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Peng Shen - One of the best experts on this subject based on the ideXlab platform.
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wave equation reflection tomography annihilators and sensitivity kernels
Geophysical Journal International, 2006Co-Authors: Maarten V De Hoop, Robert D Van Der Hilst, Peng ShenAbstract:In seismic tomography, the finite frequency content of broad-band data leads to interference effects in the process of medium reconstruction, which are ignored in traditional ray theoretical implementations. Various ways of looking at these effects in the framework of transmission tomography can be found in the literature. Here,we consider inverse scattering of bodywaves to develop a method of wave-equation reflection tomography with broad-band waveform data— which in Exploration Seismics is identified as a method of wave-equation migration velocity analysis. In the transition from transmission to reflection tomography the usual cross correlation between modelled and observedwaveforms of a particular phase arrival is replaced by the action of operators (annihilators) to the observed broad-bandwavefields. Using the generalized screen expansion for one-way wave propagation, we develop the Fr´echet (or sensitivity) kernel, and show how it can be evaluated with an adjoint state method. We cast the reflection tomography into an optimization procedure; the kernel appears in the gradient of this procedure.We include a numerical example of evaluating the kernel in a modified Marmousi model, which illustrates the complex dependency of the kernel on frequency band and, hence, scale. In heterogeneous media the kernels reflect proper wave dynamics and do not reveal a self-similar dependence on frequency: low-frequency wave components sample preferentially the smoother parts of the model, whereas the high-frequency data are—as expected—more sensitive to the stronger heterogeneity.We develop the concept for acoustic waves but there are no inherent limitations for the extension to the fully elastic case.
Maarten V De Hoop - One of the best experts on this subject based on the ideXlab platform.
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wave equation reflection tomography annihilators and sensitivity kernels
Geophysical Journal International, 2006Co-Authors: Maarten V De Hoop, Robert D Van Der Hilst, Peng ShenAbstract:In seismic tomography, the finite frequency content of broad-band data leads to interference effects in the process of medium reconstruction, which are ignored in traditional ray theoretical implementations. Various ways of looking at these effects in the framework of transmission tomography can be found in the literature. Here,we consider inverse scattering of bodywaves to develop a method of wave-equation reflection tomography with broad-band waveform data— which in Exploration Seismics is identified as a method of wave-equation migration velocity analysis. In the transition from transmission to reflection tomography the usual cross correlation between modelled and observedwaveforms of a particular phase arrival is replaced by the action of operators (annihilators) to the observed broad-bandwavefields. Using the generalized screen expansion for one-way wave propagation, we develop the Fr´echet (or sensitivity) kernel, and show how it can be evaluated with an adjoint state method. We cast the reflection tomography into an optimization procedure; the kernel appears in the gradient of this procedure.We include a numerical example of evaluating the kernel in a modified Marmousi model, which illustrates the complex dependency of the kernel on frequency band and, hence, scale. In heterogeneous media the kernels reflect proper wave dynamics and do not reveal a self-similar dependence on frequency: low-frequency wave components sample preferentially the smoother parts of the model, whereas the high-frequency data are—as expected—more sensitive to the stronger heterogeneity.We develop the concept for acoustic waves but there are no inherent limitations for the extension to the fully elastic case.
Robert D Van Der Hilst - One of the best experts on this subject based on the ideXlab platform.
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wave equation reflection tomography annihilators and sensitivity kernels
Geophysical Journal International, 2006Co-Authors: Maarten V De Hoop, Robert D Van Der Hilst, Peng ShenAbstract:In seismic tomography, the finite frequency content of broad-band data leads to interference effects in the process of medium reconstruction, which are ignored in traditional ray theoretical implementations. Various ways of looking at these effects in the framework of transmission tomography can be found in the literature. Here,we consider inverse scattering of bodywaves to develop a method of wave-equation reflection tomography with broad-band waveform data— which in Exploration Seismics is identified as a method of wave-equation migration velocity analysis. In the transition from transmission to reflection tomography the usual cross correlation between modelled and observedwaveforms of a particular phase arrival is replaced by the action of operators (annihilators) to the observed broad-bandwavefields. Using the generalized screen expansion for one-way wave propagation, we develop the Fr´echet (or sensitivity) kernel, and show how it can be evaluated with an adjoint state method. We cast the reflection tomography into an optimization procedure; the kernel appears in the gradient of this procedure.We include a numerical example of evaluating the kernel in a modified Marmousi model, which illustrates the complex dependency of the kernel on frequency band and, hence, scale. In heterogeneous media the kernels reflect proper wave dynamics and do not reveal a self-similar dependence on frequency: low-frequency wave components sample preferentially the smoother parts of the model, whereas the high-frequency data are—as expected—more sensitive to the stronger heterogeneity.We develop the concept for acoustic waves but there are no inherent limitations for the extension to the fully elastic case.
