An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves
Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circu...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Apostol, Bogdan Felix [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of seismology - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997, 23(2019), 5 vom: 26. Juni, Seite 1017-1030 |
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| Übergeordnetes Werk: |
volume:23 ; year:2019 ; number:5 ; day:26 ; month:06 ; pages:1017-1030 |
| Links: |
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| DOI / URN: |
10.1007/s10950-019-09850-1 |
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| Katalog-ID: |
SPR014927896 |
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| 100 | 1 | |a Apostol, Bogdan Felix |e verfasserin |4 aut | |
| 245 | 1 | 3 | |a An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves |
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| 520 | |a Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. | ||
| 650 | 4 | |a Seismic source |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Inverse problem |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Seismic waves |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Seismic moment |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Elasticity |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Seismic hyperbola |7 (dpeaa)DE-He213 | |
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| 773 | 1 | 8 | |g volume:23 |g year:2019 |g number:5 |g day:26 |g month:06 |g pages:1017-1030 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s10950-019-09850-1 |z lizenzpflichtig |3 Volltext |
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10.1007/s10950-019-09850-1 doi (DE-627)SPR014927896 (SPR)s10950-019-09850-1-e DE-627 ger DE-627 rakwb eng 550 ASE 38.38 bkl Apostol, Bogdan Felix verfasserin aut An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. Seismic source (dpeaa)DE-He213 Inverse problem (dpeaa)DE-He213 Seismic waves (dpeaa)DE-He213 Seismic moment (dpeaa)DE-He213 Elasticity (dpeaa)DE-He213 Seismic hyperbola (dpeaa)DE-He213 Enthalten in Journal of seismology Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 23(2019), 5 vom: 26. Juni, Seite 1017-1030 (DE-627)271177985 (DE-600)1479210-2 1573-157X nnns volume:23 year:2019 number:5 day:26 month:06 pages:1017-1030 https://dx.doi.org/10.1007/s10950-019-09850-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-GGO SSG-OPC-GEO SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 38.38 ASE AR 23 2019 5 26 06 1017-1030 |
| spelling |
10.1007/s10950-019-09850-1 doi (DE-627)SPR014927896 (SPR)s10950-019-09850-1-e DE-627 ger DE-627 rakwb eng 550 ASE 38.38 bkl Apostol, Bogdan Felix verfasserin aut An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. Seismic source (dpeaa)DE-He213 Inverse problem (dpeaa)DE-He213 Seismic waves (dpeaa)DE-He213 Seismic moment (dpeaa)DE-He213 Elasticity (dpeaa)DE-He213 Seismic hyperbola (dpeaa)DE-He213 Enthalten in Journal of seismology Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 23(2019), 5 vom: 26. Juni, Seite 1017-1030 (DE-627)271177985 (DE-600)1479210-2 1573-157X nnns volume:23 year:2019 number:5 day:26 month:06 pages:1017-1030 https://dx.doi.org/10.1007/s10950-019-09850-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-GGO SSG-OPC-GEO SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 38.38 ASE AR 23 2019 5 26 06 1017-1030 |
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10.1007/s10950-019-09850-1 doi (DE-627)SPR014927896 (SPR)s10950-019-09850-1-e DE-627 ger DE-627 rakwb eng 550 ASE 38.38 bkl Apostol, Bogdan Felix verfasserin aut An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. Seismic source (dpeaa)DE-He213 Inverse problem (dpeaa)DE-He213 Seismic waves (dpeaa)DE-He213 Seismic moment (dpeaa)DE-He213 Elasticity (dpeaa)DE-He213 Seismic hyperbola (dpeaa)DE-He213 Enthalten in Journal of seismology Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 23(2019), 5 vom: 26. Juni, Seite 1017-1030 (DE-627)271177985 (DE-600)1479210-2 1573-157X nnns volume:23 year:2019 number:5 day:26 month:06 pages:1017-1030 https://dx.doi.org/10.1007/s10950-019-09850-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-GGO SSG-OPC-GEO SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 38.38 ASE AR 23 2019 5 26 06 1017-1030 |
| allfieldsGer |
10.1007/s10950-019-09850-1 doi (DE-627)SPR014927896 (SPR)s10950-019-09850-1-e DE-627 ger DE-627 rakwb eng 550 ASE 38.38 bkl Apostol, Bogdan Felix verfasserin aut An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. Seismic source (dpeaa)DE-He213 Inverse problem (dpeaa)DE-He213 Seismic waves (dpeaa)DE-He213 Seismic moment (dpeaa)DE-He213 Elasticity (dpeaa)DE-He213 Seismic hyperbola (dpeaa)DE-He213 Enthalten in Journal of seismology Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 23(2019), 5 vom: 26. Juni, Seite 1017-1030 (DE-627)271177985 (DE-600)1479210-2 1573-157X nnns volume:23 year:2019 number:5 day:26 month:06 pages:1017-1030 https://dx.doi.org/10.1007/s10950-019-09850-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-GGO SSG-OPC-GEO SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 38.38 ASE AR 23 2019 5 26 06 1017-1030 |
