Elastic waves scattering and radiation by fractal inhomogeneity of a medium
I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid fo...
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| Autor*in: |
Shapiro, S. A. [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Oxford, UK: Blackwell Publishing Ltd ; 1992 |
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| Schlagwörter: |
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| Umfang: |
Online-Ressource |
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| Reproduktion: |
2007 ; Blackwell Publishing Journal Backfiles 1879-2005 |
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| Übergeordnetes Werk: |
In: Geophysical journal international - Oxford . Wiley-Blackwell, 1922, 110(1992), 3, Seite 0 |
| Übergeordnetes Werk: |
volume:110 ; year:1992 ; number:3 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1111/j.1365-246X.1992.tb02094.x |
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NLEJ23965384X |
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| 520 | |a I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. | ||
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10.1111/j.1365-246X.1992.tb02094.x doi (DE-627)NLEJ23965384X DE-627 ger DE-627 rakwb Shapiro, S. A. verfasserin aut Elastic waves scattering and radiation by fractal inhomogeneity of a medium Oxford, UK Blackwell Publishing Ltd 1992 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| elastic waves In Geophysical journal international Oxford . Wiley-Blackwell, 1922 110(1992), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:110 year:1992 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1992.tb02094.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 110 1992 3 0 |
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10.1111/j.1365-246X.1992.tb02094.x doi (DE-627)NLEJ23965384X DE-627 ger DE-627 rakwb Shapiro, S. A. verfasserin aut Elastic waves scattering and radiation by fractal inhomogeneity of a medium Oxford, UK Blackwell Publishing Ltd 1992 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| elastic waves In Geophysical journal international Oxford . Wiley-Blackwell, 1922 110(1992), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:110 year:1992 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1992.tb02094.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 110 1992 3 0 |
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10.1111/j.1365-246X.1992.tb02094.x doi (DE-627)NLEJ23965384X DE-627 ger DE-627 rakwb Shapiro, S. A. verfasserin aut Elastic waves scattering and radiation by fractal inhomogeneity of a medium Oxford, UK Blackwell Publishing Ltd 1992 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| elastic waves In Geophysical journal international Oxford . Wiley-Blackwell, 1922 110(1992), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:110 year:1992 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1992.tb02094.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 110 1992 3 0 |
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10.1111/j.1365-246X.1992.tb02094.x doi (DE-627)NLEJ23965384X DE-627 ger DE-627 rakwb Shapiro, S. A. verfasserin aut Elastic waves scattering and radiation by fractal inhomogeneity of a medium Oxford, UK Blackwell Publishing Ltd 1992 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| elastic waves In Geophysical journal international Oxford . Wiley-Blackwell, 1922 110(1992), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:110 year:1992 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1992.tb02094.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 110 1992 3 0 |
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10.1111/j.1365-246X.1992.tb02094.x doi (DE-627)NLEJ23965384X DE-627 ger DE-627 rakwb Shapiro, S. A. verfasserin aut Elastic waves scattering and radiation by fractal inhomogeneity of a medium Oxford, UK Blackwell Publishing Ltd 1992 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| elastic waves In Geophysical journal international Oxford . Wiley-Blackwell, 1922 110(1992), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:110 year:1992 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1992.tb02094.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 110 1992 3 0 |
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Elastic waves scattering and radiation by fractal inhomogeneity of a medium |
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I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. |
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I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. |
| abstract_unstemmed |
I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈>-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ23965384X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210707092228.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">120426s1992 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1111/j.1365-246X.1992.tb02094.x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ23965384X</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Shapiro, S. A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elastic waves scattering and radiation by fractal inhomogeneity of a medium</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford, UK</subfield><subfield code="b">Blackwell Publishing Ltd</subfield><subfield code="c">1992</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)&#x006e;̈, where θ is a scattering angle and the constant &#x006e;̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+&#x006e;̈ if &#x006e;̈>-2 and σ∝ω2 if &#x006e;̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="d">2007</subfield><subfield code="f">Blackwell Publishing Journal Backfiles 1879-2005</subfield><subfield code="7">|2007||||||||||</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">elastic waves</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Geophysical journal international</subfield><subfield code="d">Oxford . Wiley-Blackwell, 1922</subfield><subfield code="g">110(1992), 3, Seite 0</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ243927827</subfield><subfield code="w">(DE-600)2006420-2</subfield><subfield code="x">1365-246X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:110</subfield><subfield code="g">year:1992</subfield><subfield code="g">number:3</subfield><subfield code="g">pages:0</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://dx.doi.org/10.1111/j.1365-246X.1992.tb02094.x</subfield><subfield code="q">text/html</subfield><subfield code="x">Verlag</subfield><subfield code="z">Deutschlandweit zugänglich</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DJB</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">110</subfield><subfield code="j">1992</subfield><subfield code="e">3</subfield><subfield code="h">0</subfield></datafield></record></collection>
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