Weak-contrast approximation of the elastic scattering matrix in anisotropic media     

Bjørn Ursin  Geir U. Haugen 《Pure and Applied Geophysics》1996,148(3-4):685-714

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.  相似文献   

Crustal structure of the Eastern Alps along the TRANSALP profile from wide-angle seismic tomography   总被引：1，自引：1，他引：1  

Florian Bleibinhaus  Helmut Gebrande 《Tectonophysics》2006,414(1-4):51

The objective of the TRANSALP project is an investigation of the Eastern Alps with regard to their deep structure and dynamic evolution. The core of the project is a 340-km-long seismic profile at 12°E between Munich and Venice. This paper deals with the P-wave velocity distribution as derived from active source travel time tomography. Our database consists of Vibroseis and explosion seismic travel times recorded at up to 100 seismological stations distributed in a 30-km-wide corridor along the profile. In order to derive a velocity and reflector model, we simultaneously inverted refractions and reflections using a derivative of a damped least squares approach for local earthquake tomography. 8000 travel time picks from dense Vibroseis recordings provide the basis for high resolution in the upper crust. Explosion seismic wide-angle reflection travel times constrain both deeper crustal velocities and structure of the crust–mantle boundary with low resolution. In the resulting model, the Adriatic crust shows significantly higher P-wave velocities than the European crust. The European Moho is dipping south at an angle of 7°. The Adriatic Moho dips north with a gentle inclination at shallower depths. This geometry suggests S-directed subduction. Azimuthal variations of the first-break velocities as well as observations of shear wave splitting reveal strong anisotropy in the Tauern Window. We explain this finding by foliations and laminations generated by lateral extrusion. Based on the P-wave model we also localized almost 100 local earthquakes recorded during the 2-month acquisition campaign in 1999. Seismicity patterns in the North seem related to the Inn valley shear zone, and to thrusting of Austroalpine units over European basement. The alignment of deep seismicity in the Trento-Vicenza region with the top of the Adriatic lower crust corroborates the suggestion of a deep thrust fault in the Southern Alps.  相似文献   

Effects of magnetic interactions in anisotropy of magnetic susceptibility: Models, experiments and implications for igneous rock fabrics quantification     

Philippe Gaillot  Michel de Saint-Blanquat  Jean-Luc Bouchez   《Tectonophysics》2006,418(1-2):3

Besides granites of the ilmenite series, in which the anisotropy of magnetic susceptibility (AMS) is mainly controlled by paramagnetic minerals, the AMS of igneous rocks is commonly interpreted as the result of the shape-preferred orientation of unequant ferromagnetic grains. In a few instances, the anisotropy due to the distribution of ferromagnetic grains, irrespective of their shape, has also been proposed as an important AMS source. Former analytical models that consider infinite geometry of identical and uniformly magnetized and coaxial particles confirm that shape fabric may be overcome by dipolar contributions if neighboring grains are close enough to each other to magnetically interact. On these bases we present and experimentally validate a two-grain macroscopic numerical model in which each grain carries its own magnetic anisotropy, volume, orientation and location in space. Compared with analytical predictions and available experiments, our results allow to list and quantify the factors that affect the effects of magnetic interactions. In particular, we discuss the effects of (i) the infinite geometry used in the analytical models, (ii) the intrinsic shape anisotropy of the grains, (iii) the relative orientation in space of the grains, and (iv) the spatial distribution of grains with a particular focus on the inter-grain distance distribution. Using documented case studies, these findings are summarized and discussed in the framework of the generalized total AMS tensor recently introduced by Cañon-Tapia (Cañon-Tapia, E., 2001. Factors affecting the relative importance of shape and distribution anisotropy in rocks: theory and experiments. Tectonophysics, 340, 117–131.). The most important result of our work is that analytical models far overestimate the role of magnetic interaction in rock fabric quantification. Considering natural rocks as an assemblage of interacting and non-interacting grains, and that the effects of interaction are reduced by (i) the finite geometry of the interacting clusters, (ii) the relative orientation between interacting grains, (iii) their heterogeneity in orientation, shape and bulk susceptibility, and (iv) their inter-distance distribution, we reconcile analytical models and experiments with real case studies that minimize the role of magnetic interaction onto the measured AMS. Limitations of our results are discussed and guidelines are provided for the use of AMS in geological interpretation of igneous rock fabrics where magnetic interactions are likely to occur.  相似文献   