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10.1007/s10950-019-09850-1 doi (DE-627)SPR014927896 (SPR)s10950-019-09850-1-e DE-627 ger DE-627 rakwb eng 550 ASE 38.38 bkl Apostol, Bogdan Felix verfasserin aut An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. Seismic source (dpeaa)DE-He213 Inverse problem (dpeaa)DE-He213 Seismic waves (dpeaa)DE-He213 Seismic moment (dpeaa)DE-He213 Elasticity (dpeaa)DE-He213 Seismic hyperbola (dpeaa)DE-He213 Enthalten in Journal of seismology Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 23(2019), 5 vom: 26. Juni, Seite 1017-1030 (DE-627)271177985 (DE-600)1479210-2 1573-157X nnns volume:23 year:2019 number:5 day:26 month:06 pages:1017-1030 https://dx.doi.org/10.1007/s10950-019-09850-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-GGO SSG-OPC-GEO SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 38.38 ASE AR 23 2019 5 26 06 1017-1030 |
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Enthalten in Journal of seismology 23(2019), 5 vom: 26. Juni, Seite 1017-1030 volume:23 year:2019 number:5 day:26 month:06 pages:1017-1030 |
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In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Seismic source</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Inverse problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Seismic waves</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Seismic moment</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Elasticity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Seismic hyperbola</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of seismology</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997</subfield><subfield code="g">23(2019), 5 vom: 26. 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Apostol, Bogdan Felix |
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Apostol, Bogdan Felix ddc 550 bkl 38.38 misc Seismic source misc Inverse problem misc Seismic waves misc Seismic moment misc Elasticity misc Seismic hyperbola An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves |
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550 ASE 38.38 bkl An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves Seismic source (dpeaa)DE-He213 Inverse problem (dpeaa)DE-He213 Seismic waves (dpeaa)DE-He213 Seismic moment (dpeaa)DE-He213 Elasticity (dpeaa)DE-He213 Seismic hyperbola (dpeaa)DE-He213 |
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ddc 550 bkl 38.38 misc Seismic source misc Inverse problem misc Seismic waves misc Seismic moment misc Elasticity misc Seismic hyperbola |
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An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves |
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inverse problem in seismology: derivation of the seismic source parameters from p and s seismic waves |
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An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves |
| abstract |
Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. |
| abstractGer |
Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. |
| abstract_unstemmed |
Abstract This paper presents the solution of an inverse problem in Seismology, which aims at deriving the seismic source parameters from P and S seismic waves. In particular, the paper gives the deduction of the seismic-moment tensor. The problem is tackled in this paper under three particular circumstances. First, we use the amplitude of the far-field (P and S) seismic waves as input data. We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. We assume that the position of the seismic source is known. The far-field waves provide three equations for the six unknown parameters of the general tensor of the seismic moment, such that the system of equations is under-determined. Second, the Kostrov vectorial (dyadic) representation of the seismic moment for a shear faulting is used. This representation relates the seismic moment to the focal displacement in the fault and the orientation of the fault (moment-displacement relation); it reduces the seismic moment to four unknown parameters. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved and the seismic moment is determined, as well as other parameters of the seismic source, like focal volume, focal slip, fault orientation, and duration of the seismic activity in the source. It turns out that the seismic moment is traceless, its magnitude is of the order of the elastic energy stored in the focal region (as expected), and the solution is governed by the unit quadratic form associated with the seismic-moment tensor (related to the magnitude of the longitudinal displacement in the P wave). A useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). This hyperbola provides an image for the focal region: its asymptotes are oriented along the focal displacement and the normal to the fault. Also, the special case of an isotropic seismic moment is presented. Numerical examples are provided for this procedure, and the limitations are discussed. |
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5 |
| title_short |
An inverse problem in seismology: derivation of the seismic source parameters from P and S seismic waves |
| url |
https://dx.doi.org/10.1007/s10950-019-09850-1 |
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| doi_str |
10.1007/s10950-019-09850-1 |
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2024-07-04T03:30:11.884Z |
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| score |
7.4021854 |