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- Volume 48, Issue 4, 2000
Geophysical Prospecting - Volume 48, Issue 4, 2000
Volume 48, Issue 4, 2000
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Diffraction problems of 3D seismic imaging
More LessMigration is essential to seismic imaging. It is carried out by backward extrapolation of the wavefield registered on the observation surface. The quality of images depends on the accuracy of the wavefield reconstruction at interior subsurface points. From the theory based on the exact solution of the scalar wave equation it is known that, for accurate wave extrapolation, data must be obtained from an infinite observation surface. Limiting of migration apertures, which is inevitable in practice, leads to artefacts in extrapolated fields. The distortion they cause in 2D and 3D imaging is different. In 2D migration, the artefacts known as truncation effects are much weaker than the signals being extrapolated and for this reason attract no special attention. In 3D migration, diffractions caused by an aperture edge are stronger and may create serious problems. For a circular aperture, their amplitudes are comparable to the amplitudes of the signals themselves. The study of aperture diffractions is intended to help in the search for ways of either suppressing them efficiently or deliberately utilizing them in order to improve imaging.
In optics, diffractions by an aperture play a constructive role in image making. This research shows that the same may take place in seismic imaging.
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Salt‐water intrusion mapping by geoelectrical imaging surveys
Authors S.S. Abdul Nassir, M.H. Loke, C.Y. Lee and M.N.M. NawawiThe geoelectrical imaging method is a tool for mapping the intrusion boundary between fresh water and saline water due to its inherent capability to delineate the lateral changes in pore‐water salinity. A new field survey technique that can be used for environmental and geotechnical investigations has been developed. This study evaluates the multiscale survey technique as a tool employed in electrical imaging to detect the salt‐water intrusion boundary in Yan, State of Kedah, northwest Malaysia. The technique was incorporated into these surveys, and it has proved to be a robust method for accurately mapping the fresh‐water/saline‐water boundary. The resulting resistivity sections from these surveys were consistent with both the available geological and borehole information from the area and the previous resistivity surveys conducted by the Geological Survey of Malaysia at those sites.
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Estimation of an optimal mixed‐phase inverse filter
Authors Bjorn Ursin and Milton J. PorsaniInverse filtering is applied to seismic data to remove the effect of the wavelet and to obtain an estimate of the reflectivity series. In many cases the wavelet is not known, and only an estimate of its autocorrelation function (ACF) can be computed. Solving the Yule‐Walker equations gives the inverse filter which corresponds to a minimum‐delay wavelet. When the wavelet is mixed delay, this inverse filter produces a poor result.
By solving the extended Yule‐Walker equations with the ACF of lag α on the main diagonal of the filter equations, it is possible to decompose the inverse filter into a finite‐length filter convolved with an infinite‐length filter. In a previous paper we proposed a mixed‐delay inverse filter where the finite‐length filter is maximum delay and the infinite‐length filter is minimum delay.
Here, we refine this technique by analysing the roots of the Z‐transform polynomial of the finite‐length filter. By varying the number of roots which are placed inside the unit circle of the mixed‐delay inverse filter, at most 2α different filters are obtained. Applying each filter to a small data set (say a CMP gather), we choose the optimal filter to be the one for which the output has the largest Lp‐norm, with p=5. This is done for increasing values of α to obtain a final optimal filter. From this optimal filter it is easy to construct the inverse wavelet which may be used as an estimate of the seismic wavelet.
The new procedure has been applied to a synthetic wavelet and to an airgun wavelet to test its performance, and also to verify that the reconstructed wavelet is close to the original wavelet. The algorithm has also been applied to prestack marine seismic data, resulting in an improved stacked section compared with the one obtained by using a minimum‐delay filter.
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The effectiveness of azimuthal apparent‐resistivity measurements as a method for determining fracture strike orientations
By J.P. BusbyAzimuthal apparent‐resistivity measurements are made for the purpose of determining the strike direction of subvertical fracture sets. Data are collected about a common centre, with an electrode array expanded along a sufficient number of azimuths to define the variation of apparent resistivity with orientation. The apparent resistivities for any one electrode spacing are then plotted in a polar diagram. If the data form an ellipse, this is often interpreted as reflecting aligned, subvertical fracturing. However, it is also possible for heterogeneity within the rockmass to manifest itself, at the scale of the measurement, as a variation of apparent resistivity with azimuth. It is recommended that the offset Wenner array is used for all measurements and that a parameter is introduced, the homogeneity index, which defines whether the variations due to homogeneous anisotropy, such as subvertical fracturing, are greater than those due to inhomogeneity. This simple parameter, which is the quotient of two standard deviations, is valid for both single‐peaked and multiple‐peaked ellipses. A four‐stage scheme for the interpretation of azimuthal data is suggested and a consistent set of quantitative measures is recommended. These will allow data, collected by different workers over different lithologies, to be compared. There are a number of geological situations which can give rise to anisotropy within the rockmass and great care is needed when interpreting azimuthal data in terms of aligned fracturing. Numerical modelling of the response to a buried channel of a rotated offset Wenner array demonstrates that elliptical data are generated by such a linear feature. Depending on the location of the array with respect to the channel, these data are either indistinguishable from those generated by aligned fracturing, or can be recognized by application of the homogeneity index. In the case where the response can be identified as being due to a channel, diagnostic information can be derived on the location and strike of the channel.