Simoes-filho I.d.a. - One of the best experts on this subject based on the ideXlab platform.
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Birefringence Parameters: Indicators Of Anisotropic Symmetry Systems
2015Co-Authors: Simoes-filho I.d.a.Abstract:The difference in travel times between split shear waves (travel-time splitting) in anisotropic media depends on nine combinations of the density normalized elastic parameters (the birefringence parameters). These combinations are all zero in isotropic media, where there is no shear-wave splitting. The number of nonzero birefringence parameters increases with decreasing symmetry elements in the medium: from one in cubic media to nine in triclinic media. The birefringence parameters may be recovered from travel-time splitting observations. Their azimuthal behavior may then be interpreted in terms of crack orientation (strike and dip directions). Birefringence parameters, weak elastic anisotropy, shear-wave travel-time delay, anisotropic symmetry systems.1483-4X11635Aggio-Sobrinho, A., (1995) Inversion of QP and QS Waves from VSP Data in 3D Heterogeneous and Anisotropic Media with Hexagonal or Orthorhombic Symmetries, , Ph D. Thesis, UFBA, Salvador, in PortugueseAki, K., Richards, P.G., (1980) Quantitative Seismology. Theory and Methods, , Freeman, San FranciscoČervený, V., Direct and Inverse Kinematic Problems for Inhomogeneous and Isotropic Media - Linearization Approach (1982) Contr. Geophys. Inst. Slov. Acad, Sci., 13, pp. 127-133Chapman, C.H., Pratt, R.G., Travel-time Tomography in Anisotropic Media - I. Theory (1992) Geophys. J. Int., 109, pp. 1-19Crampin, S., A Review of Wave Motion in Anisotropic and Cracked Elastic Media (1981) Wave Motion, 3, pp. 343-391Crampin, S., An Introduction to Wave Propagation in Anisotropic Media (1984) Geophys. J. Roy. Astr. Soc., 76, pp. 17-28Hanyga, A., The Kinematic Inverse Problem for Weakly Laterally Inhomogeneous Anisotropic Media (1982) Tectonophysics, 90, pp. 253-262Helbig, K., (1994) Foundations of Anisotropy for Exploration Seismics, , Pergamon, OxfordHudson, J.A., Overall Properties of a Cracked Solid (1980) Math. Proc. Cambr. Phil. Soc., 88, pp. 371-384Hudson, J.A., Wave Speeds and Attenuation of Elastic Waves in Material Containing Cracks (1981) Geophys. J. Roy. Astr. Soc., 64, pp. 133-150Jech, J., Pšenčík, I., First-order Perturbation Method for Anisotropic Media (1989) Geophys. J. Int., 99, pp. 369-376Jech, J., Pšenčík, I., Kinematic Inversion for qP and qS Waves in Inhomogeneous Hexagonally Symmetric Structures (1992) Geophys. J. Int., 108, pp. 604-612Michelena, R.J., Muir, F., Harris, J.M., Anisotropic Travel-time Tomography (1993) Geophys. Prosp., 41, pp. 381-412Schoenberg, M., Mutr, F., A Calculus for Finely Layered Anisotropic Media (1989) Geophys., 54, pp. 581-589Simões-Filho, I.A., Costa, J.C., Tadepalli, S., Inversion of the Travel-time Delay between Split Shear Waves in Anisotropic Media (1994) Abstracts of the 6th International Workshop on Seismic Anisotrop
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Linearized Reflection Coefficients For Qp Waves In Anisotropic Media [linearização Dos Coeficientes De Reflexão De Ondas Qp Em Meios Anisotrópicos]
2015Co-Authors: Gomes E.n.s., Protazio J.s., Costa J.c., Simoes-filho I.d.a.Abstract:The reflection coefficients at a planar interface separating two anisotropic media have a nonlinear dependence on the elastic parameters and densities of both media. Linear approximations on the elastic parameters for the qP wave reflectivity are more convenient for AVO/AVD analysis. We present the solution of the Zoeppritz equations in terms of impedance and polarization matrices. Using this approach and assuming weak impedance contrast and weak anisotropy, a simple derivation of linearized approximations for qP the reflectivity is presented for general anisotropy. The