral resolution in the method are most important when carrying out an interpretation.Source signature, subsurface velocities and the depth of the discontinuity are the most important parameters affecting the resolution. We use, for a perfectly coherent source, the first derivative of the Gaussian function which is an antisymmetric band-limited wavelet. Rayleigh's, Ricker's and Widess' criteria are also applicable to this wavelet. The limits of vertical and lateral resolution are illustrated by using a step fault and a dike model respectively. The vertical resolution of the CFP method is found to be of the order of λ/16 which is half the theoretically predicted value for a single receiver. The lateral resolution is still limited by the size of the Fresnel zone which depends upon the velocity, two-way time and the dominant frequency of the wavelet. The resolution limits of the CFP method are compared with that of the CDP method, prestack migration and post-stack migration. Obtaining high resolution with real data is limited by the extent to which it is possible to generate a coherent source or to simulate one during computer processing with before stack seismic data. The CFP method is an artificial intelligence approach to imaging diffracting points as it localizes parts of the structure that scatter acoustic waves.

Notizen: This paper presents some results from an investigation into the utility of pattern recognition methods in seismic interpretation. The seismic instantaneous attributes of amplitude, phase and frequency provide a way of quantifying the character of a simple reflection. Measures of character can be developed from cross-plots and cluster analysis of these attributes. It is demonstrated that such seismic character can produce better-defined maps than a single attribute. These procedures can be extended to attributes derived from seismic trace segments, such as trace energy and centre frequency, and to multitrace attributes, but more effort is then needed to analyse the attributes and search out useful ones.An introduction is given to projection pursuit which has proved a useful exploratory tool for the anlysis of attribute relationships.It is important to stress that pattern recognition techniques simply help bring relationships and patterns in the data to the attention of the interpreter and the most persistent problem in applying these techniques is the evaluation of potentially interesting patterns. The decision on what use can be made of them is highly interpretive and their calibration is difficult. Well control is vital but it normally allows only very limited supervision of a seismic classifier. An example is presented to illustrate these problems.

Notizen: Seismic refraction surveying is still an important tool for determining the geometries and elastic wave propagation velocities of near-surface layers. Many analytical and graphical methods have been developed over the years for refraction interpretation, and these can be classified into two basic groups. The first group visualizes critically refracted rays converging on a common surface position, while the second group, which includes the wavefront methods, makes use of the critical rays emerging from a common point on the refractor.The method described in this paper is an analytical approach to the wavefront methods. The reverse refracted ray received by a geophone is intersected by the forward refracted rays received by subsequent geophones and a common critical refraction point on the refractor is estimated after a series of comparisons. This process is repeated for each geophone to yield the geometry and the velocity of the refractor. Several interpolations are performed to achieve a better accuracy.Palmer's models are used to test the efficiency of the algorithm. The results are presented together with those of other methods applied to the same models.

Notizen: The so-called ‘enhanced migration’ which uses diffraction tomography as the ‘repair tool’ for correction of amplitudes (reflection coefficients) of migrated sections is discussed. As with any linearized procedure, diffraction tomography requires knowledge of the initial model. It is suggested that the initial model is taken as the migrated image. It will be demonstrated that diffraction tomography applied to the data residuals improves the amplitudes of the migrated images. Migration is redefined as the reconstruction of the wavefront sets of distributions (reflection interfaces), and the inversion process as tomographic correction of migrated images.

Notizen: Three-dimensional inverse gravity modelling is used to determine the structure of the Carboniferous sediments underlying the Jurassic and Permo-Triassic formations in the Cheshire Basin. The gravity effect of the Jurassic and Permo-Triassic rocks was first removed from the observations and the resulting residual gravity field was then inverted to map variations in depth of the Carboniferous formations. The inversion technique is performed in the frequency domain, enabling rapid computation of solutions for large gridded data sets. Evaluation of results shows that there is good agreement between calculated and observed values, with interpreted depths to the base of the Carboniferous in excess of 6 km. Gravity inversion results also delineate areas of faulting on the south-western and eastern edges of the basin.

Notizen: Shear waves can provide valuable information about seismic anisotropy. On entering an anisotropic medium, a shear wave generally splits (shear-wave splitting) into a fast and a slow quasi-shear wave with polarizations fixed by the elastic properties of the medium and direction of travel. If the medium contains planar discontinuities with common normals, the fast shear wave will be suitably propagated if its polarization lies in the plane of the discontinuities. Measuring this polarization, using a VSP geometry with oriented three-component geophones in the borehole, offers the possibility of monitoring the orientation and density of the discontinuities as a function of depth.Such a shear-wave VSP was carried out in an uncased 0.3 m diameter borehole drilled to a depth of 120 m in the north of The Netherlands. The upper 80 m of the sequence, consisting of a glacial till and sands and clays of Pleistocene age, was studied. The clays in this sequence have been subjected to glacial deformation and as a result are overconsolidated and locally fissured.In our shallow VSP experiment, shear-wave splitting and therefore anisotropy was identified at various geophone depths for one source offset. Hodograms showed a consistent polarization of the fast shear-wave component over a large depth interval. Under the assumption that the anisotropy was caused by planar discontinuities with common normals, this polarization direction gives the strike of the fissures in this interval. The polarization direction of the fast S-wave did not correspond exactly with the strike which was obtained from geological information on the fissures. The geological information was from undisturbed oriented 70 mm core samples taken at 3 m intervals in the borehole. The discrepancy, however, could be explained in terms of dipping fissures, and such a dip was confirmed by the geological and geotechnical information.The orientation of fissures is an important factor in the directional deformation and strength characteristics of clays as far as geotechnical behaviour is concerned. This study thus illustrates a practical application of shear-wave splitting observed in shallow shear-wave VSP for geology and geotechnical engineering.

Notizen: Analytical solutions of vertical electrical soundings (VES) have mostly been applied to groundwater exploration and monitoring groundwater quality on terrains of fairly simple geology and geomorphology on which the electrode arrays are symmetrical (e.g. Schlumberger or Wenner configurations). The sounding interpretation assumes flat topography and horizontally stratified layers. Any deviations from these simple situations may be impossible to interpret analytically. The recently developed GEA-58 geoelectrical instrument can make continuous soundings along a profile with any colinear electrode configuration.This paper describes the use of finite-difference and finite-element methods to model complex earth resistivity distributions in 2D, in order to calculate apparent resistivity responses to any colinear current electrode distribution in terrains in which the earth resistivities do not vary along the strike. The numerical model results for simple situations are compared with the analytical solutions. In addition, a pseudo-depth section of apparent resistivities measured in the field with the GEA-58 is compared with the numerical solution of a real complex resistivity distribution along a cross-section. The model results show excellent agreement with the corresponding analytical and experimental data.

Notizen: A prestack reverse-time migration algorithm which operates on common-source gathers, recorded at the Earth's surface, from 3D structures, is conceived, implemented and tested. Reverse-time extrapolation of the recorded wavefield (a boundary-value problem), and computation of the excitation-time imaging condition for each point in a 3D volume (an initial-value problem), are both performed using a second-order finite-difference solution of the full 3D scalar wave equation. The algorithm is illustrated by processing synthetic data for a point diffractor, an oblique wedge, and the French double dome and fault model.

