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- Volume 45, Issue 5, 1997
Geophysical Prospecting - Volume 45, Issue 5, 1997
Volume 45, Issue 5, 1997
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Magnetotelluric inversion using regularized Hopfield neural networks[Link]
Authors Yuanchou Zhang and K. V. PaulsonHopfield neural networks are massive parallel automata that support specific models and are adept in solving optimization problems. They suffer from a ‘rough’ solution space and convergence properties that are highly dependent on the starting model or prior. These detractions may be overcome by introducing regularization into the network in the form of local feedback smoothing. Application of regularized Hopfield networks to over 50 optimization test cases has yielded successful results, even with uniform (minimal information) priors. In particular, the non‐linear, one‐ and two‐dimensional magnetotelluric inverse problems have been solved by means of these regularized networks. The solutions compare favourably with those produced by other methods. Such regularized networks, with either hardware or programmed, parallel‐computer implementation, can be extended to the problem of three‐dimensional magnetotelluric inversion. Because neural networks are natural analog‐to‐digital converters, it is predicted that they will be the basic building blocks of future magnetotelluric instrumentation.
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New digital linear filters for Hankel J0 and J1 transforms[Link]
Authors D. Guptasarma and B. SinghThe numerical evaluation of certain integral transforms is required for the interpretation of some geophysical exploration data. Digital linear filter operators are widely used for carrying out such numerical integration.
It is known that the method of Wiener–Hopf minimization of the error can be used to design very efficient, short digital linear filter operators for this purpose. We have found that, with appropriate modifications, this method can also be used to design longer filters. Two filters for the Hankel J0 transform (61‐point and 120‐point operators), and two for the Hankel J1 transform (47‐point and 140‐point operators) have been designed. For these transforms, the new filters give much lower errors compared to all other known filters of comparable, or somewhat longer, size. The new filter operators and some results of comparative performance tests with known integral transforms are presented.
These filters would find widespread application in many numerical evaluation problems in geophysics.
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A compact representation of magnetotelluric responses for two‐layer models[Link]
More LessIn this paper the locations where ρapp = ρ1 and ϕ = π/4 and where these parameters reach an extreme value in two‐layer magnetotelluric (MT) sounding curves are summarized in an extremely compact form. The key parameters over two‐layer models with conductivities σ1, σ2 and upper layer thickness h are the real S and α, where S is the conductivity contrast and α is the distance between the observation site and the conductivity interface, normalized to the half skindepth in the first layer. If the impedance components, various resistivity definitions ( ρRe Z, ρIm Z and ρ|Z|, based on different parts of the complex impedance Z ) and the magnetotelluric phase ϕ are derived as a function of S and α, then the conditions for the apparent resistivity ρapp and the phase ϕ are that they either satisfy ρapp = ρ1 and ϕ = π/4 or attain extreme values which can be given in terms of simple algebraic equations between S and α. All equations are valid for observation sites at any depth 0 ≤ z ≤ h in the first layer. The set of equations, presented in a tabular form, may make it possible to determine a layer boundary from the short period part of the sounding curves, in particular the ρRe Z and the ϕMT curves.
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Effects of anelasticity on reflection and transmission coefficients[Link]
Authors S. Nechtschein and F. HronIt is known that the reflection and transmission coefficients used in the zeroth order approximation of asymptotic ray theory (ART) are identical to those obtained for the plane wave impinging on a plane interface separating two perfectly elastic half‐spaces. We have used ART to compute reflection and transmission coefficients for two viscoelastic media separated by a plane interface. Our method is different from the plane‐wave approach because the ART approach requires only a local application of the boundary conditions both for the eikonal and the ray amplitudes.
Several types of viscoelastic media were studied. For a given model, the elastic case was emulated by setting all the quality factors Q equal to each other. Several anelastic cases were computed by keeping the same velocities and densities while changing the Qs. The quality factor is a relatively difficult parameter to measure exactly. Hence elastic coefficients are used in most synthetic seismogram computations, and the quality factors are chosen from experimental measurements or simply estimated.
From these computations, amplitude and phase differences between elastic coefficients and coefficients for dissipative media are observed in some cases. These differences show the importance of knowing the exact values of Q. Incorrect Q values can lead to unrealistic moduli and to noticeable phase differences of these viscoelastic coefficients.
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Theoretical study of slope effects in resistivity surveys and applications[Link]
Authors H. Sahbi, D. Jongmans and R. CharlierWhen electric soundings are made over an irregular terrain, topographic effects can influence the values of apparent resistivity and lead to erroneous 1D interpretation. A 3D finite‐element method has been applied to study the topographical effect of a slope on Schlumberger soundings parallel to the strike. When the resistivity survey is performed at the top of the slope, the apparent resistivity values can be two times higher than in the flat‐earth case, depending on the angle (α) and height (H) of the slope, and on the distance (X) between the sounding and the slope top. The results are presented as nondimensional curves which can be used for evaluating topographic anomalies for any value of the parameters α, H and X. It is numerically shown that the topographic effects can be removed from measurements on horizontally layered structures with an irregular earth surface. Real measurements were performed in different geological conditions over an irregular terrain. The correction method based on the nondimensional curves has been applied to the data and has enabled the determination of the correct layered ground configuration using 1D interpretation.
