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  • 1
    Electronic Resource
    Electronic Resource
    Asymptotic Theory For Diffusive Electromagnetic Imaging (1994)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 119 (1994), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: We propose an asymptotic theory for diffusive electromagnetic imaging. Three steps are required to perform this imaging. (1) A high-frequency solution is first constructed which mimics the one usually found in wave-propagation phenomena. (2) This solution, valid for a smooth continuous description of the resistivity in the medium, is used in a first-order Born approximation leading to a linear relation between the resistivity perturbation of the subsurface and the perturbation of the electric signal obtained at the free surface. (3) This linear relation is asymptotically inverted by using an iterative quasi-Newtonian inversion based on a least-squares criterion developed by Jin et al. (1992). Although the extension to smooth heterogeneous reference medium is possible, we have only tested the inversion scheme for homogeneous reference media as Zhdanov & Frenkel (1983) previously did with another method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1994.tb04022.x
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  • 2
    Electronic Resource
    Electronic Resource
    Two-dimensional asymptotic iterative elastic inversion (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 108 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: An asymptotic linearized iterative elastic inversion method is proposed to invert 2-D Earth parameters from multicomponent data and is tested numerically. The forward problem is solved by a combination of the Born approximation and ray theoretical methods. We express the perturbed seismogram in terms of perturbations of P- and S-wave impedances and density. The inversion method is based on generalized least squares. We introduce a special form of the ρ2 norm with a weighting function that corrects for geometrical spreading and obliquity of the reflectors. The Hessian for this norm could be estimated in a closed form that is asymptotically valid at high frequencies. We propose a quasi-Newtonian iterative method for the solution of the inverse problem. The first iteration of this inversion method resembles the operator proposed by Beylkin (1985) and Beylkin & Burridge (1990) for the asymptotic inversion of seismic data. Our method is more general than theirs because it can handle arbitrary discrete distributions of sources and receivers. Elastic inversion is generally ill-posed because the problem is overdetermined but undersampled. We study the resolution of the asymptotic inversion method for general sets of sources and receivers. We show that simultaneous inversion for both P- and S-wave impedance is generally ill-conditioned if data for a single scattering mode are available. In particular, it seems that only one parameter can be reliably resolved from marine data. Simultaneous inversion for a finite set of parameters can be resolved only for multicomponent elastic data containing both P-wave and S-wave information. Inversion tests using synthetic data calculated by finite-differences demonstrates that it is possible to invert simultaneously for P and S impedances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb04637.x
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  • 3
    Electronic Resource
    Electronic Resource
    Ray Tracing On A Heterogeneous Sphere By Lie Series (1991)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 104 (1991), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: We propose a method for fast analytical ray tracing on a heterogeneous sphere for surface waves. We first select the specific coordinates of orbital motion which have action/angle properties. We then apply the Lie perturbation approach and, when the square of the slowness is expanded in spherical harmonics, we obtain an analytical formula for the perturbed parameters of the ray. These expressions are sensitive to both the odd and even parts of the expansion. Traveltimes are computed by perturbation, while geometrical spreading is estimated numerically between two nearby perturbed rays. For the ‘Gulf of Alaska’ earthquake of November 1987, the analytical ray follows the same deviations with respect to the great circle as the numerical one, when we use the phase velocity model of Montagner & Tanimoto (1990) at period of 167s. the agreement is excellent for traveltime computations. When the numerical ray tracing predicts a focus/defocusing effect, the perturbed ray tracing gives the same trend. Moreover, variations of the shooting angles between trains can be as high as 20° which might modify the radiation pattern seen by the station for different trains. When the perturbed ray deviates too strongly, a reinitialization technique will guarantee a given accuracy. This reinitialization, which is not required for long periods (〉150s), is probably necessary at shorter periods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1991.tb02491.x
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  • 4
    Electronic Resource
    Electronic Resource
    Ray perturbation theory for interfaces (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 99 (1989), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: We propose a new formalism for the calculation of perturbations of ray trajectories and amplitudes in laterally heterogeneous medium. A Hamiltonian technique leads to a unified approach for the calculation of paraxial rays and rays perturbed by small changes of velocity distribution and interface shape. Instead of using ray centred coordinates as in the classical approach to dynamic ray tracing, we use straightforward cartesian coordinates. This has the advantage that paraxial rays may be referred to the unperturbed ray in a very flexible way. We first study perturbation of initial conditions or paraxial ray tracing. With this technique an ensemble of rays propagating in the vicinity of a central ray is traced with the help of the so-called paraxial ray propagator. This ray propagator is the basis of all the techniques discussed in this paper. Its efficient determination is discussed and we propose a finite element approach in which the medium is divided into a set of trapezoidal elements with simple velocity distribution. We propose that the simpler results are obtained when a constant gradient of the square of the slowness is adopted in each element. In the second part of the paper we calculate the effect of perturbations of the velocity structure and interfaces upon ray trajectories, amplitudes and waveforms. Our results can be easily adapted for the calculation of Frechet derivatives for the linearized inversion of travel times, amplitudes and waveforms. Finally, we present an example of the calculation of synthetic seismograms in a simple medium with a perturbed interface. Simplified expressions for the calculation of perturbed rays in a few typical reference media are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1989.tb01695.x
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  • 5
    Electronic Resource
    Electronic Resource
    Linking short-timescale deformation to long-timescale tectonics (1992)
    [s.l.] : Nature Publishing Group
    Nature 357 (1992), S. 401-404 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] We start, as in ref. 6, with the tensorial nonlinear Langevin equation: deij/dt = Ad[(S)ijd,ek,]/dxk + Bd[(S)i,d(ekmem,)/dXj]/ dxk + -rjij(x, t). Here e is the strain, riij(x, t) is the strain field and (S)ij is the equilibrium tensor field within the plate. The first term of ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/357401a0