linear approximations of reflection coefficients, qP and converted waves, for qP incidence are very close to the exact results for incidence angles up to 30 degrees considering moderate impedance contrast and anisotropy.1914760Aki, K., Richards, P.G., (1980) Quantitative Seismology: Theory and Methods, 1. , W. H. Freeman and Co., San FranciscoBanik, N.C., An effective anisotropy parameter in transversely isotropic media (1987) Geophysics, 52, pp. 1654-1664Castagna, J., AVO Analysis- Tutorial and Review (1992) Offset-dependent Reflectivity-Theory and Practice AVO Analysis: Soc. Expl. Geophys., pp. 3-35. , Castagna, J.P. & Backus, M. M. (Eds)Helbig, K., Foundations of Anisotropy for Exploration Seismics (1994) Handbook of Geophysical Exploration, 22. , Ed. PergamonHoffman, K., Ray, K., (1971) Álgebra Linear, , Polígono (ed.)Hudson, J.A., Wave speeds and attenuation of elastic waves in material containing cracks (1982) Geophys. J. R. Astr Soc., 64, pp. 133-150Musgrave, M.J.P., (1970) Crystal Acoustics, , Holden-Day Inc. San FranciscoOstrander, W.J., Plane-wave reflection coefficients for gas sand at non normal angles of incidence (1984) Geophysics, 49, pp. 1637-1648Postma, G.W., Wave propagation in stratified medium (1955) Geophysics, 20 (4), pp. 780-806Schoenberg, M., Douma, J., Elastic wave propagation in media with parallel fractures and aligned cracks (1988) Geophysics, 56, pp. 1331-1348Schoenberg, M., Protázio, J.S., Zoeppritz Rationalized and Generalized to Anisotropy (1992) Journal of Seismic Exploration, 1, pp. 125-144Thomsen, Weak elastic anisotropy (1986) Geophysics, 51, pp. 1954-1966Thomsen, Weak elastic anisotropic reflection (1993) Offset-dependent Reflectivity-Theory and Practice AVO Analysis: Soc. Exp. Geophys., pp. 103-111. , Castagna, J. P. & Backus, M. M. (Eds.)Vavrycuk, V., Psencik, I., PP-Wave reflection coefficients in weakly anisotropic elastic media (1998) Geophysics, 63 (6), pp. 2129-2141Zillmer, M., Gajewsky, D., Kashtan, B.M., Reflection coefficients for weak anisotropic media (1997) Geophys. J. Internat, 129, pp. 389-39
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Multiazimuthal Modeling And Inversion Of Qp Reflection Coefficients In Fractured Media
2015Co-Authors: Simoes-filho I.d.a., Protazio J.s., Neves F.a., Tinen J.s., Costa J.c.Abstract:We present a method for the exact modeling and inversion of multiazimuthal qP-wave reflection coefficients at an interface separating two anisotropic media. This procedure can be used for media with at least one of its planes of symmetry parallel to the interface (i.e., monoclinic or higher symmetries). To illustrate the method, we compute qP-wave reflection coefficients at an interface separating an isotropic medium (representing a seal rock) from a transversely isotropic medium (representing a reservoir rock with vertical aligned fractures). Forward modeling shows that the difference in the offset of the critical angles for different azimuths is proportional to the fracture density: the higher the fracture density, the larger the difference. In the second part of the paper, we use a global optimization technique (genetic algorithm) to invert wide-angle amplitude variation with offset (AVO) synthetic data. The model space consists of mass density and five elastic parameters of a transversely isotropic medium with a horizontal symmetry axis (HTI medium), which, to the first order, represents the fractured reservoir rock. For this model, we find that the configuration of three azimuths of data acquisition is the minimum number of acquisition planes needed to invert amplitude variation with offset/amplitude variation with azimuth (AVO/AVA) data. Further, there is a need for incidence angles up to 40°; a more narrow range of angles can lead to models that fit the data perfectly only up to the "maximum" incidence angle. We assume that the velocities