Multidimensional Seismic Inversion

Stockwell, John W.; Cohen, Jack K.

doi:10.1007/978-1-4613-0001-4_1

Cited by 29 publications

(49 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one-and two-dimensional systems, respectively.Understanding how waves propagate in heterogeneous media is fundamental to such important problems as earthquakes, underground nuclear explosions, the morphology of oil and gas reservoirs, oceanography, and medical and materials sciences [1]. For example, seismic wave propagation and reflection are used to not only estimate the hydrocarbon content of a potential oil or gas field, but also to image structures located over a wide area, ranging from the Earth's near surface to the deeper crust and upper mantle.…”

mentioning

confidence: 99%

“…Understanding how waves propagate in heterogeneous media is fundamental to such important problems as earthquakes, underground nuclear explosions, the morphology of oil and gas reservoirs, oceanography, and medical and materials sciences [1]. For example, seismic wave propagation and reflection are used to not only estimate the hydrocarbon content of a potential oil or gas field, but also to image structures located over a wide area, ranging from the Earth's near surface to the deeper crust and upper mantle.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

et al. 2005

View full text Add to dashboard Cite

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying powerlaw correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one-and two-dimensional systems, respectively.Understanding how waves propagate in heterogeneous media is fundamental to such important problems as earthquakes, underground nuclear explosions, the morphology of oil and gas reservoirs, oceanography, and medical and materials sciences [1]. For example, seismic wave propagation and reflection are used to not only estimate the hydrocarbon content of a potential oil or gas field, but also to image structures located over a wide area, ranging from the Earth's near surface to the deeper crust and upper mantle. The same essential concepts and techniques are used in such diverse fields as materials science and medicine.In condensed matter physics, a related problem, namely, the nature of electronic states in disordered materials, has been studied for several decades and shown to depend strongly on the spatial dimensionality d of the materials [2]. It was rigorously shown that, for onedimensional (1D) systems, even infinitesimally small disorder is sufficient for localizing the wave function, irrespective of the energy [3], and that the envelop of the wave function ψ(r) decays exponentially at large distances r from the domain's center, ψ(r) ∼ exp(−r/ξ), with ξ being the localization length. The most important results for d > 1 follow from the scaling theory of localization [4] which predicts that, for d ≤ 2, all electronic states are localized for any degree of disorder, while a transition to extended states -the metal-insulator transition -occurs for d > 2 if disorder is sufficiently strong. The transition between the two states is characterized by divergence of the localization length, ξ ∝ |W − W c | −ν , where W c is the critical value of the disorder intensity.Wegner [5] derived a field-theoretic formulation for the localization problem which, together with the scaling theory [4], predict a lower critical dimension, d c = 2, for the localization problem. These predictions have been confirmed by numerical simulations [6].Wave characteristics of electrons suggest that the localization phenomenon may occur in other wave propagation processes. For example, consider propagation of seismic waves in heterogeneous rock. In this case, the interference of the waves that have undergone multiple scattering, caused by the heterogeneities of t...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

et al. 2005

View full text Add to dashboard Cite

show abstract

“…The usual travel time migration imaging with the active array is done with the Kirchhoff Migration imaging function [2,3] …”

Section: Formulation Of the Imaging Problemmentioning

confidence: 99%

Signal to Noise Ratio Analysis in Virtual Source Array Imaging

Garnier¹,

Papanicolaou²,

Semin³

et al. 2015

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

Abstract. We consider correlation-based imaging of a reflector located on one side of a passive array where the medium is homogeneous. On the other side of the array the illumination by remote impulsive sources goes through a strongly scattering medium. It has been shown in [J. Garnier and G. Papanicolaou, Inverse Problems 28 (2012), 075002] that migrating the cross correlations of the passive array gives an image whose resolution is as good as if the array was active and the array response matrix was that of a homogeneous medium. In this paper we study the signal to noise ratio of the image as a function of statistical properties of the strongly scattering medium, the signal bandwidth and the source and passive receiver array characteristics. Using a Kronecker model for the strongly scattering medium we show that image resolution is as expected and that the signal to noise ratio can be computed in an essentially explicit way. We show with direct numerical simulations using full wave propagation solvers in random media that the theoretical predictions based on the Kronecker model are accurate.

show abstract

“…Another linearizing approximation that can be used for re ection from smooth surfaces is the Kirchhoff approximation, in which the scattered eld is replaced by its geometrical optics approximation [8] [25]. Here, however, we consider only the Born approximation.…”

Section: The Model For Scattering From the Targetmentioning

confidence: 99%

Imaging That Exploits Multipath Scattering

Cheney¹

2005

View full text Add to dashboard Cite

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503 AGENCY USE ONLY (Leave blank)2. REPORT DATE AUGUST 2005 REPORT TYPE AND DATES COVEREDFinal Aug 03 -May 05 Work has focused on three radar imaging problems: a) analysis of different measurement scenarios for imaging within a parallel-plate waveguide (a simple model for an urban setting), b) imaging from high-doppler-resolution radar data, and c) imaging that exploits multipath scattering. TITLE AND SUBTITLE IMAGING THAT EXPLOITS MULTIPATH SCATTERING AUTHOR(S) Margaret Cheney FUNDING NUMBERS Imaging in a parallel-plate waveguideThis is joint work with Cliff Nolan. Work on this project is still ongoing. Basic theoryThe mathematical model involves a number of ingredients: 1) a model for wave propagation in free space, 2) a model for multiple scattering from buildings, 3) a (linearized) model for scattering from the scene, and 4) a model for the array of sources. P-P P-P P− P.1: Scattering geometry. The darker walls and dot denote the true walls and a point source; the lighter ones represent virtual walls and corresponding virtual sources. Model for wave propagation in free spaceWe assume that waves propagate within the waveguide according to the scalar wave equation:where the dots denote differentiation with respect to t and c 0 is the speed of light.

show abstract

Multidimensional Seismic Inversion

Cited by 29 publications

References 0 publications

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

Signal to Noise Ratio Analysis in Virtual Source Array Imaging

Imaging That Exploits Multipath Scattering

Contact Info

Product

Resources

About