Notizen: The seismic signatures of three reefs of the Upper Elk Point Subgroup (Givetian Stage) of the Western Canada Sedimentary Basin are documented and analysed on the basis of variations in seismic image of particular lithologic units, lateral amplitude and/or phase changes, structural relief and velocity-generated relief, as rendered by the reflection data. The effects on seismic signatures of spatial geological variations resulting from such phenomena as differential compaction, reef-focused salt dissolution, palaeotopography, lateral and vertical facies variations, regional dip, and reservoir morphology are discussed. The usefulness of seismic data in clarifying relationships between reefs and their adjacent sedimentary sections, particularly in cases where well control is sparse, is also considered. Such documentation of seismic signatures from known reefs using geophysical and geological analysis can establish criteria to enable recognition of similar buildups elsewhere.Three example reefs are presented, each typical of a particular area and environment of W. Canada. The first is from the Winnipegosis Formation of SE Saskatchewan, the second and third from the Rainbow Member and Upper Keg River Reef Member, respectively, of the Keg River Formation of NW Alberta. All three of these carbonate buildups developed in the evaporitic Elk Point Basin. However, the degree of salt encasement and subsequent dissolution varied greatly, as do the resulting seismic effects. For these three reef types, the typical elements of their seismic signatures have been compiled and are here summarized.

Notizen: A modern approach to migration is to perform wavefield extrapolation, subject to an imaging condition. Correct wavefield extrapolation requires that the boundary conditions at the array of geophones satisfy the wave equation. A sufficient condition is to perform the survey with a single stationary source. Contrary to this condition, many VSPs are conducted in deviated wells, where the source is maintained vertically above the down-hole geophone at each well station. Such a survey fails to provide the boundary conditions theoretically necessary for wave-equation migration.A recently published inversion scheme, referred to as acoustic generalized Radon transform migration (GRT migration), was developed to handle any configuration of sources and geophones, including moving-source deviated-well VSP surveys. GRT migration may be viewed as a weighted version of the generalized Kirchhoff migration, derived in this paper from the exploding-reflector model.When a VSP-survey geometry has been specified, GRT migration can be expressed in terms of array parameters, and compared with the equivalent expression for Kirchhoff (wave-equation) migration. The differences between the two integrals are significant and their effect is demonstrated on VSP data.

Notizen: The ray-tracing algorithm presented in this paper is based on formulae derived for the common reflecting element (CRE) stacking method. A 2D, smooth, laterally-varying media is assumed where offset rays and traveltimes are evaluated from normal-incidence (central) rays. The method uses a second-order asymmetrical approximation for rays and an additional oblique spherical approximation of the central wavefronts for calculating offset traveltimes. In order to solve the two-point ray-tracing problem for the common midpoint (CMP) configuration of source-receiver pairs located symmetrically around the CMP stations, the central rays are perturbed to satisfy the above-mentioned asymmetrical distribution. Although the accuracy of the calculations is limited for far offsets, it is still good for distances of the order of the reflecting depths. Since only a few normal-incidence rays are traced through the medium, the method is very fast and is found to be most attractive for iterative inversions in macromodel estimation.

Notizen: Total field anomalies as defined from normal aeromagnetic surveys give good approximations of the anomalous components along the direction of the main geomagnetic field, which is generally much larger than the anomalous field. Using the relations between vertical and horizontal components of the field, the total field anomaly is related to any vertical or horizontal component and the corresponding horizontal and vertical derivatives. An example from the Siljan impact structure indicates that such directional filters may be applied to extract useful information from magnetic maps.

Notizen: Conversion of borehole Stoneley waves to channel waves was observed in data from a seismic cross-borehole experiment conducted between wellbores penetrating a thin coal layer at 2022 m depth, near Rifle, Colorado. Traveltime moveout observations show that borehole Stoneley waves underwent partial conversion to channel waves at the coal layer. The channel waves were detected directly in an adjacent borehole 35 m away at receiver positions within the coal. Stoneley waves, subsequently produced by partial conversion of channel waves, were also detected at receiver positions located up to 50 m above and below the coal layer in the adjacent borehole. We infer the channel wave to be the first-higher Rayleigh mode by comparing the observed group velocity with theoretically derived dispersion curves. Identifying the conversion between borehole and stratigraphically guided waves is significant because coal penetrated by multiple wells may be detected without placing a transmitter or receiver in the coal itself.

Notizen: Many conventional schemes of automated residual statics estimate time lags between prestack traces (sorted as CDP gathers) and a model section, and transform the collected lags into surface-consistent residuals. The method discussed in this paper aims at improving the lag estimator. ‘Externally generated’ reference traces are avoided and a principle of localized stack optimization is introduced whereby application of a multichannel filter to the stack and evaluation of the normalized power of every filtered trace gives a measure of the stack quality. One may consider the power as a function of all variable (inconsistent) shifts applied to the prestack traces. To obtain a set of optimal lag estimates the power function must be maximized. This power function is complex and the number of its variables prohibits a straightforward search for the maximum. Thus an iterative method must be employed, and steepest descent schemes have proved the most satisfactory. In the actual calculation, the repeated evaluation of the objective can be replaced by the computation of certain cross-correlations. At the last iteration (after five to ten coordinate sweeps), the global behaviour of this correlation gives some indications of how well a prestack trace is adapted to the filtered stack. This information is used to compute a weighting factor to be stored with the lag estimate. At this stage simple statistical procedures are run to eliminate the most unlikely estimates. The remaining ones are transformed to surface-consistent residuals by means of a weighted least-squares inversion according to a model which takes into account the fact that the lags have no fixed reference datum.The efficiency of the method is demonstrated by a field data example into which synthetic anomalies were introduced, and the effect of the new process is compared with that of a ‘classical’ production program using field data with genuine static problems.

Notizen: At Delft Geotechnics the technique of ground-penetrating radar is in use for the detection of buried objects such as pipes. To enable us to give our ‘measurements in the field’ a more quantitative interpretation than can be deduced from these alone, a series of experiments has been started under well-defined conditions. A cylindrical vessel containing water simulates wet soil. Mounted horizontally above the water surface is a pulsed triangular half-wave dipole which is used as a transmitting antenna (TA). It has a carrier-frequency of about 160 MHz and a pulse repetition-frequency of about 50 kHz.A movable receiving dipole (‘probe’) in the water measures the transverse, mutually orthogonal Eφ,- and Eθ-components of the pulses as a function of probe-position (r, θ, φ) and of the height h of the TA above the water surface. When these pulses are Fourier-transformed, the transverse electric fields Eφ and Eθ at 200 MHz are obtained. The resulting field patterns are compared with computational results on the basis of the theory of the continuous wave, infinitesimal electric dipole (‘point dipole’). It can be concluded that:〈list xml:id="l1" style="custom"〉1Far-field conditions have not fully developed at a depth of about 2.50 m, the largest value of the radius r at which field patterns were measured, although it represents a distance of about 15 wavelengths.2The attenuation constant of the tapwater used, as deduced from E-field measurements for θ= 0, 2.50 m 〈 r 〈 2.75 m, is slightly less than the value measured using a network analyser and air line combination, in agreement with (1).3 E φ field patterns calculated using the value of the conductivity σ corresponding to the former value of the attenuation constant agree reasonably well with the measured patterns for r≤ 2.50 m and for θ 〈 20° at all antenna heights considered. Calculated Eφ patterns do not agree so well with the measured patterns when h is close to zero. With increasing height the agreement inproves.4In accordance with the theory of the point-dipole, the angular distribution of the radiation patterns of the TA becomes wider as the frequency decreases.5The normalized underwater pulse-spectra shift to lower frequencies with increasing r. This can be explained since the attenuation constant of the water rises with rising frequency.

