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- Volume 48, Issue 1, 2000
Geophysical Prospecting - Volume 48, Issue 1, 2000
Volume 48, Issue 1, 2000
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Difficulties in determining electrical anisotropy in subsurface investigations [Link]
More LessSurface electrical and electromagnetic methods have a limited resolution capability for determining the conductivity structure of the earth. In one‐dimensional modelling a collection of many thin layers is frequently considered as one composite layer, which is then macro‐anisotropic. Neither galvanic methods nor inductive methods alone can resolve the anisotropy of the ground, but a joint inversion of galvanic and inductive data may do so. The necessity of including the coefficient of anisotropy in the joint inversion of galvanic and inductive sounding data is demonstrated. An analysis is made of the combined use of geoelectrical and transient soundings to resolve the coefficient of anisotropy of a subsurface layer for varying thickness, resistivity and coefficient of anisotropy. It is found that the coefficient of anisotropy is well resolved only for layers that are many times thicker than the overburden and for coefficients of anisotropy that are not too small. The ability of the joint inversion of geoelectrical and transient sounding data to resolve macro‐anisotropic layers is tested using realistic earth models determined from electrical logs.
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Artificial neural networks for parameter estimation in geophysics [Link]
Authors Carlos Calderón‐Macías, Mrinal K. Sen and Paul L. StoffaArtificial neural systems have been used in a variety of problems in the fields of science and engineering. Here we describe a study of the applicability of neural networks to solving some geophysical inverse problems. In particular, we study the problem of obtaining formation resistivities and layer thicknesses from vertical electrical sounding (VES) data and that of obtaining 1D velocity models from seismic waveform data. We use a two‐layer feedforward neural network (FNN) that is trained to predict earth models from measured data. Part of the interest in using FNNs for geophysical inversion is that they are adaptive systems that perform a non‐linear mapping between two sets of data from a given domain. In both of our applications, we train FNNs using synthetic data as input to the networks and a layer parametrization of the models as the network output. The earth models used for network training are drawn from an ensemble of random models within some prespecified parameter limits. For network training we use the back‐propagation algorithm and a hybrid back‐propagation–simulated‐annealing method for the VES and seismic inverse problems, respectively. Other fundamental issues for obtaining accurate model parameter estimates using trained FNNs are the size of the training data, the network configuration, the description of the data and the model parametrization. Our simulations indicate that FNNs, if adequately trained, produce reasonably accurate earth models when observed data are input to the FNNs.
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Green's function interpolations for prestack imaging [Link]
More LessA new interpolation method is presented to estimate the Green's function values, taking into account the migration/inversion accuracy requirements and the trade‐off between resolution and computing costs. The fundamental tool used for this technique is the Dix hyperbolic equation (DHE). The procedure, when applied to evaluate the Green's function for a real source position, uses the DHE to derive the root‐mean‐square velocity, vRMS, from the precomputed traveltimes for the nearest virtual sources, and by linear interpolation generates vRMS for the real source. Then, by applying the DHE again, the required traveltimes and geometrical spreading can be estimated.
The inversion of synthetic data demonstrates that the new interpolation yields excellent results which give a better qualitative and quantitative resolution of the imaging sections, compared with those carried out by conventional linear interpolation. Furthermore, the application to synthetic and real data demonstrates the ability of the technique to interpolate Green's functions from widely spaced virtual sources. Thus the proposed interpolation, besides improving the imaging results, also reduces the overall CPU time and the hard disk space required, hence decreasing the computational effort of the imaging algorithms.
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GPR study of pore water content and salinity in sand [Link]
More LessHigh‐resolution studies of hydrological problems of the near‐surface zone can be better accomplished by applying ground‐probing radar (GPR) and geoelectrical techniques. We report on GPR measurements (500 and 900 MHz antennae) which were carried out on a sorted, clean sand, both in the laboratory and at outdoor experimental sites. The outdoor sites include a full‐scale model measuring 5 × 3 × 2.4 m3 and a salinity site measuring 7.0 × 1.0 × 0.9 m3 with three buried sand bodies saturated with water of various salinities. Our studies investigate the capability of GPR to determine the pore water content and to estimate the salinity. These parameters are important for quantifying and evaluating the water quality of vadose zones and aquifers. The radar technique is increasingly applied in quantifying soil moisture but is still rarely used in studying the problems of water salinity and quality.
The reflection coefficient at interfaces is obtained from the amplitude spectrum in the frequency and time domains and is confirmed by 1D wavelet modelling. In addition, the GPR velocity to a target at a known depth is determined using techniques of two‐way traveltime, CMP semblance analysis and fitting an asymptotic diffraction curve.
The results demonstrate that the reflection coefficient increases with increasing salinity of the moisture. These results may open up a new approach for applications in environmental problems and groundwater prospecting, e.g. mapping and monitoring of contamination and evaluating of aquifer salinity, especially in coastal areas with a time‐varying fresh‐water lens. In addition, the relationship between GPR velocity and water content is established for the sand. Using this relationship, a subsurface velocity distribution for a full‐scale model of this sand is deduced and applied for migrated radargrams. Well‐focused diffractions separate single small targets (diameter of 2–3 cm, at a depth of 20–180 cm and a vertical interval of 20 cm). The results underscore the high potential of GPR for determining moisture content and its variation, flow processes and water quality, and even very small bodies inside the sand or soil.
