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- Volume 40, Issue 5, 1992
Geophysical Prospecting - Volume 40, Issue 5, 1992
Volume 40, Issue 5, 1992
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SEISMIC REFLECTION AMPLITUDES1
Authors BJØRN URSIN and TERJE DAHLAbstractSeismic amplitude variations with offset contain information about the elastic parameters. Prestack amplitude analysis seeks to extract this information by using the variations of the reflection coefficients as functions of angle of incidence. Normally, an approximate formula is used for the reflection coefficients, and variations with offset of the geometrical spreading and the anelastic attenuation are often ignored. Using angle of incidence as the dependent variable is also computationally inefficient since the data are recorded as a function of offset.
Improved approximations have been derived for the elastic reflection and transmission coefficients, the geometrical spreading and the complex travel‐time (including anelastic attenuation). For a 1 D medium, these approximations are combined to produce seismic reflection amplitudes (P‐wave, S‐wave or converted wave) as a Taylor series in the offset coordinate. The coefficients of the Taylor series are computed directly from the parameters of the medium, without using the ray parameter.
For primary reflected P‐waves, dynamic ray tracing has been used to compute the offset variations of the transmission coefficients, the reflection coefficient, the geometrical spreading and the anelastic attenuation. The offset variation of the transmission factor is small, while the variations in the geometrical spreading, absorption and reflection coefficient are all significant.
The new approximations have been used for seismic modelling without ray tracing. The amplitude was approximated by a fourth‐order polynomial in offset, the traveltime by the normal square‐root approximation and the absorption factor by a similar expression. This approximate modelling was compared to dynamic ray tracing, and the results are the same for zero offset and very close for offsets less than the reflector depth.
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MODELLING CHANNEL WAVES WITH SYNTHETIC SEISMOGRAMS IN AN ANISOTROPIC IN‐SEAM SEISMIC SURVEY1
Authors ENRU LIU, STUART CRAMPIN and BRUCE ROTHAbstractIn‐seam seismic surveys with channel waves have been widely used in the United Kingdom and elsewhere to map coal‐seams and to detect anomalous features such as dirt bands, seam thinning and thickening, and particularly in‐seam faulting. Although the presence of cleat‐induced anisotropy has been recognized in the past, almost all previous analyses have assumed homogeneous isotropic or transversely isotropic coal‐seams. Channel waves, however, exhibit properties which cannot be fully explained without introducing anisotropy into the coal‐seam. In particular, Love‐type channel waves are observed for recording geometries where, in a homogeneous isotropic or transversely isotropic structure, the source would not be expected to excite transverse motion. Similarly, modes of channel‐wave propagation display the coupled three‐component motion of generalized modes in anisotropic substrates, which would not be expected for Rayleigh and Love wave motion in isotropy or in transversely isotropic media with azimuthal isotropy.
We model the observed in‐seam seismic channel waves with synthetic seismograms to gain an understanding of the effects of cleat‐induced anisotropy on the behaviour of channel waves. The results show a reasonable good match with the observations in traveltime, relative amplitudes, dispersion characteristics and particle motions. We demonstrate that anisotropy in the surrounding country rocks contributes significantly to the coupling of channel wave particle motion, although its effect is not as strong as the anisotropy in the coal‐seam. We conclude that the effects of cleat‐ and stress‐induced anisotropy are observed and can be modelled with synthetic seismograms, and that anisotropy must be taken into account for the detailed interpretation of channel waves.
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THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A POLARIZABLE SPHERE IN A CONDUCTING HALF SPACE1
Authors TERRY LEE and LINDSAY THOMASAbstractA polarizable sphere embedded in a conducting half‐space can give rise to negative voltage transients in a coincident‐loop time‐domain electromagnetic system. Such transients have been observed in field situations. Our results are obtained from a model in which the contributions of the host rock, the currents in the sphere, and the interaction between the sphere and the host rock are separated and superposed. This model uses approximations to the integral equation solutions rather than finite‐element or finite‐difference approximations, and so allows very rapid computation.
The theoretical demonstration suggests that interpretation of the negative voltage transients as a polarization response is valid, but more detailed interpretation of polarization properties may not be possible, because the superposition of the polarization response on the normal response depends strongly on the position of the target.
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FREQUENCY‐SELECTIVE DESIGN OF THE KIRCHHOFF MIGRATION OPERATOR1
More LessAbstractIntegral migration techniques perform a sum over an aperture of input traces to obtain output at a single point. The length of the aperture is limited by a spatial Nyquist criterion, which typically prohibits imaging very steep dips at very high frequencies without generating severe migration artifacts (migration operator aliasing). For time‐domain Kirchhoff migration, this can be a fatal shortcoming. The standard way to address this problem is to interpolate traces spatially before migration. This reduces the trace spacing, thereby increasing the frequency content which can be migrated without aliasing at steep dips.
An alternative remedy to the operator aliasing problem is to modify the phase response of the Kirchhoff migration operator. This operator is frequency‐selective across the migration aperture: it passes all temporal frequencies of the input traces in the innermost portion of the aperture (referring to the shallow dips), and gradually cuts out the higher frequencies as it approaches the outer portion of the aperture. Thus, while all frequencies of the input data contribute to the shallow‐dip portion of the migrated image, only the permissible low frequencies of the input data contribute to imaging the steepest dips.
Using a simple realization of a frequency‐selective Kirchhoff migration operator, this technique is illustrated on a synthetic data set involving greater than vertical dips.
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APPLICATION OF GEOELECTRIC METHODS USING BURIED ELECTRODES IN EXPLORATION AND MINING1
Authors P. DRASKOVITS and A. SIMONAbstractVarious geoelectric methods which have been developed and applied in the last 10–20 years in ELGI are discussed. These methods which use buried electrodes are: hole‐to‐surface gradient mapping to detect bauxite deposits in sinkholes below a resistive screening layer; in‐mine gradient profiling to map the basement topography below galleries; and the hole‐to‐surface version of geoelectric layer tracing to find outcrops of mineralized zones penetrated by drillings.
Data processing procedures have been developed on the basis of common concepts and hypotheses to link theoretical models with geological structures. The objects investigated are determined as the difference between the theoretical models and geological structures. The predominant part of the real electric field measured above the geological structures is the theoretical field related to the theoretical model. The effects of the objects (the anomaly) are superposed on the theoretical field but their extent is small compared with the values of the latter. The theoretical field and the anomaly depend strongly on the separation from the sources. For this reason the anomalies are difficult to recognize. Therefore the ratio of the theoretical field to the measured one is computed, since σa, the apparent specific conductivity, is proportional to this ratio.
It is demonstrated that since the changes in the σa curve depending on the location of the observation point are small, the anomalies can easily be recognized on the curve. The σa, curve computed in the above way reflects the objects better than the originally measured electric fields.
Examples illustrate the solution of the above‐mentioned geological problems by the practical application of adequate geoelectric methods using buried electrodes.
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Volume 72 (2023 - 2024)
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Volume 46 (1998)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 2 (1954)
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Volume 1 (1953)