Notizen: Ubiquitous splitting of seismic shear-waves indicates that most rocks in the upper half of the crust are pervaded by stress-aligned fluid-filled inclusions, called EDA-cracks. These inclusions are expected to be aligned perpendicular to the minimum compressional stress by stress relationships similar to those aligning industrial hydraulic fractures. At depths where the overburden stress is sufficiently large (typically below a few hundred metres), this minimum stress is usually horizontal, so that the EDA-cracks and hydraulic fractures are typically aligned vertically, striking parallel, or subparallel, to the direction of maximum compression. This is confirmed by the polarizations of the split shear-waves along raypaths at depth in the crust. At the free surface, however, the vertical stress is zero (or approximately zero) and cracks (and hydraulic fractures) at shallow depths in intact rock tend to be horizontal. Thus, the directions of minimum stress, and the orientations of hydraulic fractures, are likely to swing through 90° near the surface of the Earth. Since the behaviour of cracks and stress is often crucial to drilling operations, the rotation of the crack- and stress-geometry near-surface has important implications, particularly for optimizing hydrocarbon production and geothermal reservoir management. Consequently, evidence gained from experiments, for example in hot-dry-rock geothermal heat extraction, in inappropriate crack geometries at shallow depths, may not be valid when applied to other crack- and stress-geometries at depth in hot rock.

Notizen: One of the basic parameters of the rock formation surrounding a fluid-filled borehole to be estimated is the shear-wave velocity. In the present contribution a novel method for carrying out this estimate, based on the use of linear prediction techniques, is proposed. It is assumed that the shape and energy content of each wave can be accurately modelled by an ARMA (Auto Regressive Moving Average) impulsive process and by an appropriate delay. The overall seismogram is then considered to be a multiple impulsive ARMA process and the estimation is carried out by using the residual at the output of an extended version of the Burg lattice predictor. The resulting algorithm is very effective as illustrated by several examples performed on synthetic and real seismograms.

Notizen: A mathematical formulation for the electric potential from point current-sources coaxial with a metal casing has been obtained. The excitation caused by the axial point-sources will produce currents in the pipe. By assuming that the pipe can be divided into many cylindrical ring segments with constant axially-directed current, the solution of the fields inside and outside the pipe can be formulated in an integral form. The integral equation applied to the segmented pipe yields a set of simultaneous linear equations which are solved for the currents in the pipe; these are then used to calculate the potentials anywhere outside the pipe in the medium.This solution has been used to study the distribution of the potentials in a half-space for a single current-source at and beyond the bottom of a finite length of casing. For a casing 0.1 m in radius and 0.006 m in wall thickness with a conductivity of 106 S/m, in a half-space of 10-2 S/m, it was found that only in a region very near the pipe does the pipe exert substantial influence on the fields of a point-source 100 casing diameters beyond the end of the pipe. It appears that cross-hole resistivity surveys can be implemented without corrections for the casing if the source is located at least 50–100 casing diameters beyond the end of the casing. Hole-to-surface surveys are much more affected by the pipe. For a pipe-source separation of 100 casing diameters, the surface measurements must not be closer than a half pipe length for a 5% or less field distortion.

Notizen: Inversion of multicomponent seismic data can be subdivided in three main processes: (1) Surface-related preprocessing (decomposition of the multicomponent data into ‘primary’ P-and S-wave responses). (2) Prestack migration of the primary P- and S-wave responses, yielding the (angle-dependent) P-P, P-S, S-P and S-S reflectivity of the subsurface. (3) Target-related post-processing (transformation of the reflectivity into the rock and pore parameters in the target). This paper deals with the theoretical aspects of surface-related preprocessing.In a multicomponent seismic data set the P- and S-wave responses of the subsurface are distorted by two main causes: (1) The seismic vibrators always radiate a mixture of P- and S-waves into the subsurface. Similarly, the geophones always measure a mixture of P- and S-waves. (2) The free surface reflects any upgoing wave fully back into the subsurface. This gives rise to strong multiple reflections, including conversions.Therefore, surface-related preprocessing consists of two steps: (1)Decomposition of the multicomponent data (pseudo P- and S-wave responses) into true P- and S-wave responses. In practice this procedure involves (a) decomposition per common shot record of the particle velocity vector into scalar upgoing P- and S-waves, followed by (b) decomposition per common receiver record of the traction vector into scalar downgoing P- and S-waves. (2) Elimination of the surface-related multiple reflections and conversions. In this procedure the free surface is replaced by a reflection-free surface. The effect is that we obtain ‘primary’ P-and S-wave responses, that contain internal multiples only.An interesting aspect of the procedure is that no knowledge of the subsurface is required. In fact, the subsurface may have any degree of complexity. Both the decomposition step and the multiple elimination step are fully determined by the medium parameters at the free surface only. After surface-related preprocessing, the scalar P- and S-wave responses can be further processed independently by existing scalar algorithms.

Notizen: The pioneering work of E. T. Jaynes in the field of Bayesian/Maximum Entropy methods has been successfully explored in a number of disciplines. The principle of maximum entropy (PME) is remarkably powerful and versatile and leads to results which are devoid of spurious structure. Minimum relative entropy (MRE) is a method which has all the important attributes of the maximum-entropy (ME) approach with the advantage that prior information may be easily included. These ‘soft’ prior constraints play a fundamental role in the solution of underdetermined problems. The MRE approach, like ME, has achieved considerable success in the field of spectral analysis where the spectrum is estimated from incomplete autocorrelations. In this paper we apply the MRE philosophy to 1D inverse problems where the model is not necessarily positive, and thus we show that MRE is a general method of tackling linear, underdetermined, inverse problems. We illustrate our discussion with examples which deal with the famous die problem introduced by Jaynes, the question of aliasing, determination of interval velocities from stacking velocities and, finally, the universal problem of band-limited extrapolation. It is found that the MRE solution for the interval velocities, when a uniform prior velocity is assumed, is exactly the Dix formulation which is generally used in the seismic industry.

