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- Volume 40, Issue 6, 1992
Geophysical Prospecting - Volume 40, Issue 6, 1992
Volume 40, Issue 6, 1992
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AUTOMATED FIRST ARRIVAL PICKING: A NEURAL NETWORK APPROACH1
Authors MICHAEL E. MURAT and ALBERT J. RUDMANAbstractA back‐propagation neural network is successfully applied to pick first arrivals (first breaks) in a background of noise. Network output is a decision whether each half‐cycle on the trace is a first or not. 3D plots of the input attributes allow evaluation of the attributes for use in a neural network. Clustering and separation of first break from non‐break data on the plots indicate that a neural network solution is possible, and therefore the attributes are suitable as network input.
Application of the trained network to actual seismic data (Vibroseis and Poulter sources) demonstrates successful automated first‐break selection for the following four attributes used as neural network input: (1) peak amplitude of a half‐cycle; (2) amplitude difference between the peak value of the half‐cycle and the previous (or following) half‐cycle; (3) rms amplitude ratio for a data window (0.3 s) before and after the half‐cycle; (4) rms amplitude ratio for a data window (0.06 s) on adjacent traces. The contribution of the attributes based on adjacent traces (4) was considered significant and future work will emphasize this aspect.
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REFLECTION AND POLARIZATION OF TUBE WAVES AS SEEN IN VSP DATA1
By R. MJELDEAbstractP‐wave and S‐wave data acquired with vertical seismic profiling (VSP) often include tube waves propagating in the borehole, although considerable efforts are generally made to ensure that these waves are not recorded. However, several theoretical studies have indicated that tube waves could provide important information about the rock formation and thus should not be considered as pure noise.
In order to study some of these aspects experimentally, tube waves were acquired by VSP in a well in the Paris Basin both before and after casing. A sparker was used as source inside the borehole, which ensured that the data recorded contained high‐amplitude tube waves.
It is shown that the casing is an obstacle which prevents the study of formation parameters, and thus further tube‐wave acquisitions should be carried out in open holes only.
The before‐casing tube‐wave reflection log is compared to a synthetic log computed from the sonic log. The high resolution of the tube waves is of particular interest, revealing layers that are too thin to be detected in body‐wave surveys.
It has recently been suggested that the projection of the tube‐wave polarization in the horizontal plane can be used to determine directions of stress‐induced anisotropy in the rock formation. Strong polarization anomalies are observed in the data sets but are attributed to tool problems rather than any rock‐formation feature.
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THE CAGNIARD METHOD IN COMPLEX TIME REVISITED1
Authors N. BLEISTEIN and J. K. COHENAbstractThe Cagniard‐de Hoop method is ideally suited to the analysis of wave propagation problems in stratified media. The method applies to the integral transform representation of the solution in the transform variables (s, p) dual of the time and transverse distance. The objective of the method is to make the p‐integral take the form of a forward Laplace transform, so that the cascade of the two integrals can be identified as a forward and inverse transform, thereby making the actual integration unnecessary. That is, the exponent (–sw(p)) is set equal to –sτ, with τ varying from some (real) finite time to infinity. As usually presented, the p‐integral is deformed onto a contour on which the exponent is real and decreases to –∞ as p tends to infinity. We have found that it is often easier to introduce a complex variable τ for the exponent and carry out the deformation of contour in the complex τ‐domain. In the τ‐domain the deformation amounts to ‘closing down’ the contour of integration around the real axis while taking due account of singularities off this axis.
Typically, the method is applied to an integral that represents one body wave plus other types of waves. In this approach, the saddle point of w(p) that produces the body wave plays a crucial role because it is always a branch point of the integrand in the τ‐domain integral. Furthermore, the paths of steepest ascent from the saddle point are always the tails of the Cagniard path along which w(p) →∞. That is, the image of the pair of steepest ascent paths in the p‐domain is a double covering of a segment of the Re τ‐axis in the τ‐domain. The deformed contour in the p‐domain will be the only pair of steepest ascent paths unless the original integrand had other singularities in the p‐domain between the imaginary axis and this pair of contours. This motivates the definition of a primary p‐domain, i.e. the domain between the imaginary axis and the steepest descent paths, and its image in the τ‐domain, the primary τ‐domain. In terms of these regions, singularities in the primary p‐domain have images in the primary τ‐domain and the deformation of contour on to the real axis in the τ‐domain must include contributions from these singularities.
