2006
DOI: 10.1098/rspa.2006.1779
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Rayleigh waves guided by topography

Abstract: We consider wave propagation along the surface of an elastic half-space, whose surface is flat except for a straight, infinite length, ridge or trench that does not vary in its cross-section. We seek to resolve the issue of whether such a perturbed surface can support a trapped wave, whose energy is localized to within some vicinity of the defect, and explain physically how this trapping occurs. First, the trapping is addressed by developing an asymptotic scheme, which exploits a small parameter associated wit… Show more

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Cited by 22 publications
(11 citation statements)
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“…By cross-multiplication followed by repeated use of (6.1) to eliminate powers of X 0 higher than 3, we have verified using MATHEMATICA that our c 4 /c 1 and c 4 /c 0 are equal to those of Adams et al [18], βA/B and A/C, respectively. Additionally, as a check on our derivations, we have used the elastic moduli given by (4.11) to compute the coefficients for increasingly small γ and have obtained the same values as the above explicit expressions.…”
Section: Isotropic Materialsmentioning
confidence: 81%
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“…By cross-multiplication followed by repeated use of (6.1) to eliminate powers of X 0 higher than 3, we have verified using MATHEMATICA that our c 4 /c 1 and c 4 /c 0 are equal to those of Adams et al [18], βA/B and A/C, respectively. Additionally, as a check on our derivations, we have used the elastic moduli given by (4.11) to compute the coefficients for increasingly small γ and have obtained the same values as the above explicit expressions.…”
Section: Isotropic Materialsmentioning
confidence: 81%
“…We have extended the analysis of Adams et al [18] to a generally anisotropic elastic material with x 3 = 0 a plane of material symmetry. It is shown that determination of the wave speed correction is also reduced to the solution of a simple eigenvalue problem.…”
Section: Discussionmentioning
confidence: 99%
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“…A potentially observable feature is that edge waves may be guided by the intersection of the effective free surface of the fault plane and the free surface of the Earth. The situation is somewhat analogous to Rayleigh waves guided by topography (Adams et al, 2007). Three-dimensional numerical models, likely including heterogeneous elastic properties, could address this process.…”
Section: Application To Shallow Sliding Faultmentioning
confidence: 99%
“…The resulting infinite family of edge waves is closely related to the Rayleigh wave propagating along the free edge. Related trapped modes in elastic structures have recently been studied in Förster & Weidl (2006), Postnova & Craster (2006) and Adams et al (2007).…”
Section: Introductionmentioning
confidence: 99%