Notizen: Recent years have seen an increasing need for high-precision gravity meters. A widely used and the most accurate one is the LaCoste-Romberg, model D (LCR-D) meter, equipped with electronic readout. According to the manual the reading accuracy is 5 μGal. A way of reducing most of the instrumental factors limiting the accuracy is the use of an electronic feedback system.We have fitted the LCR-D 34 with a Schnüll-Röder-Wenzel, model D (SRW-D) feedback. After installation the readout voltage was calibrated, the instrumental behaviour tested, and the accuracy of the system determined. By repeat readings in the laboratory without moving the meter, the standard deviation for a single reading is better than 4 μGal in normal mode and better than 1 μGal in feedback mode. The accuracy of gravity differences - this is usually observed in field practice - is the mean value of the repeat errors of several sets of differences observed in a short time to avoid any corrections. This accuracy is better than 9 μGal in normal mode and better than 5 μGal in feedback mode. With this, the accuracy of a single reading becomes more than 6 μGal and more than 3 μGal, respectively.As the described improvement of accuracy was found to be not as good as expected, additional improvements should centre on the use of electronic levels instead of the standard liquid ones.

Notizen: A fundamental step in the solution of most non-linear inverse problems is to establish a relationship between changes in a proposed model and resulting changes in the forward modelled data. Once this relationship has been established, it becomes possible to refine an initial model to obtain an improved fit to the observed data. In a linearized analysis, the Fréchet derivative is the connecting link between changes in the model and changes in the data. In some simple cases an analytic expression for the Fréchet derivative may be derived. In this paper we present three techniques to accomplish this and illustrate them by computing the Fréchet derivative for the ID resistivity problem. For more complicated problems, where it is not possible to obtain an expression for the Fréchet derivative, it is necessary to parameterize the model and solve numerically for the sensitivities - partial derivatives of the data with respect to model parameters. The standard perturbation method for computing first-order sensitivities is discussed and compared to the more efficient sensitivity-equation and adjoint-equation methods. Extensions to allow for the calculation of higher order, directional and objective function sensitivities are also presented. Finally, the application of these various techniques is illustrated for both the 1D and 2D resistivity problems.

Notizen: Geoelectrical sounding profiles were collected on the southern part of the Fraser River delta, to provide a geophysical estimate of the subsurface structure and geotechnical properties. The differences between emergent and intertidal areas were assessed, and the geoelectric technique was found to be a viable one in an intermittently exposed tidal-flat environment. The subsurface geoelectric structure provides a link between reflection seismic data sets for Georgia Strait and the lower mainland. The survey was intentionally designed to complement the conventional exploration information for this basin and the shallow high-resolution seismic and drilling which focused on the unconsolidated Quaternary section. The electrical models consist of three layers: (I) electrically-conductive, porous, saturated and under-saturated marine silts, sands and gravels, overlying (II) less conductive and more consolidated marine clays, and variably reworked glaciomarine deposits together with weathered clastic sedimentary bedrock, which in turn overlies (III) less porous, more resistive, relatively unweathered bedrock. Estimates of thickness and geotechnical properties are obtained for shallow layers which are not available from either the short boreholes or shallow high-resolution seismic lines. This information is particularly useful in appraising the liquefaction potential of the unconsolidated layers due to earthquake risk.

Notizen: In the linear digital filter theory for calculation of Hankel transforms it is possible to find explicit series expansions for the filter coefficients. A method is presented for optimizing the Hankel filters calculated in this way. For a certain desired accuracy of computation, the sampling density and filter length are minimized by choosing the parameters determining the filter characteristics according to the analytical properties of the input function. A new approach to the calculation of the filter coefficients has been developed for these optimized filters. The length of the filters may be further reduced by introducing a shift in the sampling scheme.

Notizen: The time-varying deconvolution operator designed by dividing time-varying sequence has been extended to include an optimal division of the input data. A numerical example illustrates that the error energy is less in the case of optimally divided input in comparison with arbitrary division.

Notizen: The aim of refracted arrivals inversion is the computation of near-surface information, i.e. first-layer thicknesses and refractor velocities, in order to estimate the initial static corrections for the seismic data. The present trend is moving towards totally automatic inversion techniques, which start by picking the first breaks and end by aligning the seismic traces at the datum plane.Accuracy and computational time savings are necessary requirements. These are not straightforward, because accuracy means noise immunity, which implies the processing of large amounts of data to take advantage of redundancy; moreover, owing to the non-linearity of the problem, accuracy also means high-order modelling and, as a consequence, complex algorithms for making the inversion.The available methods are considered here with respect to the expected accuracy, i.e. to the model they assume. It is shown that the inversion of the refracted arrivals with a linear model leads to an ill-conditioned problem with the result that complete separation between the weathering thickness and the refractor velocity is not possible. This ambiguity is carefully analysed both in the spatial domain and in the wavenumber domain. An error analysis is then conducted with respect to the models and to the survey configurations that are used.Tests on synthetic data sets validate the theories and also give an idea of the magnitude of the error. This is largely dependent on the structure; here quantitative analysis is extended up to second derivative effects, whereas up to now seismic literature has only dealt with first derivatives. The topographical conditions which render the traditional techniques incorrect are investigated and predicted by the error equations.Improved solutions, based on more accurate models, are then considered: the advantages of the Generalized Reciprocal Method are demonstrated by applying the results of the error analysis to it, and the accuracy of the non-linear methods is discussed with respect to the interpolation technique which they adopt. Finally, a two-step procedure, consisting of a linear model inversion followed by a local non-linear correction, is suggested as a good compromise between accuracy and computational speed.

Notizen: The signal-to-noise (S/N) ratio of seismic reflection data can be significantly enhanced by stacking. However, stacking using the arithmetic mean (straight stacking) does not maximize the S/N ratio of the stack if there are trace-to-trace variations in the S/N ratio. In this case, the S/N ratio of the stack is maximized by weighting each trace by its signal amplitude divided by its noise power, provided the noise is stationary. We estimate these optimum weights using two criteria: the amplitude-decay rate and the measured noise amplitude for each trace. The amplitude-decay rates are measured relative to the median amplitude-decay rate as a function of midpoint and offset. The noise amplitudes are measured using the data before the first seismic arrivals or at late record times. The optimum stacking weights are estimated from these two quantities using an empirical equation.Tests with synthetic data show that, even after noisy-trace editing, the S/N ratio of the weighted stack can be more than 10 dB greater than the S/N ratio of the straight stack, but only a few decibels more than the S/N ratio of the trace equalized stack. When the S/N ratio is close to 0 dB, a difference of 4 dB is clearly visible to the eye, but a difference of 1 dB or less is not visible. In many cases the S/N ratio of the trace-equalized stack is only a few decibels less than that of the optimum stack, so there is little to be gained from weighted stacking. However, when noisy-trace editing is omitted, the S/N ratio of the weighted stack can be more than 10 dB greater than that of the trace-equalized stack. Tests using field data show that the results from straight stacking, trace-equalized stacking, and weighted stacking are often indistinguishable, but weighted stacking can yield slight improvements on isolated portions of the data.

