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- Volume 46, Issue 1, 1998
Geophysical Prospecting - Volume 46, Issue 1, 1998
Volume 46, Issue 1, 1998
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Interpreting non‐orthogonal split shear waves for seismic anisotropy in multicomponent VSPS
Authors Xiang‐Yang Li, Colin MacBeth and Stuart CrampinThere are two main sources of non‐orthogonality in multicomponent shear‐wave seismics: inherent non‐orthogonal split shear waves arising from substantial ray deviation in off‐symmetry planes due to strong anisotropy or complex overburden, and apparent non‐orthogonal split shear waves in the horizontal plane due to variation of the angle of incidence even if the two shear waves along the raypath are orthogonal. Many techniques for processing shear‐wave splitting in VSP data ignore these kinds of non‐orthogonality of the split shear waves.
Assuming inherent non‐orthogonality in zero‐offset VSPs, and apparent non‐orthogonality in offset VSPs, we derive equations for the four‐component data matrix. These can be solved by extending the linear‐transform technique (LTT) to determine the shear‐wave polarizations in zero‐offset and offset VSPs. Both full‐wave synthetic and field data are used to evaluate the technique and to examine the effects of non‐orthogonal polarized split shear waves.
If orthogonality is incorrectly assumed, errors in polarization measurements increase with the degree of non‐orthogonality, which introduces a consistent decreasing trend in the polarization measurements. However, the effect of non‐orthogonality on the estimation of geophone orientation and time delays of the two split shear waves is small and negligible in most realistic cases. Furthermore, for most cases of weak anisotropy (less than 5% shear‐wave anisotropy) apparent non‐orthogonality is more significant than inherent non‐orthogonality. Nevertheless, for strong anisotropy (more than 10% shear‐wave anisotropy) with complicated structure (tilted or inclined symmetry axis), inherent non‐orthogonality may no longer be negligible.
Applications to both synthetic and real data show that the extended linear‐transform techniques permit accurate recovery of polarization measurements in the presence of both significant inherent and apparent non‐orthogonality where orthogonal techniques often fail.
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Estimation of reservoir fracturing from marine VSP using local shear‐wave conversion
Authors Colin MacBeth, Mark Boyd, William Rizer and John QueenA marine VSP is designed to estimate the orientation and density of fracturing within a gas‐producing dolomite layer in the southern North Sea. The overburden anisotropy is firstly estimated by analysing shear waves converted at or just below the sea‐bed, from airgun sources at four fixed offset azimuths. Full‐wave modelling helps confirm that the background has no more than 3% vertical birefringence, originating from TIH anisotropy with a symmetry axis orientated perpendicular to the maximum horizontal compressive stress of NW–SE. This finding concurs with current hypotheses regarding the background rock matrix in the upper crust. More detailed anisotropy estimates reveal two thin zones with possible polarization reversals and a stronger anisotropy. The seismic anisotropy of the dolomite is then determined from the behaviour of locally converted shear waves, providing a direct link with the physical properties of its fractures. It is possible to utilize this phenomenon due to the large seismic velocity contrast between the dolomite and the surrounding evaporites. Two walkaway VSPs at different azimuths, recorded on three‐component receivers placed inside the target zone, provide the appropriate acquisition design to monitor this behaviour. Anisotropy in the dolomite generates a transverse component energy which scales in proportion to the degree of anisotropy. The relative amplitudes, for this component, between the different walkaway azimuths relate principally to the orientation of the anisotropy. Full‐wave modelling confirms that a 50% vertical birefringence from TIH anisotropy with a similar orientation to the overburden is required to simulate the field observations. This amount of anisotropy is not entirely unexpected for a fine‐grained brittle dolomite with a potentially high fracture intensity, particularly if the fractures contain fluid which renders them compliant to the shear‐wave motion.
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Background velocity estimation using non‐linear optimization for reflection tomography and migration misfit
Authors Carlos L. Varela, Paul L. Stoffa and Mrinal K. SenWe show that it is possible to estimate the background velocity for prestack depth migration in 2D laterally varying media using a non‐linear optimization technique called very fast simulated annealing (VFSA). We use cubic splines in the velocity model parametrization and make use of either successive pairs of shot gathers or several constant‐offset sections as input data for the inversion. A Kirchhoff summation scheme based on first‐arrival traveltimes is used to migrate/model the input data during the velocity analysis. We evaluate and compare two different measures of error. The first is defined in the recorded data or (x,t) domain and is based on a reflection‐tomography criterion. The second is defined in the migrated data or (x,z) domain and is based on a migration‐misfit criterion. Depth relaxation is used to improve the convergence and quality of the velocity analysis while simultaneously reducing the computational cost. Further, we show that by coarse sampling in the offset domain the method is still robust.
Our non‐linear optimization approach to migration velocity analysis is evaluated for both synthetic and real seismic data. For the velocity‐analysis method based on the reflection‐tomography criterion, traveltimes do not have to be picked. Similarly, the migration‐misfit criterion does not require that depth images be manually compared. Interpreter intervention is required only to restrict the search space used in the velocity‐analysis problem. Extension of the proposed schemes to 3D models is straightforward but practical only for the fastest available computers.
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Some unintended features of elastic finite‐difference models
Authors A.J. Wild and S.C. SinghWhile finite‐difference methods have been used extensively for many years to model wave propagation in elastic media, some of the more subtle effects observable in such models are very inadequately documented in the geophysical literature, especially in regard to their practical numerical consequences.
In addition to the intended travelling waves, and the undesirable exponential instability revealed by the von Neumann test, typical second‐order‐time finite‐difference equations also support drifting linear solutions, as can be verified, both theoretically and by numerical experiment. The necessity of these solutions, and their relationship to the incompleteness of the set of travelling‐wave eigenfunctions of the finite‐difference operator, can be exposed by a matrix‐based analysis, and exact expressions for them can be obtained by using standard algebraic techniques.
A further peculiarity of the finite‐difference formulation is numerical anisotropy, which emerges in a grid of more than one spatial dimension, even when the modelled medium is intended to be isotropic. This anisotropy can be explained and quantified in terms of the exact eigenfunction solutions to the finite‐difference equation, which, it is found, can be obtained in a simple, closed form, for a typical modern 3D staggered scheme.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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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)