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- Volume 35, Issue 2, 1987
Geophysical Prospecting - Volume 35, Issue 2, 1987
Volume 35, Issue 2, 1987
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THE GENERALIZED SPECTRAL FUNCTION OF A PLANE LAYERED MEDIUM*
By R.‐G. FERBERABSTRACTThe spectral function of a plane layered medium, which represents the net downgoing energy in the first layer due to a normally incident impulsive plane wave, plays an important role in the solution of the one‐dimensional inverse problem in reflection seismology. Hitherto the extension to non‐normal incidence was known only for a medium with free surface. By giving the extension for arbitrary surface reflection coefficients, this paper fills a gap.
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ATTENUATION OF RANDOM NOISE BY 2‐D AND 3‐D CDP STACKING AND KIRCHHOFF MIGRATION*
By TH.C. KREYABSTRACTThree‐dimensional seismic surveys, in general, do not need the same high degree of CDP coverage as 2‐D surveys to achieve a certain signal‐to‐noise ratio after migration.
This can be shown theoretically for Kirchhoff migration and laterally uncorrelated noise. More precisely, there exists a formal relationship between the multiplicity of CDP coverage of a 3‐D survey and that of a 2‐D survey with the same signal‐to‐uncorrelated‐noise ratio. Frequency and aperture are parameters in the corresponding expression. Heuristically the relationship can be obtained by applying the concept of the Fresnel zone.
Though the mathematics in this paper refer to laterally uncorrelated noise, the underlying concepts can probably also be used for weakly correlated noise, e.g., for multiple reflections and for the low‐frequency remnants of surface waves.
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DATA ACQUISITION AND PROCESSING OF CONVERTED pS‐WAVES*
Authors J. FERTIG and M.K. HENTSCHKEABSTRACTThe earth's surface can be an effective means of generating converted pS‐waves. Due to their nearly symmetrical ray path, conventional processing techniques can be used. As the wave is generated by reflection at the surface or at the base of surface layers one can expect a general filtering effect in the data for individual ray paths of a single shot gather.
To balance the spectra of the traces a multiple‐trace filter was used. This filter can be fully determined in the time domain using the prediction‐error operators of the individual traces. The preferred mean spectrum to colour the traces was the geometric mean.
As the process of spectral balancing requires a minimum‐delay wavelet, the recording instrument was replaced by its corresponding minimum‐phase equivalent. This process can also be carried out effectively in the time domain.
Results of the application of minimum‐delay transform and spectral balancing are discussed for single shot gathers and for the general improvement of the final stack.
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EVANESCENT EFFECTS IN ACOUSTICAL WAVE PROPAGATION*
By M. J. KUHNABSTRACTThe propagation of transient acoustic pressure waves in a layer enclosed between two, not necessarily identical, half‐spaces is considered. The source and the receivers are always located in the same half‐space and at the same depth. The source excitation function is a narrow causal spike. Several thicknesses of the layer are examined including the case in which the embedded layer vanishes.
The phenomena of ‘constricted’ head waves and wide‐angle reflections in the layer are examined in detail using a ‘numerical experimentation’ approach. First, a closed‐form solution is numerically evaluated. Then this solution is developed in series and each term is evaluated separately using the same numerical techniques. When the contribution of an individual high‐order term becomes unimportant, all higher order terms are discarded, and the response is constructed by superposition of the previously computed low‐order terms only.
Propagation by wide‐angle reflections from inside the layer is of interest. When the thickness of the layer is reduced to a fraction of the wavelength, these events consist typically of a low amplitude, high frequency, geometrical acoustics arrival, followed by higher amplitude, low frequency, non‐geometrical coda. When all important low‐order terms are added, the non‐geometrical events tend to interfere destructively, leaving a waveform nearly identical to that obtained by integration of the closed‐form solution.
When the thickness of the embedded layer is measured in fractions of the dominant wavelength, none of the individual terms of the series development can be duplicated by asymptotic ray tracing. However, because the codas of the various terms interfere destructively, the total response may be well‐represented by the addition of a few low‐order rays, using asymptotic approximation. This discovery extends the usefulness of Huygens‐Kirchhoff ray tracing to modeling of wave propagation in thin layers.
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IN SITU MEASUREMENTS OF SHEAR‐WAVE VELOCITY IN SEDIMENTS WITH HIGHER‐MODE RAYLEIGH WAVES*
Authors P. GABRIELS, R. SNIEDER and G. NOLETABSTRACTA seismic survey was carried out on a tidal flat in the SW‐Netherlands in order to determine shear‐wave velocities in sediments by means of higher‐mode Rayleigh waves. The dispersion properties of these Rayleigh waves were measured in the 2‐D amplitude spectrum–or f, k‐spectrum–and resulted in phase velocities for six different modes as a function of frequency (5–30 Hz). These observed phase velocities were inverted for a nine‐layer model for the shear‐wave velocity to a depth of 50 m.
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ANALYSIS AND IMPROVEMENT OF THE PRIMARY FIELD WAVEFORM OF THE GROUND TEM METHOD*
By BIN QIANABSTRACTMany ground TEM systems use an on‐off type of primary field waveform and measure the secondary field only in the transmitter off‐time, so as to realize the pure secondary field measurement. The width of the trailing edge of the primary pulses and the duration of the transmitter on‐time form a time‐constant (Tc) window. Most effective excitation is achieved if the target conductor has a Tc falling into this window.
To be able to measure in the transmitter on‐time, two primary field waveforms are proposed. The first is a series of unipolar pulses with identical steep ramps at both leading and trailing edges. Measurements made in the on‐time after the leading edges simply reduce the stacking time needed and power consumption by half. Also, long‐ Tc conductors are better excited. The second is a series of bipolar pulses with long ramps as the leading edges and short ramps as the trailing edges. This waveform presents two different Tc‐windows at the same time and helps to improve the detection of long‐Tc conductors in the presence of short‐ Tc ones.
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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 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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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 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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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 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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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)