and density of the isotropic rock are known, but use no prior information on the values of the model space parameters of the fractured rock except for reasonable velocity values in crustal rocks and constraints of elastic stability of solid media. After inversion for the model space parameters, we compute statistics of the 30 best models and likelihood functions, which provide information on the nonuniqueness and quality of the AVO/AVA inverse problem.64411431152Abreu, C.E.B.S., Simões-Filho, I.A., Modelagem sísmica para caracterização de fraturamento (1995) I Conf. Latin-American Union of Geophys., pp. 823-826. , Expanded AbstractsBasu, A., Frazer, L.N., Rapid determination of the critical temperature in simulated annealing inversion (1990) Science, 249, pp. 1409-1412Cary, P.W., Chapman, C.H., Automatic 1D inversion of marine refraction data (1988) J. Geophys. Res., 93, pp. 527-546Crampin, S., Effective anisotropic elastic constants for wave propagation through cracked solids (1984) Geophys. J. Roy. Astr. Soc., 76, pp. 135-145Evaluation of anisotropy by shear-wave splitting (1985) Geophysics, 50, pp. 142-152De Hass, J.C., Berkhout, A.J., Practical approach to non-linear inversion of amplitude versus offset information (1989) 59th Ann. Internat. Mtg., Soc. Expl. Geophys., pp. 27-36. , Expanded AbstractsDocherty, P., Singh, S., A global technique for migration velocity analysis (1995) 65th Ann. Internat. Mtg., Soc. Expl. Geophys., pp. 1137-1140. , Expanded AbstractsEstill, R., Wrolstad, K., Interpretative aspects of AVO - Application to offshore Gulf Coast bright-spot analysis (1993) Offset-dependent Reflectivity: Theory and Practice of AVO Analysis, pp. 267-284. , Castagna, J. P., and Backus, M. M., Eds., Soc. Expl. GeophysFrazer, L.N., Basu, A., Freeze-bath inversion (1990) 60th Ann. Internat. Mtg., Soc. Expl. Geophys., pp. 1123-1125. , Expanded AbstractsGoldberg, D.E., (1989) Genetic Algorithms in Search, Optimization and Machine Learning, , Addinson-Wesley Publ. CoHelbig, K., (1994) Foundations of Anisotropy for Exploration Seismics, , Pergamon PressHolland, J.H., (1975) Adaptation in Natural and Artificial Systems, , Univ. of Michigan PressHorne, S., MacBeth, C., Inversion for seismic anisotropy using genetic algorithms (1994) Geophys. Prosp., 42, pp. 953-974Horne, S., MacBeth, C., Queen, J., Rizer, W., Cox, V., Fracture characterization from near-offset VSP inversion (1996) Geophys. Prosp., 45, pp. 141-164Hudson, J.A., Overall properties of a cracked solid (1980) Math. Proc. Cambr. Phil. Soc., 88, pp. 371-384Wave speeds and attenuation of elastic waves in material containing cracks (1981) Geophys. J. Roy. Astr. Soc., 64, pp. 133-150Jin, S., Madariaga, R., Background velocity inversion with a genetic algorithm (1993) Geophys. Res. Lett., 20, pp. 93-96Kim, K.Y., Wrolstad, K.H., Aminzadeh, F., Effects of transverse isotropy on P-wave AVO for gas sands (1993) Geophysics, 58, pp. 883-888Lefeuvre, F., Fracture related anisotropy detection and analysis: "and if the P-waves were enough?" (1994) 64th Ann. Internat. Mtg., Soc. Expl. Geophys., pp. 942-945. , Expanded AbstractsMacdonald, C., Davis, P.M., Jackson, D.D., Inversion of reflection traveltimes and amplitudes (1987) Geophysics, 52, pp. 606-617Mallick, S., Model-based inversion of amplitude-variations-with-offset data using a genetic algorithm (1995) Geophysics, 60, pp. 939-954Mallick, S., Frazer, N.L., Reflection/transmission coefficients and azimuthal anisotropy in marine seismic studies (1991) Geophys. J. Internat., 105, pp. 241-252Martinez, R.D., Wave propagation effects on amplitude variation with offset measurements: A modeling study (1993) Geophysics, 58, pp. 534-543Musgrave, M.P.J., (1970) Crystal Acoustics, , Holden-DayNeves, F.A., DeHoop, M., Some remarks on non-linear AVA inversion (2000) Geophysics, , scheduled for early 2000Nolte, B., Frazer, L.N., Vertical