饱和岩石的各向异性及非线性黏弹性响应   总被引：25，自引：2，他引：25       下载免费PDF全文

席道瑛  刘斌  田象燕 《地球物理学报》2002,45(1):109-118

在MTS伺服压机上对不同饱和状态的砂岩、大理岩标本进行了垂直层理和平行层理两个方向的正弦波加载试验,研究了饱和岩石的各向异性及非线性黏弹性行为. 在最大载荷低于岩石的屈服点时,获得的衰减、杨氏模量、泊松比、波速都表现出显著的各向异性,同时它们还具有较明显的应变振幅效应和频率效应. 随着应变振幅的增大,衰减近似呈线性增长,杨氏模量和泊松比近似呈线性下降. 在0.005-4Hz频段内除衰减不明显依赖频率以外,杨氏模量、泊松比、波速对频率的依赖性都较强; 当频段扩大到15Hz时,这4个参数都表现出较强的频率效应. 饱和岩石的衰减、杨氏模量、泊松比、波速均随饱和液体的黏滞系数增大而增大.  相似文献   

Combined analysis of SKS splitting and regional P traveltimes in Siberia   总被引：3，自引：0，他引：3  

S. Oreshin  L. Vinnik  L. Makeyeva  G. Kosarev  R. Kind  F. Wentzel 《Geophysical Journal International》2002,151(2):393-402

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Fermat's principle for seismic rays in elastic media     

Andrej Bna  Michael A. Slawinski 《Journal of Applied Geophysics》2003,54(3-4):445

We prove that rays in linearly elastic anisotropic nonuniform media obey Fermat's principle of stationary traveltime. First, we formulate the concept of rays, which emerges from the Hamilton equations. Then, we show that these rays are solutions of the variational problem stated by Fermat's principle. This proof is valid for all rays except the ones associated with infection points on the phase-slowness surface.  相似文献   

Practical VTI approximations: a systematic anatomy   总被引：3，自引：0，他引：3  

Paul J. Fowler   《Journal of Applied Geophysics》2003,54(3-4):347

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a₁₃ with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109).  相似文献   

Seismic wave velocity and anisotropy of serpentinized peridotite in the Oman ophiolite     

Benoît Dewandel  Franoise Boudier  Hartmut Kern  Waris Warsi  David Mainprice 《Tectonophysics》2003,370(1-4):77-94

Shallow seismic measurements in harzburgite from the Oman ophiolite performed in a zone where the maximum horizontal anisotropy is expected (vertical foliation and horizontal lineation) point to a dominant dependence of seismic properties on fracturing.

Optical microscopy studies show that microcracks are guided by the serpentine (lizardite) penetrative network oriented subparallel to the harzburgite foliation and subperpendicular to the mineral lineation, and that serpentine (lizardite) vein filling has a maximum concentration of (001) planes parallel to the veins walls. The calculated elastic properties of the oriented alteration veins filled with serpentine in an anisotropic matrix formed by oriented crystals of olivine and orthopyroxene are compared with seismic velocities measured on hand specimens.

Laboratory ultrasonic data indicate that open microcracks are closed at 100 MPa pressure, e.g. (J. Geophys. Res. 65, (1960) 1083) and (Proc. ODP Sci. Results Leg 118, (1990) 227). Above this pressure, laboratory measurements and modeling show that P-compressional and S-shear wave velocities are mainly controlled by the mineral preferred orientation. Veins sealed with serpentine are effective in slightly lowering P and S velocities and increasing anisotropy. The penetrative lizardite network does not affect directly the geometry of seismic anisotropy, but contributes indirectly in the fact that this network controls the microcrack orientations.