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Complex polynomials for the computation of 2D gravity anomalies[Link]
Authors Sergio E. Oliva and Claudia L. RavazzoliWe present an efficient algorithm using a complex variables formulation for the computation of the gravity effect of 2D polygonal bodies having densities varying both laterally and with depth. The first derivatives of the gravity effect are also provided in order to enable the computation of the Jacobian matrix, which is necessary for linear inverse gravity problems. A geophysical example based on numerical assumptions about the density contrast on a well‐studied basin area shows the applicability of the algorithm.
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A hexagonal sampling grid for 3D recording and processing of 3D seismic data[Link]
More Less3D seismic data are usually recorded and processed on rectangular grids, for which sampling requirements are generally derived from the usual 1D viewpoint. For a 3D data set, the band region (the region of the Fourier space in which the amplitude spectrum is not zero) can be approximated by a domain bounded by two cones. Considering the particular shape of this band region we can use the 3D sampling viewpoint, which leads to weaker sampling requirements than does the 1D viewpoint; i.e. fewer sample points are needed to represent data with the same degree of accuracy. The 3D sampling viewpoint considers regular nonrectangular sampling grids.
The recording and processing of 3D seismic data on a hexagonal sampling grid is explored. The acquisition of 3D seismic data on a hexagonal sampling grid is an advantageous economic alternative because it requires 13.4% fewer sample points than a rectangular sampling grid. The hexagonal sampling offers savings in data storage and processing of 3D seismic data.
A fast algorithm for 3D discrete spectrum evaluation and trace interpolation in the case of a 3D seismic data set sampled on a hexagonal grid is presented and illustrated by synthetic examples. It is shown that by using this algorithm the hexagonal sampling offers, approximately, the same advantage of saving 13.4% in data storage and computational time for 3D phase‐shift migration.
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The reliability of aeroplane attitude determination using the main geomagnetic field with application to tensor VLF data analysis[Link]
Authors M. Bastani and L.B. PedersenThe attitude angles of an aeroplane used for geophysical measurements are necessary in order to calculate field components in a fixed reference frame. In this paper it is shown analytically how the measurement of static magnetic field components can be used to determine the attitude angles. Error analysis shows that when magnetic anomalies are small to moderate (less than 5% of the total field), the attitude angles can be determined to within a few degrees at high latitudes. For a given area the maximum error is linearly related to the magnitude of the anomaly.
The technique is illustrated on a tensor VLF data set from an area in Sweden with local magnetic anomalies less than 1% of the regional total magnetic field. Attitude errors propagated into tensor VLF transfer functions are of the same order as their random errors.
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Self‐potential global tomography including topographic effects[Link]
More LessThis paper is an extension of a previous study, in which the principles of self‐potential ground surface tomography were outlined. The new arguments which are here set forth are the proper accounting for the topographic effects and a robust approach to global 3D tomography. The 2D case is initially considered in order to facilitate a full understanding of the new method. In order to gauge the topographic distortions, the concepts of slope effect and surface regularization are introduced, as suitable means to compute point by point correction factors of the measured self‐potential data, prior to the recognition of the tomographic images of the primary and induced electric sources underground. The tomographic approach is then developed by introducing again the concepts of the scanning function and of the charge occurrence probability function, which were amply dealt with in the previous paper. The new approach to 3D global tomography means here the composition of charge occurrence probability functions related to any two orthogonal surface components of the natural electric field, in order to account fully for the total surface component of the self‐potential field and hence to elicit the greatest amount of information. Two field examples are presented to show the full effectiveness of the proposed method. They refer, respectively, to a near‐surface investigation for archaeological purposes and to a very deep investigation in an active volcanic area.
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Migration velocity analysis using a genetic algorithm[Link]
Authors Paul Docherty, Ron Silva, Satish Singh, Zhong‐Min Song and Margaret WoodMigration velocity analysis, a method for determining long wavelength velocity structure, is a critical step in prestack imaging. Solution of this inverse problem is made difficult by a multimodal objective function; a parameter space often vast in extent; and an evaluation procedure for candidate solutions, involving the calculation of depth‐migrated image gathers, that can be prohibitively expensive. Recognizing the global nature of the problem, we employ a genetic algorithm (GA) in the search for the optimum velocity model. In order to describe a model efficiently, regions of smooth variation are identified and sparsely parametrized. Region boundaries are obtained via map migration of events picked on the zero‐offset time section. Within a region, which may contain several reflectors, separate components describe long and short wavelength variations, eliminating from the parameter space, models with large velocity fluctuations. Vital to the success of the method is rapid model evaluation, achieved by generating image gathers only in the neighbourhood of specific reflectors. Probability of a model, which we seek to maximize, is derived from the flatness of imaged events. Except for an initial interpretation of the zero‐offset time section, our method is automatic in that it requires no picking of residual moveout on migrated gathers. Using an example data set from the North Sea, we show that it is feasible to solve for all velocity parameters in the model simultaneously: the method is global in this respect also.
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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)