seismic profile inversion with genetic algorithms (1994) Geophys. J. Internat., 117, pp. 162-178Ross, C.P., Kinmam, D.L., Nonbright spot AVO: Two examples (1995) Geophysics, 60, pp. 1398-1408Rüger, A., P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry (1997) Geophysics, 62, pp. 713-722Sambridge, M.S., Drijkoningen, G.G., Genetic algorithms in seismic waveform inversion (1992) Geophys. J. Internat., 109, pp. 323-342Sambridge, M.S., Gallagher, K., Earthquake hypocenter location using genetic algorithms (1993) Bull. Seism. Soc. Am., 83, pp. 1467-1491Sayers, C.M., Rickett, J.E., Azimuthal variation of AVO response for fractured gas sands (1997) Geophys. Prosp., 45, pp. 165-182Schoenberg, M., Protázio, J.S., Zoeppritz rationalized and generalized to anisotropy (1992) J. Seis. Expl., 1, pp. 125-144Sen, M.K., Stoffa, P.L., Rapid sampling of model space using genetic algorithm: Examples from seismic waveform inversion (1992) Geophys. J. Internat., 108, pp. 281-292Stoffa, P.L., Sen, M.K., Nonlinear multiparameter optimization using genetic algorithms: Inversion of plane-wave seismograms (1991) Geophysics, 56, pp. 1794-1810Thomsen, L., Weak elastic anisotropy (1986) Geophysics, 51, pp. 1954-1966Tinen, J.S., (1998) Modelagem e Inversão de Coeficientes de Reflexão e Transmissão em meios Fraturados, Usando Algoritmo Genético, , M.Sc. thesis, Univer. of CampinasTsvankin, I., Body-wave radiation patterns and AVO in transversely isotropic media (1995) Geophysics, 60, pp. 1409-1425Wiggins, R.A., Monte Carlo inversion of body wave observations (1969) J. Geophys. Res., 74, pp. 3171-3181Wright, J., The effects of transverse isotropy on reflection amplitude versus offset (1987) Geophysics, 52, pp. 564-56
Ryberg Andm. T. Weber - One of the best experts on this subject based on the ideXlab platform.
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Receiver function arrays: a re£ection seismic approach
2016Co-Authors: Ryberg Andm. T. WeberAbstract:The receiver function method (RFM) is a commonly used technique to study the crustal and upper mantle velocity structure. Early receiver function (RF) investigations were performed mostly at individual permanent stations. They were focused on crustal structures, and later on upper mantle velocity discontinuities (410 km and 660 km discontinuities). Only recently has research been directed towards the study of the lateral (2- and 3-D) variability of major velocity boundaries in the crust and upper mantle by receiver function arrays using temporary and permanent, three-component, short-period and broad-band seismic stations. To improve the signal-to-noise ratio, receiver functions are calculated for individual earthquakes and are then binned, moveout corrected and stacked.We show that this processing sequence is similar to that applied routinely in Exploration seismology. Therefore, existing tools from the near-vertical data processing can be adopted for receiver functions: velocity analysis tools, solutions for static and residual static problems, coherence enhancement of seismic phases, migration, etc. The high spatial density of seismic stations of recent and future receiver function experiments provides the opportunity (and obligation) to use the more sophisticated migration methods (full wave¢eld migration) commonly and successfully used in Exploration Seismics. Synthetics calculated by the ¢nite di¡erence method for simple 2-D crustal models are employed here to test our processing approach and to show the potentials and limitations of stacking and migrating RF data. We show that binning, normal move-out (NMO) corrections, stacking and post-stack migration of the synthetic data can reconstruct the models reliably with a high spatial resolution. Key words: crustal structure, ¢nite di¡erence methods, re£ection seismology, seismic wave propagation, synthetic seismograms.
