Energy equipartition in theoretical and recovered seismograms

Sánchez‐Sesma, Francisco J.; Victoria-Tobon, Ehecatl; Carbajal-Romero, Manuel; Rodríguez-Sánchez, José Efraín; Rodríguez-Castellanos, Alejandro

doi:10.1016/j.jappgeo.2018.01.032

Cited by 6 publications

(7 citation statements)

References 19 publications

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“…The coherent behavior of the elastic wave in the presence of many edge dislocations is described by the average Green function G , where G, according to [31] and Eqs. (1,9,11,12), should be the solution of…”

Section: Coherent Propagationmentioning

confidence: 99%

“…Here, we used the expression for perturbation potential of a single edge dislocation from Eqn. (11).…”

Section: Acknowledgementsmentioning

confidence: 99%

“…The definition of remaining entities in Eqns. (11)(12)(13)(14) is the same as in [29]. It means that the replacement of g(ω) does not affect the form of results for D R , D ∆G 1q up to replacement of a, providing us with a final result for diffusion constant of screw dislocations D = B 2 q 2 ω (1 + a) k P (k; q)G(k)G * (k)P (k; q) (16) In order to analyze the modified result for screw dislocations we have to find the explicit expression for D. It is established on the basis of the result for the diffusion constant (we denote it as D Isc ) from [29], which reads as…”

Section: Appendix C: Optical Theoremmentioning

confidence: 99%

“…In this way the specifics of wave interference arising from specific obstacles is lost, but the resuting algebra is much simpler to deal with. This approach has been describe by Ryzhik et al [10] and is widely used in seismology, where the nature of the scatterers that are obstacles to the propagation of seismic elastic waves is largely unknown [11] Topological defects, such as dislocations, present an obstacle of a different nature to the propagation of elastic waves. For wavelengths longer than a few interatomic spaces, a continuum approximation is appropriate, and this is the approach we shall adopt in this work.…”

Section: Introductionmentioning

confidence: 99%

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Coherent propagation and incoherent diffusion of elastic waves in a two dimensional continuum with a random distribution of edge dislocations

Churochkin¹,

Lund²

2020

Preprint

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We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls-Nabarro force the dislocations can oscillate around an equilibrium position with frequency ω 0 . The coupling between waves and dislocations is given by the Peach-Koehler force.This leads to a wave equation with an inhomogeneous term that involves a differential operator.In the coherent case, a Dyson equation for a mass operator is set up and solved to all orders in perturbation theory in independent scattering approximation (ISA). As a result, a complex index of refraction is obtained, from which an effectve wave velocity and attenuation can be read off, for both longitudinal and transverse waves. In the incoherent case a Bethe-Salpeter equation is set up, and solved to leading order in perturbation theory in the limit of low frequency and wave number.A diffusion equation is obtained and the (frequency-dependent) diffusion coefficient is explicitly calculated. It reduces to the value obtained with energy transfer arguments at low frequency.An important intermediate step is the obtention of a Ward-Takahashi identity (WTI) for a wave equation that involves a differential operator, which is shown to be compatible with the ISA.

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Section: Coherent Propagationmentioning

confidence: 99%

“…Here, we used the expression for perturbation potential of a single edge dislocation from Eqn. (11).…”

Section: Acknowledgementsmentioning

confidence: 99%

Section: Appendix C: Optical Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coherent propagation and incoherent diffusion of elastic waves in a two dimensional continuum with a random distribution of edge dislocations

Churochkin¹,

Lund²

2020

Preprint

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“…The Einstein summation convention is assumed, i.e repeated index implies summation over the range of that index. From Equation A.2, it is possible to derive the classical Somigliana representation theorem (e.g Wapenaar & Fokkema, 2006;van Manen et al, 2006;Snieder et al, 2007;Sánchez-Sesma et al, 2008;Sánchez-Sesma et al, 2018)…”

mentioning

confidence: 99%

A generalized theory for full microtremor horizontal-to-vertical [H/V(z, f)] spectral ratio interpretation in offshore and onshore environments

Lontsi

García‐Jerez

Molina‐Villegas

et al. 2019

Geophysical Journal International

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Advances in the field of seismic interferometry have provided a basic theoretical interpretation to the full spectrum of the microtremor horizontal-to-vertical spectral ratio [H/V (f )]. The interpretation has been applied to ambient seismic noise data recorded both at the surface and at depth. The new algorithm, based on the diffuse wavefield assumption, has been used in inversion schemes to estimate seismic wave velocity profiles that are useful input information for engineering and exploration seismology both for earthquake hazard estimation and to characterize surficial sediments. However, until arXiv:1907.04606v1 [physics.geo-ph]

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