This approach to the Cagniard‐de Hoop method represents a return from de Hoop's modification to Cagniard's original method, but with simplifications that make the original method more tractable and straightforward. This approach is also reminiscent of van der Waerden's approach to the method of steepest descents, which starts exactly the same way. Indeed, after the deformation of contour in the τ‐domain, the user has the choice of applying asymptotic analysis to the resulting ‘loop’ integrals (Watson's lemma) or continuing to obtain the exact, although usually implicit, time‐domain solution by completing the Cagniard‐de Hoop analysis.
In developing the method we examine the transformation from a frequency‐domain representation of the solution (ω) to a Laplace representation (s). Many users start from the frequency‐domain representation of solutions of wave propagation problems. In this case issues arising from the movement of singularities under the transformation from ω to s must be considered. We discuss this extension in the context of the Sommerfeld half‐plane problem.
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IP RESPONSE FOR A 2D HORIZONTAL CYLINDER1
Authors B. B. BHATTACHARYA and D. BISWASAbstractThe induced polarization response for a 2D horizontal cylinder embedded in a half‐space is calculated for a uniform electric source. Response curves, in the form of apparent charge‐ability taking into account the effect of the air‐earth interface, exhibit a sharp decrease in amplitude with an increase in depth of burial of the target. The resistivity contrast between the cylinder and the host plays a dominant role in determining the IP response, i.e. the amplitude decreases considerably with the increase in resistivity contrast. The decrease is due to the defocusing effect caused by the resistive cylinder. The current lines tend to deviate away from the cylindrical target. In the case of a highly conducting cylinder, apparent defocusing takes place as current lines are confined to the surface of the conducting cylinder. An increase in chargeability contrast is reflected as a steady rise in the response. The peak response at the centre is reduced by about half the magnitude when the air–earth interface is not considered. The variation of response along the profile, though noticeable, is not as high as that obtained at the centre.
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SEISMIC MODELLING OF SEAM WAVES EXCITED BY ENERGY TRANSMISSION INTO A SEAM1
More LessAbstractThe traditional method of exciting channel waves in coal deposits underground consists of firing explosive sources in a mid‐seam position generating seam waves of the Rayleigh and Love type. We investigate various source positions and excitation mechanisms within the bedrock structure surrounding the seam to evaluate the effects of source positions adjacent to the seam. The investigation is based on analogue and numerical modelling of half‐ and full‐space cases, for which the excitation and the nature of Rayleigh channel waves are examined.
In the analogue modelling, sources, located from mid‐seam out into the bedrock, along the edge of a 2D plate model, excited channel waves through a conversion of the free surface Rayleigh wave at the edge of the plate. The excited channel wave belongs to the normal mode range. Frequency‐wavenumber analysis shows that the symmetric 2nd mode of the channel wave is excited with frequencies comparable to the forcing frequency of the source signal. The polarization changes from retrograde to prograde, as the wave develops from the front to the rear of the seam, respectively. The amplitude‐depth distribution resembles that of an ordinarily excited seam wave, for the symmetric component. However, the antisymmetric component does not show the characteristic change of sign in amplitudes across the mid‐seam axis.
Numerical modelling with sources located in the bedrock (full‐space case) shows that relocating the source away from the seam lowers the frequency content of the excited channel wave. Based on these investigations, the influence of a lower‐frequency source signal on the excitation of the channel wave is examined in an analogue experiment. Sources are sited in the bedrock adjacent to the seam at three locations. A lower‐frequency wavelet is calculated for each source location from the results obtained in the numerical analysis. For comparison, a higher‐frequency wavelet is also used which is known to be optimal for this model geometry when excited by a mid‐seam source location. It is found that in two cases the use of the lower‐frequency wavelet improves the channel wave excitation, while no amplification is achieved in one case.
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 35 (1987)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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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 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)