Notizen: The purpose of deconvolution is to retrieve the reflectivity from seismic data. To do this requires an estimate of the seismic wavelet, which in some techniques is estimated simultaneously with the reflectivity, and in others is assumed known. The most popular deconvolution technique is inverse filtering. It has the property that the deconvolved reflectivity is band-limited. Band-limitation implies that reflectors are not sharply resolved, which can lead to serious interpretation problems in detailed delineation.To overcome the adverse effects of band-limitation, various alternatives for inverse filtering have been proposed. One class of alternatives is Lp-norm deconvolution, L1norm deconvolution being the best-known of this class.We show that for an exact convolutional forward model and statistically independent reflectivity and additive noise, the maximum likelihood estimate of the reflectivity can be obtained by Lp-norm deconvolution for a range of multivariate probability density functions of the reflectivity and the noise. The L∞-norm corresponds to a uniform distribution, the L2-norm to a Gaussian distribution, the L1-norm to an exponential distribution and the L0-norm to a variable that is sparsely distributed. For instance, if we assume sparse and spiky reflectivity and Gaussian noise with zero mean, the Lp-norm deconvolution problem is solved best by minimizing the L0-norm of the reflectivity and the L2-norm of the noise. However, the L0-norm is difficult to implement in an algorithm. From a practical point of view, the frequency-domain mixed-norm method that minimizes the L1norm of the reflectivity and the L2-norm of the noise is the best alternative.Lp-norm deconvolution can be stated in both time and frequency-domain. We show that both approaches are only equivalent for the case when the noise is minimized with the L2-norm.Finally, some Lp-norm deconvolution methods are compared on synthetic and field data. For the practical examples, the wide range of possible Lp-norm deconvolution methods is narrowed down to three methods with p= 1 and/or 2. Given the assumptions of sparsely distributed reflectivity and Gaussian noise, we conclude that the mixed L1norm (reflectivity) L2-norm (noise) performs best. However, the problems inherent to single-trace deconvolution techniques, for example the problem of generating spurious events, remain. For practical application, a greater problem is that only the main, well-separated events are properly resolved.

Notizen: The decrease of density contrast in sedimentary basins may be approximated by a quadratic function. A sedimentary basin may be viewed as a number of prisms placed in juxtaposition. Equations in closed form for the gravity anomalies of 3D and 2½ D prismatic models are derived. Approximate equations for these models are also derived for rapid calculations. Efficient methods are developed for anomaly calculation by an appropriate use of the exact and approximate equations, and hence, for 3D and 2½ D modelling. The depths to the basement are adjusted iteratively by comparing the calculated anomalies with the observed anomalies. These methods are applied for analysis of the residual anomaly map of the Los Angeles Basin, California.

Notizen: The results of a physical scale model study of the conventional mode of operation of fixed loop electromagnetic systems and an alternative mode called the tx-parallel mode in which traverses are run parallel to the long axis of the rectangular transmitter loop are presented. The results show that over thick or dipping conductors, the tx-parallel configuration provides coupling with the target which is comparable with that provided by the conventional configuration. In addition, the tx-parallel configuration is shown to provide more consistent indications of the direction and magnitude of conductor dip. Over wide conductors, where separate conventional surveys are needed to define the opposite edges of such conductors, it is shown that only a single tx-parallel survey is needed to locate both edges of the conductor.The tx-parallel results were found to allow better resolution of the individual anomalies due to closely spaced parallel conductors.The tx-parallel response of identical sheet conductors of opposite dip indicated that the response of the separate sheets could be recognized even when the two sheets were placed at zero separation. This was found to be due in part to spatial displacement of the individual current vortices within each conductor owing to their mutual repulsion.

Notizen: Much of the success of modern seismic data processing derives from the use of the stacking process. Unfortunately, as is well known, conventional normal moveout correction (NMO) introduces mispositioning of data, and hence mis-stacking, when dip is present. Dip moveout correction (DMO) is a technique that converts non-zero-offset seismic data after NMO to true zero-offset locations and reflection times, irrespective of dip. The combination of NMO and DMO followed by post-stack time migration is equivalent to, but can be implemented much more efficiently than, full time migration before stack.In this paper we consider the frequency-wavenumber DMO algorithm developed by Hale. Our analysis centres on the result that, for a given dip, the combination of NMO at migration velocity and DMO is equivalent to NMO at the appropriate, dip-dependent, stacking velocity. This perspective on DMO leads to computationally efficient methods for applying Hale DMO and also provides interesting insights on the nature of both DMO and conventional stacking.

Notizen: First breaks of 2D deep reflection data were used to construct velocity-depth models for improved static corrections to a deeper datum level and for geological interpretations. The highly redundant traveltime data were automatically picked and transformed directly into a velocity-depth model by maximum depth methods such as the Giese- and the Slichter-method. Comparisons with the results of synthetic calculations and a tomographic approach using iterative inversion methods (ART, SIRT) showed that maximum depth methods provide reliable velocity models as a basis for the computation of static corrections. These methods can economically be applied during data acquisition in the field. They provide particularly long-period static anomalies, which are of the order of 20–40 ms (0.5-1 wavelength) within CMP gathers of an example of a deep reflection profile in SW-Germany sited on crystalline basement. Reprocessing of this profile, which was aimed at the comparison between the effects of the originally used and the new statics, did not result in dramatically improved stacking quality but showed a subtle influence on the detailed appearance of deep crustal events.

Notizen: Converted waves require special data processing as the wave paths are asymmetrical. The CMP concept is not applicable for converted PS waves, instead a sorting algorithm for a common conversion point (CCP) has to be applied. The coordinates of the conversion points in a single homogeneous layer can be calculated as a function of the offset, the reflector depth and the velocity ratio vP/ vs. For multilayered media, an approximation for the coordinates of the conversion points can be made.Numerical tests show that the traveltime of PS reflections can be approximated with sufficient accuracy for a certain offset range by a two-term series truncation. Therefore NMO corrections can be calculated by standard routines which use the hyperbolic approximation of the reflection traveltime curves.The CCP-stacking technique has been applied to field data which have been generated by three vertical vibrators. The in-line horizontal components have been recorded. The static corrections have been estimated from additional P- and SH-wave measurements for the source and geophone locations, respectively. The data quality has been improved by processes such as spectral balancing.A comparison with the stacked results of the corresponding P- and SH-wavefield surveys shows a good coherency of structural features in P-, SH- and PS-time sections.

Notizen: It is advantageous to consider inversion of multi-source (wide-aperture) cross-hole data using methods that (i) are based on the wave equation rather than its high-frequency ray approximation, and (ii) use the full information content of the recorded wavefield rather than only first-arrival times. Wave-theoretical methods require the ability to forward-model appropriate wave equations for all source positions in arbitrary reference media. This can be achieved using a frequency-domain elastic wave propagator that facilitates the modelling of multi-source data at the cost of temporal bandwidth. The trade-off is deliberate; the propagator is applied to the cross-hole imaging problem, in which wide spatial bandwidths are more important than temporal bandwidth.By using the frequency-domain propagator, non-linear inverse techniques are applied to data from a very large number of source positions. The method can be applied in 2D media of arbitrary a priori complexity. In a synthetic example, compressional and shear-velocity perturbations are successfully resolved with one iteration using only a single frequency component of wide-aperture elastic wave cross-hole data.

