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- Volume 42, Issue 6, 1994
Geophysical Prospecting - Volume 42, Issue 6, 1994
Volume 42, Issue 6, 1994
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Backus averaging, scattering and drift1
Authors M.S. Sams and P.R. WilliamsonAbstractDifferences between traveltimes from sonic to seismic frequencies, commonly known as drift, can be attributed to a combination of multiple scattering and absorption. The portion due to scattering can be estimated directly by calculating synthetic seismograms from sonic logs. A simple alternative approach is suggested by the long‐wave equivalent averaging formulae for the effective elastic properties of a stack of thin layers, which gives the same traveltime delays as the low‐frequency limit of the scattering dispersion. We consider the application of these averaging formulae over a frequency‐dependent window with the hope of extending their use to frequencies higher than those allowed by the original validity conditions. However, comparison of the time delay due to window‐averaging with the scattering dispersion predicted by the O'Doherty‐Anstey formula reveals that it is not possible to specify a form of window that will fit the dispersion across the spectrum for arbitrary log statistics. A window with a width proportional to the wavelength squared matches the behaviour at the low‐frequency end of the dispersive range for most logs, and allows an almost exact match of the drift across the entire spectrum for exponential correlation functions.
We examine a real log, taken from a hole in nearly plane‐layered geology, which displays strong quasi‐cyclical variations on one scale as well as more random, smaller‐scale fluctuations. The details of its drift behaviour are studied using simple models of the gross features. The form of window which gave a good theoretical fit to the dispersion for an exponential log correlation function can only fit the computed drift at high or low frequencies, confirming that there are at least two significant scale‐lengths of fluctuation. A better overall fit is obtained for a window whose width is proportional to the wavelength. The calculated scattering drift is significantly less than that observed from a vertical seismic profile, but the difference cannot be wholly ascribed to absorption. This is because the source frequency of the sonic tool is not appropriate for its resolution (receiver spacing) so that the scattering drift from sonic to seismic frequencies cannot be fully estimated from the layer model derived from the log.
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Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples1
Authors William W. Symes and Michel KernAbstractSeismograms predicted from acoustic or elastic earth models depend very non‐linearly on the long wavelength components of velocity. This sensitive dependence demands the use of special variational principles in waveform‐based inversion algorithms. The differential semblance variational principle is well‐suited to velocity inversion by gradient methods, since its objective function is smooth and convex over a large range of velocity models. An extension of the adjoint state technique yields an accurate estimate of the differential semblance gradient. Non‐linear conjugate gradient iteration is quite successful in locating the global differential semblance minimum, which is near the ordinary least‐squares global minimum when coherent data noise is small. Several examples, based on the 2D primaries‐only acoustic model, illustrate features of the method and its performance.
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Radar experiments in isotropic and anisotropic geological formations (granite and schists)1
More LessAbstractIn order to understand various aspects of radar wave propagation, a survey of electromagnetic wave behaviour relative to the geological characteristics of the formations prospected was undertaken. The sites chosen for the tests were a granite quarry and an underground schist working. By investigating an electrically resistive isotropic site and a conductive anisotropic site, it was demonstrated that non‐conventional use of a radar system (antennae raised, various orientations of the transmitter/receiver, etc.) could improve data quality, and could allow information other than reflector depth to be collected (volume scattering intensity, isotropy, etc.). By studying wave propagation velocities, we underlined the difficulties encountered in establishing a velocity versus depth law, despite recourse to seismic data processing, such as NMO corrections. The results of field experiments, complemented by laboratory measurements of dielectric permittivities, clearly showed anisotropy effects: in the case of a path that is perpendicular to the schistosity plane, an electromagnetic wave propagates more slowly and is more attenuated than a wave parallel to the schistosity plane.
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Sign‐change correction for prestack migration of P‐S converted wave reflections1
Authors A.H. Balch and Cemal ErdemirAbstractThe polarization direction or 'sign’ of reflected converted P–S waves depends upon the angle of incidence of the incident P‐wave. Sign reversal due to reversal of the angle of incidence is often encountered and is an impediment to P–S wave processing and imaging, because when P–S events or P‐S migrated images with mixed signs are stacked, destructive interference occurs. We have created and demonstrated a means of correcting for this reversal. To do this, a P‐wave angle of incidence is calculated for every point in the image space. This is done by calculating a P–S reflected waveform for every point, by extrapolating the reflected S‐wavefield backwards from the receiver line, and then cross‐correlating this waveform with the S‐wave reflections observed at the receiver line. A multiplier, (sgn α) is assigned to each point in the image space, where α is the angle of incidence of the P‐wave.
