Elastic Dislocations in a Layered Half-Space?I. Basic Theory and Numerical Methods

Jovanovich, Dushan B.; Husseini, Moujahed I.; Chinnery, Michael A.

doi:10.1111/j.1365-246x.1974.tb05451.x

Cited by 72 publications

(34 citation statements)

References 18 publications

(12 reference statements)

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“…The solution of surface displacements derived by Sato (1971) has been cited as an example of numerically unstable solutions (e.g. Jovanovich et al 1974a; Wang et al 2003), but Sato's solution obtained with the down‐going algorithm was actually stable at the surface. As stated in Sato (1971), the oscillations of kernel functions in figs 3–5 of his paper do not cause numerical instability, because these kernel functions are multiplied by a function exponentially decreasing with wavenumber.…”

Section: Discussionmentioning

confidence: 99%

“…Substituting these solutions into the original matrix , we can obtain the formal solutions of the surface displacements Y 0 1 , Y 0 2 and Y ′ 0 1 but with the ξ dependence of exp( d ξ) for m ≠ n or exp{(2 H n −1 − d )ξ} for m = n at large ξ. This means that numerical stability in computing the surface deformation fields is not guaranteed, if we use the up‐going algorithm like Singh (1970), Jovanovich et al (1974a) and Rundle (1978).…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Singh's solution was, however, numerically unstable, because he used the up‐going propagator matrix. Jovanovich et al (1974a,b) proposed an approximation method to suppress the numerical instability and showed some examples of computed surface displacement and strain fields. Rundle (1978, 1980, 1981, 1982) developed another elaborate method to compute surface deformation fields and extended Singh's elastic solution to a viscoelastic‐gravitational case.…”

Section: Introductionmentioning

confidence: 99%

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General expressions for internal deformation fields due to a dislocation source in a multilayered elastic half-space

Fukahata

Matsu’ura

2005

Geophysical Journal International

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S U M M A R YWe have obtained general expressions for internal displacement and stress fields due to a point dislocation source in a multilayered elastic half-space under gravity. Most previous expressions for the internal deformation fields were obtained by applying one of two different types of Thomson-Haskell propagator matrix, namely the up-going propagator matrix proposed by Singh (1970) and the down-going propagator matrix proposed by Sato (1971). The solution derived with the up-going propagator matrix is stable below the source, but becomes unstable above the source. In contrast, the solution derived with the down-going propagator matrix is stable above the source, but becomes unstable below the source. We succeeded in unifying the up-going and the down-going propagator matrices into a generalized propagator matrix, and applied it to obtain general expressions that are stable at any depth. By integrating the effects of point sources distributed along an infinitely long horizontal line, we also obtained general expressions for a line dislocation source. We give some examples of internal displacement fields computed with these expressions to examine the effects of layering. Applying the correspondence principle of linear viscoelasticity to the derived elastic solutions, we can obtain the internal viscoelastic displacement and stress fields due to dislocation sources.

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Section: Discussionmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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General expressions for internal deformation fields due to a dislocation source in a multilayered elastic half-space

Fukahata

Matsu’ura

2005

Geophysical Journal International

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“…The problems related to seismic sources in elastic media have been studied extensively by many researchers (Burridge and Knopoff 1964, Singh and BenMenahem 1969, Singh 1970, Sato 1971, Singh et al 1973, Sato and Matsu'ura 1973, Jovanovich et al 1974aFreund and Barnett 1976, etc.). The detailed description about seismic sources is given in the classical texts: Aki and Richards (1980), Ben-Menahem and Singh (1981), Lay and Wallace (1995), and Stein and Wysession (2003).…”

Section: Introductionmentioning

confidence: 99%

Quasi-static Planar Deformation in a Medium Composed of Elastic and Thermoelastic Solid Half Spaces Due to Seismic Sources in an Elastic Solid

Vashisth

Rani²,

Singh

2015

Acta Geophys.

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A b s t r a c t A two-dimensional problem of quasi static deformation of a medium consisting of an elastic half space in welded contact with thermoelastic half space, caused due to seismic sources, is studied. Source is considered to be in the elastic half space. The basic equations, governed by the coupled theory of thermoelasticity, are used to model for thermoelastic half space. The analytical expressions for displacements, strain and stresses in the two half spaces are obtained first for line source and then for dip slip fault. The results for two particular cases, adiabatic conditions and isothermal conditions, are also obtained. Numerical results for displacements, stresses and temperature distribution have also been computed and are shown.

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“…Numerous studies have been undertaken by many scientists to study coseismic deformation in a half‐space earth model. Among them are Steketee (1958), Maruyama (1964), Press (1965), Jovanovich et al (1974a,b) and Okada (1985). Those studies presented analytical expressions for calculating surface displacement, tilt, and strain resulting from various dislocations buried in a semi‐infinite (half‐space) medium.…”

Section: Introductionmentioning

confidence: 99%

Green's functions of coseismic strain changes and investigation of effects of Earth's spherical curvature and radial heterogeneity

Sun

Okubo

2006

Geophysical Journal International

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S U M M A R YA set of Green's functions is presented for calculating the coseismic strain caused by four independent seismic sources in a spherically symmetric, non-rotating, perfectly elastic, and isotropic (SNREI) earth model. Corresponding expressions are derived assuming that the seismic sources are located at the polar axis. The proper combination of these expressions allows calculation of the coseismic strain components resulting from an arbitrary seismic source at any Earth position. Calculations of strain components are made for the near field resulting from the four independent sources at a depth of 32 km inside the 1066A earth model. Results agree well with those calculated for a half-space earth model, thus confirming the validity of the theory presented in this research. A case study is performed and earth model effects are investigated. Furthermore, this paper investigates effects of spherical curvature and the stratified structure of the Earth in computing coseismic strain changes. Curvature effects are small for three types of seismic sources, but extremely large for the horizontal tensile opening on the vertical fault plane. Because a general coseismic deformation comprises four independent solutions, the large curvature effect on the horizontal tensile opening source contributes to the general result. Effects of Earth's stratified structure are large for all depths and epicentral distances. They reach a discrepancy greater than 30 per cent almost everywhere, and 100 per cent in a very far field. Results show that effects of crustal structure mainly exist in the near field; they do not affect results for a far field.

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Elastic Dislocations in a Layered Half-Space?I. Basic Theory and Numerical Methods

Cited by 72 publications

References 18 publications

General expressions for internal deformation fields due to a dislocation source in a multilayered elastic half-space

General expressions for internal deformation fields due to a dislocation source in a multilayered elastic half-space

Quasi-static Planar Deformation in a Medium Composed of Elastic and Thermoelastic Solid Half Spaces Due to Seismic Sources in an Elastic Solid

Green's functions of coseismic strain changes and investigation of effects of Earth's spherical curvature and radial heterogeneity

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