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  • 1
    Electronic Resource
    Electronic Resource
    Numerical modelling of airborne electromagnetic anomalies originating from low-conductivity 3D bodies (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 44 (1996), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Responses of a multifrequency, multicoil airborne electromagnetic (AEM) system were modelled numerically for 3D electrical conductors embedded in a resistive bedrock and overlain by an overburden of low to moderate conductivity. The results cover a horizontal coplanar coil configuration and two frequencies, 7837 Hz and 51 250 Hz. The models studied are single or multiple, poor conductors (conductance lower than 0.1 S) embedded in a host rock of high but finite resistivity (5000 Ωm) and overlain by a layer of overburden with finite thickness and low to moderate conductivity (conductance up to 2 S).On the basis of the modelling results, limits of detectability for poor conductors have been studied for the various model structures. The results indicate that the anomaly from a steeply dipping, plate-like conductor will decrease significantly when the conductor is embedded in a weakly conductive host rock and is overlain by a conductive overburden. However, an anomaly is obtained, and its magnitude can even increase with increasing overburden conductivity or frequency. The plate anomaly remains practically constant when only the overburden thickness is varied. Changes in overburden conductivity will cause the plate-anomaly values to change markedly. If the plate conductance is less than that of the overburden, a local anomaly opposite in sign to the normal type of anomaly will be recorded. Another major consequence is that conductors interpreted with free-space models will be heavily overestimated in depth or underestimated in conductance, if in reality induction and current channelling in the host rock and overburden make even a slight contribution to the anomalous EM field.The lateral resolution for the horizontal coplanar coil system was found to be about 1.7 times the sensor altitude. Similarly, the lateral extension of a horizontal conductive ribbon, required to reach the semi-infinite (half-space) behaviour, is more than three times the sensor altitude. Finally, screening of a steeply dipping plate, caused by a small, conductive horizontal ribbon, is much more severe than screening of the same plate by an extensive horizontal layer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1996.tb00139.x
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 43 (1995), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A 3D frequency-domain EM modelling code has been implemented for helicopter electromagnetic (HEM) simulations. A vector Helmholtz equation for the electric fields is employed to avoid convergence problems associated with the first-order Maxwell's equations when air is present. Additional stability is introduced by formulating the problem in terms of the scattered electric fields. With this formulation the impressed dipole source is replaced with an equivalent source, which for the airborne configuration possesses a smoother spatial dependence and is easier to model. In order to compute this equivalent source, a primary field arising from dipole sources of either a whole space or a layered half-space must be calculated at locations where the conductivity is different from that of the background.The Helmholtz equation is approximated using finite differences on a staggered grid. After finite-differencing, a complex-symmetric matrix system of equations is assembled and preconditioned using Jacobi scaling before it is solved using the quasi-minimum residual (QMR) method. The modelling code has been compared with other 1D and 3D numerical models and is found to produce results in good agreement.We have used the solution to simulate novel HEM responses that are computationally intractable using integral equation (IE) solutions. These simulations include a 2D conductor residing at a fault contact with and without topography. Our simulations show that the quadrature response is a very good indicator of the faulted background, while the in-phase response indicates the presence of the conductor. However when interpreting the in-phase response, it is possible erroneously to infer a dipping conductor due to the contribution of the faulted background.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1995.tb00294.x
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  • 3
    Electronic Resource
    Electronic Resource
    Deep transient electromagnetic soundings with a grounded source over near-surface conductors (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 98 (1989), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Three-dimensional (3-D) transient electromagnetic (TEM) responses are assessed for near-surface conductors beneath and remote from a grounded-wire transmitter. When a conductor is located close to the transmitter the time derivative of the magnetic field (vertical component), after early times, is shifted in amplitude from that of the layered host. Depending on the location of the transmitter, the response that is observed can be shifted above or shifted below the layered-host response. The conductor's response does not vanish at late times and is important for large transmitter–receiver separations. When the conductor is near to a receiver that is remote from the transmitter, the conductor is detectable only at early times. During these times the conductor can produce responses with sign reversals and other behaviour not characteristic of a layered earth. At later times the responses are more or less that of the layered half-space. An exception to this is when the receiver is located over the edge or close to the edge of the conductor. In this case the conductor produces a response at later time which is like that of the transmitter close to the conductor. The response is shifted in amplitude compared to the layered-earth response. If the transmitter is located close to a near-surface conductor it distorts layered-earth interpretations of the deeper geoelectric section. However, the effect of the conductor can be removed to a large degree by scaling the amplitude of the layered-earth curves that are used to fit the data by an arbitrary constant. This scaling can be determined in the inversion process and allows for acceptable data fits. Alternatively, prior to inversion, the data can be rescaled so that the area beneath the decay curve equals the DC magnetic field of the transmitter. This type of scaling also allows for acceptable data fits. In either situation the layered-earth interpretation then provides an accurate estimate of the deeper geoelectric section. Nevertheless, the interpreted layering in the near surface is still biased by conductors in the near surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1989.tb02292.x
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  • 4
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    Iterative finite-difference solution analysis of acoustic wave equation in the Laplace-Fourier domain (2012)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2012-03-01