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Quantitative estimate of VTI parameters from AVA responses [Link]
Authors René‐Edouard Plessix and Jonathan BorkThe influence of the vertical transverse isotropy (VTI) on amplitude versus angle (AVA) responses is first studied on the linearized formula of the PP‐reflection coefficient. Up to medium angles of incidence, as in the isotropic case, only two quantities can be retrieved, the second with less accuracy than the first. These quantities are the P‐impedance and the S‐impedance multiplied by 1− δ/2, where δ is one of the two anisotropic parameters introduced by Thomsen. To extend these results to the exact formulae, the AVA analysis is then formulated as an inverse problem and a least‐squares cost function is defined. A study of the eigenvalues and eigenvectors of the Hessian of the least‐squares cost function confirms these results. Though these results are dependent on the amount of data and on the maximum angle of incidence available, they are appropriate for small and medium angles of incidence. Thanks to this inverse formulation, this work can be extended to the case of multicomponent AVA responses. The addition of PS‐reflection data further constrains the problem, but the S‐impedance and δ are still coupled. However, the addition of SS‐reflection data gives an estimation of both P‐ and S‐impedances and δ. The last two parameters, the density and the second anisotropic parameter ɛ, remain difficult to determine, at least with small‐to‐medium angular apertures.
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Non‐linear three‐dimensional inversion of cross‐well electrical measurements [Link]
Authors Aria Abubakar and Peter M. Van Den BergCross‐well electrical measurement as known in the oil industry is a method for determining the electrical conductivity distribution between boreholes from the electrostatic field measurements in the boreholes. We discuss the reconstruction of the conductivity distribution of a three‐dimensional domain. The measured secondary electric potential field is represented in terms of an integral equation for the vector electric field. This integral equation is taken as the starting point to develop a non‐linear inversion method, the so‐called contrast source inversion (CSI) method. The CSI method considers the inverse scattering problem as an inverse source problem in which the unknown contrast source (the product of the total electric field and the conductivity contrast) in the object domain is reconstructed by minimizing the object and data error using a conjugate‐gradient step, after which the conductivity contrast is updated by minimizing only the error in the object. This method has been tested on a number of numerical examples using the synthetic ‘measured’ data with and without noise. Numerical tests indicate that the inversion method yields a reasonably good reconstruction result, and is fairly insensitive to added random noise.
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A platform for Kirchhoff data mapping in scalar models of data acquisition [Link]
More LessKirchhoff data mapping (KDM) is a procedure for transforming data from a given input source/receiver configuration and background earth model to data corresponding to a different output source/receiver configuration and background model. The generalization of NMO/DMO, datuming and offset continuation are three examples of KDM applications. This paper describes a ‘platform’ for KDM for scalar wavefields. The word, platform, indicates that no calculations are carried out in this paper that would adapt the derived formula to any one of a list of KDMs that are presented in the text. Platform formulae are presented in 3D and in 2.5D. For the latter, the validity of the platform equation is verified — within the constraints of high‐frequency asymptotics — by applying it to a Kirchhoff approximate representation of the upward scattered data from a single reflector and for an arbitrary source/receiver configuration. The KDM formalism is shown to map this Kirchhoff model data in the input source/receiver configuration to Kirchhoff data in the output source/receiver configuration, with one exception. The method does not map the reflection coefficient. Thus, we verify that, asymptotically, the ray theoretical geometrical spreading effects due to propagation and reflection (including reflector curvature) are mapped by this formalism, consistent with the input and output modelling parameters, while the input reflection coefficient is preserved. In this sense, this is a ‘true‐amplitude’ formalism. As with earlier Kirchhoff inversion, a slight modification of the kernel of KDM provides alternative integral operators for estimating the specular reflection angle, both in the input configuration and in the output configuration, thereby providing a basis for amplitude‐versus‐angle analysis of the data.
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2D multiscale non‐linear velocity inversion
Authors Side Jin and Wafik BeydounAn efficient and robust non‐linear inversion method for velocity optimization combining a global random search followed by a simplex technique is presented. The background velocity field is estimated at different spatial scales by analysing image gathers after iterative prestack depth migrations. First, the global random search is used to determine the main features/trends of the velocity model (large‐scale component). Then, the simplex technique improves the resolution of the velocity field by estimating smaller‐scale features. A measure of the quality of the velocity model (objective function) is based on flattening offset events in depth‐migrated image gathers. To help constrain the solution, the algorithm can incorporate a priori information about the model and a smoothness condition. This 2D velocity estimation offers the benefit of being semi‐automatic (requiring minimal human intervention) as well as providing a global and objective solution (which is a useful approach to an interpretation‐derived velocity‐estimation technique). The method is applied to a real data set where AVO analysis is carried out after prestack depth migration, as structural effects are non‐negligible. It is demonstrated that the method can successfully estimate a laterally inhomogeneous velocity model at a computational cost modest compared with an interpretation‐based iterative prestack depth velocity‐analysis technique.
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Short note on electrode charge‐up effects in DC resistivity data acquisition using multi‐electrode arrays
More LessThe measurement sequence used in DC resistivity data using multi‐electrode arrays should be carefully designed so as to minimize the effects of electrode charge‐up effects. These effects can be some orders of magnitude larger than the induced signal and remain at significant levels for tens of minutes. Even when using a plus‐minus‐plus type of measurement cycle, one should avoid making potential measurements with an electrode that has just been used to inject current, as the decay immediately after current turn‐off is clearly non‐linear.
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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)