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Practical aspects of wavefield separation of two‐component surface seismic data based on polarization and slowness estimates
Authors Sandra Richwalski, Kabir Roy‐Chowdhury and Jaap C. MondtThe processing of multicomponent seismic data, carried out individually on the different wavetypes (P‐, S‐ and converted waves), should result in an improved image of the subsurface. We examine the wavefield‐separation method proposed by Cho and Spencer. We discuss practical aspects related to the separation of interfering waves on two‐component surface seismic data and illustrate these using synthetic data. A sliding spatial window is used for analysis. The choice of its width represents a trade‐off between stabilizing the method in the presence of random noise and ensuring a good spatial resolution. No a priori knowledge of the subsurface is required, but locally, the characteristic parameters of the waves, i.e. horizontal slowness and polarization, are assumed to be constant inside the analysis window. These parameters are estimated at each frequency, but a statistical analysis provides a more robust estimate, especially in the presence of random noise. This approach also solves the problem of eigenvalue sharing and switching. Additional smoothing of the estimates according to a model may further improve the results. The width of the analysis window may be decreased if the waves inside the data window differ significantly in amplitude. The dominant wave in each case is separated from the lower‐amplitude waves and subtracted from the data. This novel iterative approach thereby allows for the isolation of low‐amplitude events.
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3D adaptive tomography using Delaunay triangles and Voronoi polygons
Authors Gualtiero Böhm, Paolo Galuppo and Aldo VesnaverThe solutions of traveltime inversion problems are often not unique because of the poor match between the raypath distribution and the tomographic grid. However, by adapting the local resolution iteratively, by means of a singular value analysis of the tomographic matrix, we can reduce or eliminate the null space influence on our earth image: in this way, we get a much more reliable estimate of the velocity field of seismic waves. We describe an algorithm for an automatic regridding, able to fit the local resolution to the available raypaths, which is based on Delaunay triangulation and Voronoi tessellation. It increases the local pixel density where the null space energy is low or the velocity gradient is large, and reduces it elsewhere. Consequently, the tomographic image can reveal the boundaries of complex objects, but is not affected by the ambiguities that occur when the grid resolution is not adequately supported by the available raypaths.
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Detection and identification of north–south trending magnetic structures near the magnetic equator
By Les P. BeardLong, structurally undeformed north–south trending structures show no magnetic anomaly at the magnetic equator, except at the north and south truncations of the structure. However, folding, faulting, differential erosion or other structural deformation can produce detectable magnetic anomalies in a generally north–south trending equatorial structure. Spatial variation in magnetic susceptibility or remanent magnetization can also produce anomalies in equatorial north–south structures. These anomaly patterns are often more complicated than patterns produced by similar structures at high latitudes, but interpretational insight can be gained through numerical modelling of common structures. Reduction‐to‐pole and analytic signal filters can aid in interpretation of equatorial anomalies, but these must be applied carefully because of instabilities deriving from filter design and noise amplification.
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Large‐offset approximation to seismic reflection traveltimes
Authors Emmanuel Causse, Geir Ultveit Haugen and Björn Eino RommelConventional approximations of reflection traveltimes assume a small offset‐to‐depth ratio, and their accuracy decreases with increasing offset‐to‐depth ratio. Hence, they are not suitable for velocity analysis and stacking of long‐offset reflection seismic data. Assuming that the offset is large, rather than small, we present a new traveltime approximation which is exact at infinite offset and has a decreasing accuracy with decreasing offset‐to‐depth ratio. This approximation has the form of a series containing powers of the offset from 1 to −∞. It is particularly accurate in the presence of a thin high‐velocity layer above the reflector, i.e. in a situation where the accuracy of the Taner and Koehler series is poor. This new series can be used to gain insight into the velocity information contained in reflection traveltimes at large offsets, and possibly to improve velocity analysis and stacking of long‐offset reflection seismic data.
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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)