Notizen: Frequency-domain methods are well suited to the imaging of wide-aperture cross-hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source-receiver geometries, are overcome by applying inverse techniques that operate in the frequency-space domain.In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency-domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite-difference equations to be factored in-place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions.Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non-linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non-linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time-lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.

Notizen: Alekseev and Mikhailenko have developed a wavenumber-summation method which combines a finite integral transformation with a finite-difference calculation and involves no approximations other than numerical ones. However, numerical anisotropy causes velocity errors for shear waves which are unacceptable if Poisson's ratios are larger than 0.4 and unless the number of grid points per wavelength is chosen considerably higher than the value generally regarded as sufficient in finite-difference computations. To overcome this limitation in the applicability of the otherwise very powerful modelling scheme, the method is applied to the elastodynamic equations for the velocity vector. Thus, instead of solving a second-order hyperbolic system as in the case of the wave equation, solutions to a first-order hyperbolic system are computed. The finite-difference iteration is performed in a staggered grid. In addition to mastering the numerical difficulties in cases where the Poisson's ratio is unusually high, this approach results in a code which can be used for the modelling of liquid layers.With the new scheme, water reverberations are investigated in terms of normal modes. It is found that for realistic sea-bottom velocities the critical and supercritical cases exist only for P-waves. It means that compressional waves are trapped within the water layer but energy leaks into the substratum through converted shear waves. These leaky compressional normal modes attain properties similar to those of shear normal modes or Pseudo-Love waves. Due to their origin from conversion of dispersed multi-modal compressional waves the shear waves generated at the sea-bottom form a long complex wavetrain. They were found to mask the reflections from the target horizon in an offset-VSP field section.

Notizen: This paper describes a field evaluation of an algebraic reconstruction technique for the tomographic imaging of sub-surface velocity anomalies. We describe the construction of a three-dimensional concrete model and the acquisition and processing of seismic traveltime data through the model. Image reconstructions of the data sets, using an algebraic reconstruction technique and incorporating prior knowledge are presented and these are compared with the actual model. Reconstructions show that it is essential that accurate data are obtained as we demonstrate that relatively small errors in the traveltime data can seriously degrade the reconstruction. We also show that raypath effects are very important limiting factors to the analysis.

Notizen: Wavefront charts in anisotropic gradient media are a useful tool in ray geometric constructions, particular in shear-wave exploration. They can be constructed by: (i) a family of wavefronts that contains a vertical plane as member - it is convenient to choose constant time increments; (ii) tracing one ray that makes everywhere the angle with the normal to the wavefront that is required by the anisotropy of the medium; (iii) scaling this ray to obtain a set of rays with different ray parameters; (iv) shifting these rays (with wavefront elements attached) so that they pass through a common source point; (v) interpolating the wavefronts between the elements.The construction is particularly simple in linear-gradient media, since here all members of the family of wavefronts are planes. Since the ray makes everywhere the angle prescribed by the anisotropy with the normal of the (plane) wavefronts, the ray has the shape of the slowness curve rotated by −π/2.For isotropic media the slowness curve is a circle, and thus rays are circular arcs. The circles themselves intersect in the source point and in a second point above the surface of the earth. This provides a simple proof that wavefronts emanating from a point source in an isotropic linear-gradient medium are spheres: inversion of the set of circular rays with the source as centre maps the pencil of circular rays into a pencil of straight lines passing through a point. A pencil of concentric spheres around this point is perpendicular to the pencil of straight lines. On inverting back the pencil of spheres is mapped into another pencil of spheres that is perpendicular to the circular rays.

Notizen: A multichannel lattice filter structure is utilized to represent seismic waves propagating in adjacent layers in an elastic medium. Using this model, an explicit time-domain solution for arbitrary source and receiver locations is obtained as an ARMA (AutoRegressive and Moving-Average) process. The lattice and ARMA structures have given rise to an effective algorithm for the calculation of offset/downhole synthetic seismograms.A large range of recently developed offset/downhole seismic survey geometries, such as the ‘Yo-Yo’ arrangement, can thus be simulated. In addition, the explicit solutions for upgoing and downgoing waves provide new insight into the properties of general downhole seismic signals, including wave-mode conversion effects and multiple reflections. Furthermore, offset/downhole seismograms generated by a line source (i.e. 2D point source) can also be constructed by superposition of plane waves with different incidence angles.Synthetic seismograms generated using a different source-receiver arrangement indicate that the properties especially associated with offset/downhole seismic signals can be predicted by this modelling method. These properties include arrival times, amplitude attenuation and wave-mode conversion effects. Finally, utilizing this numerical modelling method to a real downhole survey with Yo-Yo geometry may lead to a proper data acquisition and processing procedure, and improves the interpretation confidence of the field section.

Notizen: The elastic Kirchhoff-Helmholtz integral expresses the components of the monochromatic displacement vector at any point A in terms of the displacement field and the stress field at any closed surface surrounding A. By introducing Green's functions for P- and S-waves, the elastic Kirchhoff-Helmholtz integral is modified such that it expresses either the P-wave or the S-wave at A in terms of the elastic wavefield at the closed surface. This modified elastic Kirchhoff-Helmholtz integral is transformed into one-way elastic Rayleigh-type integrals for forward extrapolation of downgoing and upgoing P- and S-waves. We also derive one-way elastic Rayleigh-type integrals for inverse extrapolation of downgoing and upgoing P- and S-waves. The one-way elastic extrapolation operators derived in this paper are the basis for a new prestack migration scheme for elastic data.

Notizen: Spectral analysis is one of the most ubiquitous signal processing tools used in exploration geophysics. Among many applications, it is used simply to look at the frequency content of seismic traces, to find notches, to estimate wavelets under the minimum-phase assumption, and to match broadband synthetic seismograms to seismic data.Seismic spectra exhibit very large dynamic ranges, particularly at low frequencies. Estimation of low-frequency decay is very important for accurate modelling. However, when using traditional spectral estimates incorporating smoothing windows, too much sidelobe energy leaks from high power into low power areas, spoiling our ability to estimate low-frequency spectral decay. The multitaper method of spectral analysis due to D. Thomson does not employ just a single window, but rather a set of orthogonal data tapers. It is possible to have much less sidelobe contamination, while maintaining a stable estimate.The trace is tapered by each of a subset of the orthogonal tapers, and a raw spectral estimate produced in each case. These are combined to produce a final spectral estimate. The technique can be made adaptive by applying different weights to the different raw spectra at different frequencies.A comparison of seismic spectral estimation using this multitaper technique with a traditional approach having the same analysis bandwidth and stability demonstrates the very different estimates of spectral decay in the areas of high dynamic range. The multitaper approach provides estimates with much reduced sidelobe leakage, and hence is a very appealing method for reflection seismology.

