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- Volume 38, Issue 8, 1990
Geophysical Prospecting - Volume 38, Issue 8, 1990
Volume 38, Issue 8, 1990
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TRACE INTERPOLATION BY SLANT‐STACK MIGRATION1
By M. NOVOTNÝAbstractThe 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.
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A FAST ALGORITHM FOR THE COMPUTATION OF RADON TRANSFORMS1
Authors C. J. HANEVELD and G. C. HERMANAbstractA 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.
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THE USE OF MARINE SEISMIC PROFILING FOR ENVIRONMENTAL ASSESSMENT1
By T. M. McGEEAbstractOne 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.
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DIRECTIONAL DECONVOLUTION OF MARINE SEISMIC REFLECTION DATA: NORTH SEA EXAMPLE1
Authors G. A. ROBERTS and N. R. GOULTYAbstractDirectional 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.
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SEISMIC MODELLING WITH CHANNEL WAVES IN SEAM STRUCTURES INFLUENCED BY MYLONITE ZONES1
Authors I. M. GELDMACHER, L. DRESEN and T. STÜRZNICKELAbstractChannel 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.
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THE RESOLUTION POSSIBLE IN IMAGING WITH DIFFRACTED SEISMIC WAVES1
Authors SUHAS PHADKE and ERNEST R. KANASEWICHAbstractThe 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.
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ELASTIC WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA USING FINITE DIFFERENCES1
Authors C. TSINGAS, A. VAFIDIS and E. R. KANASEWICHAbstractWhen 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.
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SEISMIC CHARACTER MAPPING OVER RESERVOIR INTERVALS1
Authors V. LENDZIONOWSKI, A. T. WALDEN and R. E. WHITEAbstractThis 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.
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AN ANALYTICAL RAYPATH APPROACH TO THE REFRACTION WAVEFRONT METHOD1
By M. ALI AKAbstractSeismic 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.
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ANISOTROPY DETECTED IN SHALLOW CLAYS USING SHEAR‐WAVE SPLITTING IN A VSP SURVEY1
Authors JAN DOUMA, HENK DEN ROOIJEN and FLORIS SCHOKKINGAbstractShear 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.
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3D GRAVITY INVERSION OF THE CHESHIRE BASIN1
Authors A. ABDOH, D. COWAN and M. PILKINGTONAbstractThree‐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.
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