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  • 1
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    Elsevier
    In:  Amsterdam, 628 pp., Elsevier, vol. 31, no. 1, pp. 1-40, (ISBN 0-691-01019-6)
    Publication Date: 2002
    Keywords: Textbook of geophysics ; Inversion ; instability ; well-posed ; ill-posed ; problems ; Least-squares ; Backus ; Gilbert ; Non-linear effects ; regularization ; potential ; Electromagnetic methods/phenomena ; Seismology ; Gram ; Schmidt ; Singular value decomposition ; Lanczos ; Green's function ; Tikhonov ; potential ; methods ; Seismics (controlled source seismology) ; Gravimetry, Gravitation ; Geomagnetics ; Textbook of mathematics ; seismic Migration
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  • 2
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    Springer Verlag
    In:  Berlin, Springer Verlag, vol. 4, no. 1, pp. 1-40, (ISBN 0-691-01019-6)
    Publication Date: 1988
    Keywords: Handbook of geophysics ; Data analysis / ~ processing ; Transformations ; Handbook of mathematics
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  • 3
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    Elsevier
    In:  Amsterdam, Elsevier, vol. 31, no. 1, pp. 1-40, (ISBN 0-691-01019-6)
    Publication Date: 1994
    Keywords: Textbook of geophysics ; Geoelectrics ; Applied geophysics
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  • 4
    Publication Date: 2017-11-30
    Description: The magnetotelluric (MT) data collected as a part of the EarthScope project provided a unique opportunity to study the conductivity structure of the deep interior of the North American continent. Besides the scientific value of the recovered subsurface models, the data also allowed inversion practitioners to test the robustness of their algorithms applied to regional long-period data. In this paper, we present the results of MT inversion of a subset of the second footprint of the MT data collection covering the East Central United States. Our inversion algorithm implements simultaneous inversion of the full MT impedance data both for the 3D conductivity distribution and for the distortion matrix. The distortion matrix provides the means to account for the effect of the near-surface geoelectrical inhomogeneities on the MT data. The long-period data do not have the resolution for the small near-surface conductivity anomalies, which makes an application of the distortion matrix especially appropriate. The determined conductivity model of the region agrees well with the known geologic and tectonic features of the East Central United States. The conductivity anomalies recovered by our inversion indicate a possible presence of the hotspot track in the area.
    Print ISSN: 0094-8276
    Electronic ISSN: 1944-8007
    Topics: Geosciences , Physics
    Published by Wiley on behalf of American Geophysical Union (AGU).
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  • 5
    Publication Date: 2016-07-20
    Description: This paper introduces a novel approach to constructing an effective pre-conditioner for finite-difference (FD) electromagnetic modelling in geophysical applications. This approach is based on introducing an FD contraction operator, similar to one developed for integral equation formulation of Maxwell's equation. The properties of the FD contraction operator were established using an FD analogue of the energy equality for the anomalous electromagnetic field. A new pre-conditioner uses a discrete Green's function of a 1-D layered background conductivity. We also developed the formulae for an estimation of the condition number of the system of FD equations pre-conditioned with the introduced FD contraction operator. Based on this estimation, we have established that the condition number is bounded by the maximum conductivity contrast between the background conductivity and actual conductivity. When there are both resistive and conductive anomalies relative to the background, the new pre-conditioner is advantageous over using the 1-D discrete Green's function directly. In our numerical experiments with both resistive and conductive anomalies, for a land geoelectrical model with 1:10 contrast, the method accelerates convergence of an iterative method (BiCGStab) by factors of 2–2.5, and in a marine example with 1:50 contrast, by a factor of 4.6, compared to direct use of the discrete 1-D Green's function as a pre-conditioner.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 6
    Publication Date: 2013-06-11
    Description: Fundamental to complex analysis is the Cauchy integral theorem, and the derivation of Cauchy-type integrals. For over 40 yr, Cauchy-type integrals have been used to describe analytical continuation, establish the location of singular points, and study non-single-valued solutions of inverse problems in 2-D potential field theory. In this paper, we revive this interesting and fundamental area of potential field theory to introduce Cauchy-type integrals for 3-D potential fields. In particular, we show how one can evaluate the gravity and gravity gradiometry responses of 3-D bodies as surface integrals over arbitrary volumes that may contain spatially variable densities. This method of 3-D spatial-domain potential field modelling has never been realized before, and we show how it is particularly suited to the terrain correction of airborne gravity and gravity gradiometry data. The surface integrals are evaluated numerically on a topographically conforming grid with a resolution equal to the digital elevation model. Thus, our method directly avoids issues related to prismatic discretization of the digital elevation model and their associated volume integration which may result in inappropriate discretization of the earth model, particularly for regions of rugged topography. We demonstrate our method with a model study for airborne gravity gradiometry data simulated for a next-generation 1 Eö/ $\sqrt{\text{Hz}}$ system over the Kauring test site in Western Australia.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 7
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    Society of Exploration Geophysicists (SEG)
    Publication Date: 2017-11-01
    Description: We have developed a novel approach for inversion of gravity and gravity gradiometry data based on multinary transformation of the model parameters. This concept is a generalization of binary density inversion to the models described by any number of discrete model parameters. The multinary inversion makes it possible to explicitly exploit the sharp contrasts of the density between the host media and anomalous targets in the inversion of gravity and gravity gradiometry data. In the framework of the multinary inversion method, we use the given values of density and error functions to transform the density distribution into the desired step-function distribution. To accommodate a possible deviation of the densities from the fixed discrete values, we develop an adaptive technique for selecting the corresponding standard deviations, guided by the inversion process. The novel adaptive multinary inversion algorithm is demonstrated to be effective in determining the shape, location, and densities of the anomalous targets. We find that this method can be effectively applied for the inversion of the full tensor gravity gradiometry (FTG) data computer simulated for the SEG salt density model and for the field FTG data collected in the Nordkapp Basin, Barents Sea.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
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  • 8
    Publication Date: 2012-11-16
    Description: Explorers are moving to increase the "discovery space" by exploring under cover and to greater depths, e.g., subsalt and sub-basalt exploration for oil and gas, and beneath transported cover for minerals. With this shift, there becomes an increased reliance on geophysical methods to delineate resources with no recognized geological or geochemical expressions. Different geophysical fields provide information about different physical properties of the Earth. Multiple geophysical surveys spanning gravity, magnetic, electromagnetic, and seismic methods are often interpreted to infer geology from models of different physical properties. In many cases, the various geophysical data are complementary, making it natural to consider a formal mathematical framework for their joint inversion to a shared Earth model. There are different approaches to joint inversion. The simplest case of joint inversion is where the physical properties are identical between different geophysical methods (e.g., Jupp and Vozoff, 1975). In other cases, joint inversion may infer theoretical, empirical, or statistical correlations between different physical properties (e.g., Hoversten et al., 2003, 2006). In cases where the physical properties are not correlated but, nevertheless, can be assumed to share a similar structure, joint inversions have been formulated as a minimization of the cross-gradients between different physical properties (e.g., Haber and Oldenburg, 1997; Gallardo and Meju, 2003, 2004). The latter has now been widely adopted by joint inversion practitioners as the de facto standard (e.g., Colombo and De Stefano, 2007; Hu et al., 2009; Jegen et al., 2009; De Stefano et al., 2011).
    Print ISSN: 1070-485X
    Electronic ISSN: 1938-3789
    Topics: Geosciences
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  • 9
  • 10
    Publication Date: 2010-08-01
    Print ISSN: 1069-3513
    Electronic ISSN: 1555-6506
    Topics: Geosciences
    Published by Springer
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