Notizen: Multichannel filters are used to eliminate coherent noise from surface seismic data, for wavefield separation from VSP stacks, and for signal enhancement. Their success generally depends on the choice of the filter parameters and the domain of application. Multichannel filters can be applied to shots (monitors), common-receiver traces, CDP traces and stacked sections. Cascaded applications in these domains are currently performed in the seismic industry for better noise suppression and for signal enhancement. One-step shot-domain filtering is adequate for some applications. However, in practice, cascaded applications in shot-and common-receiver domains usually give better results when the S/N ratio is low. Multichannel filtering after stacking (especially after repeated applications in shot and/or receiver domains) may create undesirable results such as artificial continuations, or smearing and smoothing of small features such as small throw faults and fine stratigraphic details. Consequently, multichannel filtering after stacking must be undertaken with the utmost care and occasionally only as a last resort.Multichannel filters with fan-shaped responses (linear moveout filters) should be applied after NMO correction. These are the filters commonly used in the seismic industry where they have such names as velocity filters, moveout filters, f-k filters and coherency filters. Filtering before NMO correction may result in break-up and flattening especially of those shallow reflection events with relatively higher curvatures and diffractions. NMO correction is needed prior to wavefield separation from VSP stacks for the same practical reasons outlined above whenever source-receiver offsets are involved.Creation of artificial lineup and smearing at the outputs of multichannel filters is presently the common practical concern. Optimum multichannel filters with well-defined pass, reject and transition bands overcome the latter problems when applied before stacking and after NMO correction. The trace dimension of these filters must be kept small to avoid such lineups and the smoothing of small structures. Good results can be obtained with only five traces, but seven traces seems to be a better compromise both in surface and well seismic applications. The so-called f-k filtering and τ-p domain filtering are no exceptions to the above practical considerations.Residual static computations after multichannel filtering also need special consideration. Since multichannel filtering improves spatial continuity, residual static algorithms using local correlation, i.e. nonsurface-consistent algorithms, may be impractical especially after multichannel filtering.

Notizen: Calculations of emf induced in a vertical axis coil by a current step in a straight wire segment of finite length were carried out using an equivalent dipole placed along the source wire. An approximation is valid for homogeneous and layered earth models. The location of the equivalent dipole is calculated by forcing the early- and late-time asymptotes of the transient sounding curve of the equivalent dipole to match those of the finite wire. This approximation works because the early-time asymptote of the emf depends on the component of the receiver position which is parallel to the wire while the late-time asymptote does not. Analytical integration of the early-time asymptote yields an expression for the equivalent dipole location in closed form.The coil can be placed anywhere in the vicinity of the finite wire. Square or rectangular loop sources can be simulated by one or more finite wire segments depending on the source-receiver geometry. The equivalent radius calculated for central loop soundings agrees well with the value derived using a circular loop with the same area as the square loop.Results show that acceptable sounding curves can be generated by the equivalent dipole for coils placed as close as 0.5 source lengths from the finite wire segment. Higher accuracy can be obtained by splitting the finite wire into two or more subsegments. Results for layered models are slightly better than homogeneous earth models when the resistivity increases with depth and slightly worse for models with resistivity decreasing with depth. Approximate calculations are about 10 times less expensive than exact calculations depending on the method used for the numerical integration.

Notizen: This study investigates the propagation of borehole Stoneley waves across permeable structures. By modelling the structure as a zone intersecting the borehole, a simple 1D theory is formulated to treat the interaction of the Stoneley wave with the structure. This is possible because the Stoneley wave is a guided wave, with no geometric spreading as it propagates along the borehole. The interaction occurs because the zone and the surrounding formation possess different Stoneley wavenumbers. Given appropriate representations of the wavenum-ber, the theory can be applied to treat a variety of structures, including a fluid-filled fracture. Of special interest are the cases of permeable porous zones and fracture zones. The results show that, while Stoneley wave reflections are generated, strong Stoneley wave attenuation is produced across a very permeable zone. This result is particularly important in explaining the observed strong Stoneley wave attenuation at major fractures where it has been difficult to explain the attenuation in terms of the single planar fracture theory. In addition, by using a simple and sufficiently accurate theory to model the effects of the permeable zone, a fast and efficient method is developed to characterize the fluid transport properties of a permeable fracture zone.

Notizen: A reflection response function for a 1D discretized earth model can be obtained using ray-theory and Z-transforms with the Goupillaud model. This is usually done by taking the source function as a plane wave impinging normally on the layered earth. Two important problems have been tackled with this basic idea. The first, extraction of the source wavelet, and the second, a description of the free-surface related problems.In the Goupillaud model, the one-way traveltime in each layer is taken to be the same time interval At, which is also the time unit for the Z-transform. The two-way traveltime in any layer is 2Δt, corresponding to a multiplication by Z2. The reflection impulse response therefore contains only even powers of Z. The convolution of the reflection response with the wavelet yields a seismogram whose Z-transform contains both odd and even powers of Z. However, even though the seismogram contains more coefficients than unknowns, the wavelet cannot be extracted, because the coefficients are not independent: later coefficients are functions of earlier ones, which does not make sense physically. To overcome this physical problem for the reflection seismogram, the two-way traveltime through the layer should be Δt. It is then impossible to extract the wavelet, as there are fewer coefficients in the seismogram than unknowns.Szaraniec has proposed a modification to the Goupillaud model, known as the odd-depth model, that includes the free surface and a top layer whose two-way traveltime Δt is half the two-way traveltime 2Δt of all the other layers. Using what Szaraniec calls the fundamental identity of the odd-depth model, it is possible to extract the source wavelet from the seismogram. We show that this fundamental identity holds only if reflection coefficients of deeper interfaces are functions of the reflection coefficients of shallower interfaces; that is, for extremely improbable geologies.Neither of these approaches offers a solution to the deconvolution problem. It is better to obtain the source signature from measurements in the field. Only Szaraniec's model offers the possibility of tackling the problem of the free surface but because of an inherent flaw in the model, it fails to address the problem.

Notizen: P-wave velocity anisotropy determined from a cross-hole survey at the Imperial College borehole test site compares favourably with that measured in the laboratory on core from the holes. The holes penetrate a layered sequence of sandstones, shales and carbonates of the Namurian Upper Limestone Group. The Laboratory measurements of the vertical and horizontal velocities of core samples indicate that the shales exhibit P-wave anisotropies of over 20% but that the sandstones and limestones are only slightly anisotropic. These discrete measurements have been used in combination with wireline data to produce a log of P-wave anisotropy. Including the anisotropic information vastly improves the match between observed and synthetic traveltimes from the cross-hole data set. This implies that there is little frequency dependence of intrinsic P-wave anisotropy.Inversion of the cross-hole traveltimes highlights the need for good angular coverage in order to resolve the anisotropy parameters. The observed P-wave anisotropy of the field data is due to the combined effect of sedimentary layering and the intrinsic anisotropy of the rocks. The intrinsic anisotropy is found to be the dominant factor.