Comparison between seismic measurements of peridotite and gabbro in the same conditions suggest that P- and S-waves anisotropies are a possible discriminating factor between the two lithologies in the suboceanic lithosphere.  相似文献   

地壳介质弹性和电性各向异性研究的新进展   总被引：3，自引：2，他引：3       下载免费PDF全文

李清河  阮爱国  范小平  金淑梅 《地震工程学报》2004,26(1):10-17

分析了地壳介质各向异性研究的现状，指出了弹性和电性各向异性研究中存在的问题，提出了联合利用弹性和电性各向异性研究地球介质特征及提取物性参数的正反演方法．理论研究和地震过程的实际资料表明，将弹性和电性结合起来研究地壳介质各向异性具有清晰明确的物理意义，是各向异性研究的一个非常有发展前景的新领域。  相似文献   

Seismic velocities of granulite-facies xenoliths from Central Ireland: Implications for lower crustal composition and anisotropy     

Riana van den Berg  J. Stephen Daly  Matthew H. Salisbury   《Tectonophysics》2005,407(1-2):81-99

V_p and V_s values have been measured experimentally and calculated for granulite-facies lower crustal xenoliths from central Ireland close to the Caledonian Iapetus suture zone. The xenoliths are predominantly foliated and lineated metapelitic (garnet–sillimanite–K-feldspar) granulites. Their metapelitic composition is unusual compared with the mostly mafic composition of lower crustal xenoliths world-wide. Based on thermobarometry, the metapelitic xenoliths were entrained from depths of c. 20–25 ± 3.5 km and rare mafic granulites from depths of 31–33 ± 3.4 km. The xenoliths were emplaced during Lower Carboniferous volcanism and are considered to represent samples of the present day lower crust.V_p values for the metapelitic granulites range between 6.26 and 7.99 km s^{− 1} with a mean value of 7.09 ± 0.4 km s^{− 1}. Psammite and granitic orthogneiss samples have calculated V_p values of 6.51 and 6.23 km s^{− 1}, respectively. V_s values for the metapelites are between 3.86 and 4.34 km s^{− 1}, with a mean value of 4.1 ± 0.15 km s^{− 1}. The psammite and orthogneiss have calculated V_s values of 3.95 and 3.97 km s^{− 1}, respectively.The measured seismic velocities correlate with density and with modal mineralogy, especially the high content of sillimanite and garnet. V_p anisotropy is between 0.15% and 13.97%, and a clear compositional control is evident, mainly in relation to sillimanite abundance. Overall V_s anisotropy ranges from 1% to 11%. Poisson's ratio (σ) lies between 0.25 and 0.35 for the metapelitic granulites, mainly reflecting a high V_p value due to abundant sillimanite in the sample with the highest σ. Anisotropy is probably a function of deformation associated with the closure of the Iapetus ocean in the Silurian as well as later extension in the Devonian. The orientation of the bulk strain ellipsoid in the lower crust is difficult to constrain, but lineation is likely to be NE–SW, given the strike-slip nature of the late Caledonian and subsequent Acadian deformation.When corrected for present-day lower crustal temperature, the experimentally determined V_p values correspond well with velocities from the ICSSP, COOLE I and VARNET seismic refraction lines. Near the xenolith localities, the COOLE I line displays two lower crustal layers with in situ V_p values of 6.85–6.9 and 6.9–8.0 km s^{− 1}, respectively. The upper (lower velocity) layer corresponds well with the metapelitic granulite xenoliths while the lower (higher velocity) layer matches that of the basic granulite xenoliths, though their metamorphic pressures suggest derivation from depths corresponding to the present-day upper mantle.  相似文献