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  • 6
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    Ray Tracing On A Heterogeneous Sphere By Lie Series (1991)
    Oxford University Press
    Details
    Publication Date: 1991-01-01
    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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  • 7
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    Structural Analogues of Selfotel (2016)
    American Chemical Society (ACS)
    Details
    Publication Date: 2016-06-02
    Description: The Journal of Organic Chemistry DOI: 10.1021/acs.joc.6b00220
    Print ISSN: 0022-3263
    Electronic ISSN: 1520-6904
    Topics: Chemistry and Pharmacology
    Published by American Chemical Society (ACS)
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  • 8
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    Shallow-structure characterization by 2D elastic full-waveform inversion (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-05-01
    Description: Assessing the effectiveness of elastic full-waveform-inversion (FWI) algorithms when applied to shallow 2D structures in the presence of a complex topography is critically important. By using FWI, we overcome inherent limitations of conventional seismic methods used for near-surface prospecting (acoustic tomography and multichannel spectral analysis of surface waves). The elastic forward problem, formulated in the frequency domain, is based on a mixed finite-element P0-P1 discontinuous Galerkin method to ensure accurate modeling of complex topography effects at a reasonable computing cost. The inversion problem uses an FWI algorithm to minimize the misfit between observed and calculated data. Based on results from a numerical experiment performed on a realistic landslide model inspired from the morphostructure of the Super-Sauze earthflow, we analyzed the effect of using a hierarchical preconditioning strategy, based on a simultaneous multifrequency inversion of damped data, to mitigate the strong nonlinearities coming from the surface waves. This strategy is a key point in alleviating the strong near-surface effects and avoiding convergence toward a local minimum. Using a limited-memory quasi-Newton method improved the convergence level. These findings are analogous to recent applications on large-scale domains, although limited source-receiver offset ranges, low-frequency content of the source, and domination of surface waves on the signal led to some difficulties. Regarding the impact of data decimation on the inversion results, we have learned that an inversion restricted to the vertical data component can be successful without significant loss in terms of parameter imagery resolution. In our investigations of the effect of increased source spacing, we found that a sampling of 4 m (less than three times the theoretical maximum of one half-wavelength) led to severe aliasing.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 9
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    An efficient frequency-domain full waveform inversion method using simultaneous encoded sources (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-07-01
    Description: Three-dimensional full waveform inversion (FWI) still suffers from prohibitively high computational costs that arise because of the seismic modeling for multiple sources that is performed at each nonlinear iteration of FWI. Building supershots by assembling several sources allows mitigation of the number of simulations per FWI iteration, although it adds crosstalk artifacts because of interference between the individual sources of the supershots. These artifacts themselves can be reduced by encoding each individual source with a random phase shift during assembling of the sources. The source encoding method is applied to an efficient frequency-domain FWI, in which a limited number of discrete frequencies or coarsely sampled frequency groups are inverted successively following a multiscale approach. Random codes can be regenerated at each FWI iteration or for each frequency of a group during each FWI iteration, to favor the destructive summation of crosstalk artifacts over FWI iterations. Either a limited number of sources (partial assembling) or the total number of sources (full assembling) can be combined into supershots. Wide-aperture acquisition geometries such as land or marine node acquisitions are considered, to allow one to stack a large number of shots in the full computational domain and to test different partial assembling strategies involving sources that are close to or distant from each other. Two-dimensional case studies show that partial-source assembling of distant shots has a limited sensitivity to noise, for a computational saving that is roughly proportional to the number of shots assembled into the supershots. On the other hand, full assembling is more sensitive to noise, and it requires successive inversions of finely sampled frequency groups with a large number of FWI iterations. In contrast, refining the shot interval to improve the fold degrades the models when full assembling is applied to noisy data. Preliminary 3D application of the method leads to the same conclusions that 2D case studies do, with regard to the footprint of crosstalk noise in the imaging.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 10
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    Wave propagation in heterogeneous porous media formulated in the frequency-space domain using a discontinuous Galerkin method (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-07-01
    Description: Biphasic media with a dynamic interaction between fluid and solid phases must be taken into account to accurately describe seismic wave amplitudes in subsurface and reservoir geophysical applications. Consequently, the modeling of the wave propagation in heteregeneous porous media, which includes the frequency-dependent phenomena of the fluid-solid interaction, is considered for 2D geometries. From the Biot-Gassmann theory, we have deduced the discrete linear system in the frequency domain for a discontinuous finite-element method, known as the nodal discontinuous Galerkin method. Solving this system in the frequency domain allows accurate modeling of the Biot wave in the diffusive/propagative regimes, enhancing the importance of frequency effects. Because we had to consider finite numerical models, we implemented perfectly matched layer techniques. We found that waves are efficiently absorbed at the model boundaries, and that the discretization of the medium should follow the same rules as in the elastodynamic case, that is, 10 grids per minimum wavelength for a P0 interpolation order. The grid spreading of the sources, which could be stresses or forces applied on either the solid phase or the fluid phase, did not show any additional difficulties compared to the elastic problem. For a flat interface separating two media, we compared the numerical solution and a semianalytic solution obtained by a reflectivity method in the three regimes where the Biot wave is propagative, diffusive/propagative, and diffusive. In all cases, fluid-solid interactions were reconstructed accurately, proving that attenuation and dispersion of the waves were correctly accounted for. In addition to this validation in layered media, we have explored the capacities of modeling complex wave propagation in a laterally heterogeneous porous medium related to steam injection in a sand reservoir and the seismic response associated to a fluid substitution.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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