    Description: We have investigated numerical characteristics of iterative solutions to the acoustic wave equation in the Laplace-Fourier (LF) domain. We transformed the time-domain acoustic wave equation into the LF domain; the transformed equation was discretized with finite differences and was solved with iterative methods. Finite-difference modeling experiments demonstrate that iterative methods require an infinitesimal stopping tolerance to accurately compute the pressure field especially at long offsets. To understand the requirement for such infinitesimal tolerance values, we analyzed the evolution of intermediate solution vectors, residual vectors, and search direction vectors during the iteration. The analysis showed that the requirement arises from the fact that in the solution space, the amplitude of the pressure field varies more than sixty orders of magnitude on the common log scale. Accordingly, we propose a rule of thumb for choosing a proper stopping tolerance value. We also examined numerical dispersion errors in terms of the grid sampling resolutions per skin depth and wavelength. We found that despite the similarity of the form of the acoustic wave and electromagnetic diffusion equations, the former is different from the latter due to the fact that in the LF domain, the skin depth of the acoustic wave equation is decoupled from its wavelength. This aspect requires that in the LF domain, its grid size be determined by considering the minimum grid sampling resolutions based not only the wavelength but also the skin depth.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 5
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    3D induced-polarization data inversion for complex resistivity (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-05-01
    Description: The conductive and capacitive material properties of the subsurface can be quantified through the frequency-dependent complex resistivity. However, the routine three-dimensional (3D) interpretation of voluminous induced polarization (IP) data sets still poses a challenge due to large computational demands and solution nonuniqueness. We have developed a flexible methodology for 3D (spectral) IP data inversion. Our inversion algorithm is adapted from a frequency-domain electromagnetic (EM) inversion method primarily developed for large-scale hydrocarbon and geothermal energy exploration purposes. The method has proven to be efficient by implementing the nonlinear conjugate gradient method with hierarchical parallelism and by using an optimal finite-difference forward modeling mesh design scheme. The method allows for a large range of survey scales, providing a tool for both exploration and environmental applications. We experimented with an image focusing technique to improve the poor depth resolution of surface data sets with small survey spreads. The algorithm's underlying forward modeling operator properly accounts for EM coupling effects; thus, traditionally used EM coupling correction procedures are not needed. The methodology was applied to both synthetic and field data. We tested the benefit of directly inverting EM coupling contaminated data using a synthetic large-scale exploration data set. Afterward, we further tested the monitoring capability of our method by inverting time-lapse data from an environmental remediation experiment near Rifle, Colorado. Similar trends observed in both our solution and another 2D inversion were in accordance with previous findings about the IP effects due to subsurface microbial activity.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 6
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    3D finite-difference modeling of elastic wave propagation in the Laplace-Fourier domain (2012)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2012-07-01
    Description: With the recent interest in the Laplace-Fourier domain full waveform inversion, we have developed new heterogeneous 3D fourth- and second-order staggered-grid finite-difference schemes for modeling seismic wave propagation in the Laplace-Fourier domain. Our approach is based on the integro-interpolation technique for the velocity-stress formulation in the Cartesian coordinate system. Five averaging elastic coefficients and three averaging densities are necessary to describe the heterogeneous medium, with harmonic averaging of the bulk and shear moduli, and arithmetic averaging of density. In the fourth-order approximation, we improved the accuracy of the scheme using a combination of integral identities for two elementary volumes — “small” and “large” around spatial gridpoints where the wave variables are defined. Two solution approaches are provided, both of which are solved with iterative Krylov methods. In the first approach, the stress variables are eliminated and a linear system for the velocity components is solved. In the second approach, we worked directly with the first-order system of velocity and stress variables. This reduced the computer memory required to store the complex matrix, along with reducing (by 30%) the number of arithmetic operations needed for the solution compared to the fourth-order scheme for velocity only. Numerical examples show that our finite-difference formulations for elastic wavefield simulations can achieve more accurate solutions with fewer grid points than those from previously published second and fourth-order frequency-domain schemes. We applied our simulator to the investigation of wavefields from the SEG/EAGE model in the Laplace-Fourier domain. The calculation is sensitive to the heterogeneity of the medium and capable of describing the structures of complex objects. Our technique can also be extended to 3D elastic modeling within the time domain.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 7
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    FDTD modelling of induced polarization phenomena in transient electromagnetics (2017)
    Oxford University Press
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    Publication Date: 2017-01-25
    Description: The finite-difference time-domain scheme is augmented in order to treat the modelling of transient electromagnetic signals containing induced polarization effects from 3-D distributions of polarizable media. Compared to the non-dispersive problem, the discrete dispersive Maxwell system contains costly convolution operators. Key components to our solution for highly digitized model meshes are Debye decomposition and composite memory variables. We revert to the popular Cole–Cole model of dispersion to describe the frequency-dependent behaviour of electrical conductivity. Its inversely Laplace-transformed Debye decomposition results in a series of time convolutions between electric field and exponential decay functions, with the latter reflecting each Debye constituents’ individual relaxation time. These function types in the discrete-time convolution allow for their substitution by memory variables, annihilating the otherwise prohibitive computing demands. Numerical examples demonstrate the efficiency and practicality of our algorithm.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Royal Astronomical Society.
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  • 8
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    Solution accelerators for large-scale three-dimensional electromagnetic inverse problems (2004)
    Institute of Physics
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    Publication Date: 2004-11-09
    Print ISSN: 0266-5611
    Electronic ISSN: 1361-6420
    Topics: Mathematics , Physics
    Published by Institute of Physics
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  • 9
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    Solution strategies for two- and three-dimensional electromagnetic inverse problems (2000)
    Institute of Physics
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    Publication Date: 2000-10-01
    Print ISSN: 0266-5611
    Electronic ISSN: 1361-6420
    Topics: Mathematics , Physics
    Published by Institute of Physics
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  • 10
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    Massively parallel electrical conductivity imaging of the subsurface: Applications to hydrocarbon exploration (2009)
    Institute of Physics
    Details
    Publication Date: 2009-07-01
    Print ISSN: 1742-6588
    Electronic ISSN: 1742-6596
    Topics: Physics
    Published by Institute of Physics
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