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- Volume 34, Issue 2, 1986
Geophysical Prospecting - Volume 34, Issue 2, 1986
Volume 34, Issue 2, 1986
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WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS.
Authors C. P. A. WAPENAAR and A. J. BERKHOUTABSTRACTIn one‐way wave field extrapolation downgoing and upgoing waves are treated independently, which is allowed if propagation at small angles against the vertical in (weakly) inhomogeneous media is considered. In practical implementation the slow convergence of the square‐root operator causes numerical deficiencies. On the other hand, in two‐way wave field extrapolation no assumptions need to be made on the separability of downgoing and upgoing waves. Furthermore, in practical implementation the use of the square‐root operator is avoided. To put the two‐way techniques into perspective, it is shown that two‐way wave field extrapolation could be described in terms of one‐way processes, namely: (1) decomposition of the total wave field into downgoing and upgoing waves; (2) one‐way wave field extrapolation; (3) composition of the total wave field from its downgoing and upgoing constituents. This alternative description of two‐way wave field extrapolation is valid for media which are homogeneous along the z‐coordinate as well as for small dip angles in arbitrarily inhomogeneous media. In addition, it is shown that this description is also valid for large dip angles in 1‐D (vertically) inhomogeneous media, including critical‐angle events, when the WKBJ one‐way wave functions discussed in part I of this paper are considered.
For large dip angles in arbitrarily inhomogeneous media the two‐way wave equation is solved by means of Taylor series expansion. For practical implementation a truncated operator is designed, assuming gentle horizontal variations of the medium properties. This operator is stable and converges already in the first order approximation, also for critical‐angle events.
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WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS.
Authors C. P. A. WAPENAAR and A. J. BERKHOUTAbstractWave field extrapolation including critical angle events in modeling, migration and inversion can be handled with algorithms based on both the one‐way wave equations and the two‐way wave equation. It is shown that for 1‐D inhomogeneous media, critical angle events as well as multiple reflections may elegantly be included in pre‐stack modeling, pre‐stack migration and velocity inversion. For 2‐D and 3‐D inhomogeneous media a powerful pre‐stack migration scheme can be developed which includes critical angle events as well as multiple reflections. Finally, suggestions for practical applications are given.
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A NEW APPROACH TO THE INVERSION OF SEISMIC DATA*
Authors B. S. THORNTON and G. R. SUTTONABSTRACTA new inversion method for seismic reflection data is based on impedance concepts and uses transformations to reduce the essentially non‐linear problem to a linear eigenvalue formulation without approximation. A set of reflection data has been inverted using this method. The characteristic impedances of the layers so determined are compared with log data from a reference borehole.
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QUANTITATIVE INTERPRETATION OF PULSE EM MEASUREMENTS OVER A WEATHERED KIMBERLITE DIATREME*
Authors S. S. RAI and B. B. BHATTACHARYAAbstractThe application of pulse EM and MAXMIN II systems in search of a kimberlite diatremes under conducting cover has been demonstrated through a field example. The effectiveness of the PEM system in the search for conductive zones of economic importance and in discrimination against geologic noise such as overburden has been investigated. The transient observation has been transformed to equivalent half‐space resistivities at various times. The feasibility of mapping thin conducting overburden using the PEM system has been studied by inverting the transient measurement to the thin infinite horizontal sheet conductance. The PEM measurement is shown to be an economic and effective tool for shallow geoelectric mapping.
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IN‐LOOP PULSE EM RESPONSE OF A STRATIFIED EARTH*
Authors S. S. RAI and G. S. SARMAABSTRACTThe in‐loop pulse electromagnetic response of a stratified earth has been expressed in terms of an apparent resistivity‐ time plot using the PEM response over a homogeneous half‐space which is typically unipolar with monotonic decay. This half‐space response characteristic provides a unique relationship between Crone PEM channel amplitude and the apparent half‐space resistivity. The possibility to resolve a thin intermediate conductive and resistive layer with the in‐loop PEM system has been investigated. The system is well in shallow geoelectric mapping.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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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 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)