Notizen: One simulation and two field examples from New Jersey illustrate resolution improvement in geoelectrical soundings applied to groundwater exploration. Layered-earth parameter resolution is derived from data obtained with the commonly used methods of resistivity, induced polarization (IP) and transient electromagnetic (TEM) soundings. Resolution improvement is achieved by simultaneous inversion of two or more data sets and by constraining parameters of the inverse problem.A quantitative analysis showing the contribution of IP data to the resolution of geo-electric sections is presented. Simultaneous inversion of simple IP data with conventional resistivity and resistivity-TEM data sets resulted in improved parameter resolution. IP data improved resolution in three ways: (1) by decoupling correlated layered-earth parameters, (2) by adding information to a geological interpretation about a second physical property, namely chargeability, and (3) by increasing the electrical information available.

Notizen: A depth migration method is presented that uses Radon-transformed common-source seismograms as input. It is shown that the Radon depth migration method can be extended to spatially varying velocity depth models by using asymptotic ray theory (ART) to construct wavefield continuation operators. These operators downward continue an incident receiver-array plane wave and an assumed point-source wavefield into the subsurface. The migration velocity model is constrained to have longer characteristic wavelengths than the dominant source wavelength such that the ART approximations for the continuation operators are valid.This method is used successfully to migrate two synthetic data examples:〈list xml:id="l1" style="custom"〉1a point diffractor, and2a dipping layer and syncline interface model.It is shown that the Radon migration method has a computational advantage over the standard Kirchhoff migration method in that fewer rays are computed in a main memory implementation.

Notizen: The use of the gravity method to predict rock bursts in mines is based on the relationship between the development of a dilatancy process in the exploited rock mass and the time-dependent gravity anomalies induced by this phenomenon. The differences between successive observations of anomalies and the time behaviour of their trend amplitudes as precursors of preceding changes of rock stability are interpreted. The centres of zones of induced rock density variation are determined by computing the position of singular points of the differences between anomalies.Two gravity surveys have been carried out in the Radbod coal mine (Germany). The first survey took place at the level of the Dickebank seam (depth 1030 m), the second in the Sonnenschein seam (depth 1090 m). The observations were made with Worden and LaCoste-Romberg (D-type) gravimeters. The differences between successive anomalies were less than 100 μGal.In the case of the Dickebank seam, the position of singular points demonstrates the effect of two approaching longwalls on a previously mined-out seam and on the gallery in which the gravity observations were made. In the case of the Sonnenschein seam, the trend amplitudes show distinct variations in the formation of the approaching longwall below the edges of all previously mined-out seams. In particular, the effect of a remnant pillar has caused the largest gravity gradients. This result corresponds to the existence of a zone of rock-burst hazard known from test drilling. The computed singular points are grouped together under the remnant pillar indicating two local hazard zones.Both results, the observed development of rock instability with time and the information about the position of the disturbed rock mass relative to the mine workings, are of importance, subsurface gravity surveying can therefore be a valuable tool for predicting rock-bursts.

Notizen: The Pelton DRTM Servovalve Enhancement causes the natural output of a vibrator to resemble the desired output more closely. This simplifies the control problem and reduces harmonic distortion.The traditional type of servovalve used on seismic vibrators is a flow-control servovalve. Flow is proportional to a vibrator's baseplate velocity, with respect to its reaction mass.The new servovalve control parameter is pressure rather than flow. The differential pressure applied to a vibrator's actuator piston, multiplied by the area of the piston, equals the force applied to the vibrator's baseplate structure. This may be defined as actuator force. There is a simpler and more linear relationship between actuator force and ground force than between actuator velocity and ground force. Thus, it is better for the servovalve to control pressure into the actuator rather than flow.A flow-control servovalve can be made to control pressure by sensing the differential pressure across a vibrator's actuator piston and applying it as a negative feedback around the servovalve main stage. This has been carried out and tested. The result is more accurate vibrator control and reduced harmonic distortion.

Notizen: Reiter, E.C., Toksoz, M.N. and Purdy, G.M. 1992. A semblance-guided median filter. Geophysical Prospecting41, 15–41.A slowness selective median filter based on information from a local set of traces is described and implemented. The filter is constructed in two steps, the first being an estimation of a preferred slowness and the second, the selection of a median or trimmed mean value to replace the original data point. A symmetric window of traces defining the filter aperture is selected about each trace to be filtered and the filter applied repeatedly to each time point. The preferred slowness is determined by scanning a range of linear moveouts within the user-specified slowness passband. Semblance is computed for each trial slowness and the preferred slowness selected from the peak semblance value. Data points collected along this preferred slowness are then sorted from lowest to highest and in the case of a pure median filter, the middle point(s) selected to replace the original data point. The output of the filter is therefore quite insensitive to large amplitude noise bursts, retaining the well-known beneficial properties of a traditional 1D median filter. Energy which is either incoherent over the filter aperture or lies outside the slowness passband, may be additionally suppressed by weighting the filter output by the measured peak semblance.This approach may be used as a velocity filter to estimate coherent signal within a specified slowness passband and reject coherent energy outside this range. For applications of this type, other velocity estimators may be used in place of our semblance measure to provide improved velocity estimation and better filter performance. The filter aperture may also be extended to provide increased velocity estimation, but will result in additional lateral smearing of signal. We show that, in addition to a velocity filter, our approach may be used to improve signal-to-noise ratios in noisy data. The median filter tends to suppress the amplitude of random background noise and semblance weighting may be used to reduce the amplitude of background noise further while enhancing coherent signal.We apply our method to vertical seismic profile data to separate upgoing and downgoing wavefields, and also to large-offset ocean bottom hydrophone data to enhance weak refracted and post-critically reflected energy.

Notizen: MT data from a detailed 84-site grid array (28 × 12 km) in the Paraná Basin (Brazil) reveal a high degree of frequency-independent and parallel amplitude distortion. The Palaeozoic sediments across the survey area are covered by 1.2 km of flood basalts. A deep well-log provides some control regarding the emplacement of thin diabase sills but information regarding vertical feeder dikes is non-existent. The degree of parallel behaviour is identified using anisotropy ratios which quantify the extent and bandwidth of the distortion characteristics.A 2D modelling study is carried out using the concept of a horizontally layered (1D) basin with superimposed, small-scale inhomogeneities. Two likely geological distortion structures are considered. The first represents at- or near-surface (0 to 100 m) inhomogeneities. The second represents thin but vertically elongate dikes. The two distortion effects are found to produce different and characteristic behaviour in the H-polarization (TM) mode model data. The modelled E-polarization (TE) mode data are undistorted and provide control. The model developed to represent vertical dikes gives rise to a characteristic frequency dependence which is distinct from that of the undistorted response. This model also generates subparallel distortion effects which give rise to a form of variance in the response estimates as a function of location. The behaviour occurs, importantly, in both the amplitude and phase of the distorted data. A comparison of the normalized amplitude data, observed and modelled, indicates a high degree of correspondence down to a low frequency limit (〈 0.1 Hz) where additional and deep contributions to the observed response become apparent. The modelling results and data characteristics indicate that the survey area is underlain by a series of closely parallel, thin intrusive dikes (a dike swarm).