The mechanism at the focus of deep earthquakes

Randall, M. J.; Knopoff, L.

doi:10.1029/jb075i026p04965

Cited by 71 publications

(24 citation statements)

References 5 publications

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“…In geophysics, Burridge and Willis (1969) treated briefly the ellipsoidal inclusion with transformation strain in an anisotropic material expanding self-similarly, and suggested that it may be an earthquake source model. Some transformation strain models applied to geophysics are referenced here and concern: the mechanisms at the focus of deep earthquakes (Randall and Knopoff, 1970), analysis based on successive transformation strains applied quasi-statically presented by Mendlguren and Aki, 1978, as a self-organizing mechanism of faulting (Green and Burnley, 1989), fault reactivation at great depth (Houston and Williams, 1991;Wiens and Snider, 2001), shearing instabilities due to transformation strains modeling the mechanics of deep earthquakes (H.W. Green II, 2007).…”

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confidence: 99%

“Driving forces” and radiated fields for expanding/shrinking half-space and strip inclusions with general eigenstrain

Markenscoff

2011

Quart. Appl. Math.

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Abstract.A half-space constrained Eshelby inclusion (in an infinite elastic matrix) with general uniform eigenstrain (or transformation strain) is analyzed when the plane boundary is moving in general subsonic motion starting from rest. The radiated fields are calculated based on the Willis expression for constrained time-dependent inclusions, which involves the three-dimensional dynamic Green's function in an infinite tractionfree body, and they constitute the unique elastodynamic solution, with initial condition the Eshelby static fields obtained as the unique minimum energy solutions by a limiting process from the spherical inclusion. The mechanical energy-release rate and associated "driving force" to create dynamically an incremental region of eigenstrain (due to any physical process) is calculated for general uniform eigenstrain. For dilatational eigenstrain the solution coincides with the one obtained by a limiting process from a spherically expanding inclusion, while for shear eigenstrain the fields are due to the propagation of the rotation. The "driving force" has the same expression both for expanding and shrinking motions, resulting in expenditure of the energy rate for motion of the boundary in both cases. By superposition from the half-space inclusions, the fields and "driving force" for a strip inclusion with both boundaries moving are obtained. The "driving force" consists also of a contribution from the other boundary when it has time to arrive. The presence of applied loading contributes the counterpart of the Peach-Koehler force of dislocations, in addition to the self-force.

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confidence: 99%

“Driving forces” and radiated fields for expanding/shrinking half-space and strip inclusions with general eigenstrain

Markenscoff

2011

Quart. Appl. Math.

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“…Many of the criticisms then made have now been satisfactorily answered, but an important consequence of them was the series of mathematical papers by Randall ( , 1964aRandall ( , b, 1966Randall ( , 1968Randall ( , 1970bRandall ( , d, e, 1972aRandall ( , 1973aRandall and Knopoff 1970), dealing with source mechanism and the spectral properties of radiation from seismic sources. The analysis of deep-focus shocks is summarised in Randall (1972b).…”

Section: Earthquake Mechanismmentioning

confidence: 97%

“…Both these regions possess structures of quite different type. The main islands of New Zealand have a typical continental crustal thickness of 30-35 kin, established in limited regions from a small number of records of explosions and natural earthquakes (Eiby, 1957(Eiby, , 1968cGarrick, 1968;Hamilton, 1966), from surface-wave dispersion (Thomson and Evison, 1962) and more widely from gravity measurements (Reilly, 1962).…”

Section: Seismicity and Structurementioning

confidence: 99%

Seismology in New Zealand

Eiby

1975

Geophysical Surveys

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Abstract. New Zealand is a country of moderate seismicity. Its earthquakes are well-located and their magnitudes found with closely-spaced modern seismographs. Historical catalogues have been prepared. Deep and shallow shocks are associated with two active continental margins having the usual geophysical associations. The northern one is orientated towards the Pacific and the southern one towards the Tasman Sea. The structure is complex, and below the continental-type crust there are large lateral inhomogeneities in the upper mantle. There is a marked lack of correlation between all except the most superficial earthquake loci and the geological faults and this persists to the microearthquake level. New Zealand seismologists have made theoretical studies of earthquake mechanism and examined the statistical properties of earthquake occurrence. They have also studied the fine structure of the Earth's core, and made microzoning and other studies with engineering implications.R~sum~. Le niveau de la sismicit6 de la Nouvelle Z61ande n'est que moyen, mais ses tremblements de terre et leurs associations g6ologiques et g6ophysiques sont extramement bien document6s. Chaque ann6e plusieurs centaines de s6ismes sont localis6s avec pr6cision par utilisation des instruments modernes dispos6s en r6seau/~ maille 6troite (Voir La structure est complexe. Sous nne 6corce de type continental existent des inhomog6n6it6s importantes du manteau sup6rieur. Entre les failles g6ologiques et les s6ismes (saul les plus surficiels, mais avec l'ensemble des plus petits) nulle correlation 6vidente n'existe.Outre leurs recherches concemant la structure et la sismicit~, les sismologues n6oz61andais ont fait des &udes th6oriques du m6canisme des tremblements de terre, et ils ont 6tudi6 les propri6t6s statistiques de leurs incidences. De plus, des recherches actuelles concernent la structure fine du noyau terrestre, l'6tablissement des zones de sous-sol pour la construction antisismique, et d'autres probl~mes d'importance pour l'ing~nieur et pour la sur~t6 publique. Zusammenfassung

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“…A general moment tensor can be viewed as a mixture of isotropic sources, double couples and compensated linear vector dipoles (CLVD sources) (Randall & Knopoff 1970;Geller 1976;and Strelitz 1978), or in physical terms, a volume change, a shear dislocation and a sudden loss of rigidity. The decomposition is the description of the source sought, not the elements of the moment tensor itself.…”

Section: Introductionmentioning

confidence: 99%

Choosing the ‘best’ double couple from a moment-tensor inversion

Strelitz

1989

Geophysical Journal International

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General moment-tensor solutions contain double couples, compensated linear vector dipoles (CLVD's) and isotropic sources. Since double-couple solutions are considered to be standard, it is important to find the best double-couple solution that is consistent with the original solution. It is proved that for a number of reasonable measures of fit, the best double couple is the one formed by removing a CLVD source with a magnitude of the intermediate non-zero eigenvalue. It is also shown that mixtures of double couple and CLVD's may result from near-source changes in rigidity.

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The mechanism at the focus of deep earthquakes

Cited by 71 publications

References 5 publications

“Driving forces” and radiated fields for expanding/shrinking half-space and strip inclusions with general eigenstrain

“Driving forces” and radiated fields for expanding/shrinking half-space and strip inclusions with general eigenstrain

Seismology in New Zealand

Choosing the ‘best’ double couple from a moment-tensor inversion

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