The multiplier was applied to a set of prestack reverse time migration images derived from a cross‐borehole physical elastic model data set. The improvement in the stacked image when the sign correction is applied is spectacular. The P‐S image quality is comparable to, or better than, stacked migrated P‐P images.
The method appears to be applicable to all reflection modes and to all recording geometries.
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An analytic signal approach to the interpretation of total field magnetic anomalies1
By Shuang QinAbstractThe analytic signal (AS) is defined as the square root of the sum of the squares of the vertical and the two horizontal derivatives of the total magnetic field ΔT. This paper verifies theoretically that peaks of the AS correlate directly with their magnetic causative bodies and are positioned symmetrically over them, i.e. the main feature of the AS is that it is independent of the inclination of the magnetic field. This avoids the difficulties that are often faced in the conventional process of reduction to pole for ΔT, when the direction of magnetization of the causative bodies is not known. In addition, the AS has characteristics similar to the derivative features of the magnetic field, so that it is very sensitive to edge effects of the causative magnetic bodies. The theoretical derivations are tested by comparison with calculations on models, and, in a field example from Hunan Province, China, the AS is applied successfully to the interpretation of ΔT, whereas the conventional process of reduction to pole fails, due to the reverse magnetization of the causative body.
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Using fractal crustal magnetization models in magnetic interpretation1
Authors M. Pilkington, M.E. Gregotski and J.P. TodoeschuckAbstractEvidence from borehole susceptibility logs and the spectral analysis of aeromagnetic data suggests that the three‐dimensional distribution of magnetization within the crust can be described as fractal. This property can be exploited in magnetic interpretation methods which explicitly require statistical information on the spatial variation of magnetization. Specifically, we address the problem of magnetic source depth estimation through downward continuation and gridding aeromagnetic survey data using the method of kriging.
When magnetic data are continued downwards the depth at which the power spectrum flattens out (the ‘white’ depth) can be taken to be an estimate of the top of the source distribution. This procedure assumes that individual sources are uncorrelated with each other. Taking into account the correlation of the magnetization using a fractal description leads to a reduction in this depth estimate.
Gridding of randomly distributed magnetic measurements using kriging requires an estimate of the covariance of the data. Compared with the assumption of a white (uncorrelated) magnetization distribution, using fractal covariances for kriging produces gridded estimates which more closely reflect the statistics of the underlying magnetization process and produce maps with a justifiable degree of smoothness.
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Pore pressure profiles in fractured and compliant rocks1
Authors Özdoǧan Yilmaz, Richard C. Nolen‐Hoeksema and Amos NurAbstractFluid permeability in fractured rocks is sensitive to pore‐pressure changes. This dependence can have large effects on the flow of fluids through rocks. We define the permeability compliance γ= 1/k(k/δpp)pc, which is the sensitivity of the permeability k to the pore pressure pp at a constant confining pressure pc, and solve the specific problems of constant pressure at the boundary of a half‐space, a cylindrical cavity and a spherical cavity. The results show that when the magnitude of permeability compliance is large relative to other compliances, diffusion is masked by a piston‐like pressure profile. We expect this phenomenon to occur in highly fractured and compliant rock systems where γ may be large. The pressure profile moves rapidly when fluids are pumped into the rock and very slowly when fluids are pumped out. Consequently, fluid pressure, its history and distribution around injection and production wells may be significantly different from pressures predicted by the linear diffusion equation. The propagation speed of the pressure profile, marked by the point where δpp/δx is a maximum, decreases with time approximately as and the amplitude of the profile also dissipates with time (or distance).
The effect of permeability compliance can be important for fluid injection into and withdrawal from reservoirs. For example, excessive drawdown could cause near‐wellbore flow suffocation. Also, estimates of the storage capacity of reservoirs may be greatly modified when γ is large. The large near‐wellbore pressure gradients caused during withdrawal by large γ can cause sanding and wellbore collapse due to excessive production rates.
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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)