Rayleigh waves guided by topography

Adams, Samuel D.M.; Williams, Duncan P.

doi:10.1098/rspa.2006.1779

Cited by 22 publications

(11 citation statements)

References 16 publications

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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%

“…This case has previously been studied by Adams et al [18] using a procedure that is particularly developed for isotropic materials. We now show that our formulae recover their results in this special case.…”

Section: Isotropic Materialsmentioning

confidence: 99%

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Surface waves guided by topography in an anisotropic elastic half-space

Rogerson

Wang

2013

Proc. R. Soc. A.

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We consider the propagation of free surface waves on an elastic half-space that has a localized geometric inhomogeneity perpendicular to the direction of wave propagation (such waves are known as topographyguided surface waves). Our aim is to investigate how such a weak inhomogeneity modifies the surfacewave speed slightly. We first recover previously known results for isotropic materials and then present additional results for a generally anisotropic elastic half-space assuming only one plane of material symmetry. It is shown that a topography-guided surface wave in the present context may or may not propagate depending on a number of factors. In particular, they cannot propagate if the original two-dimensional surface wave on a flat half-space is supersonic with respect to the speed of anti-plane shear waves. For the case when a topographyguided surface wave may exist, the existence and computation of wave speed correction is reduced to the solution of a simple eigenvalue problem whose properties are previously well understood. As a byproduct of our analysis, we deduce that there exists at least one topography-guided surface wave on an isotropic elastic half-space, and that it is unique when the geometric inhomogeneity has sufficiently small amplitude.

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Section: Isotropic Materialsmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

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Surface waves guided by topography in an anisotropic elastic half-space

Rogerson

Wang

2013

Proc. R. Soc. A.

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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%

Nonlinear Interaction of High‐Frequency Seismic Waves With Sliding Fault Planes

Sleep

2019

JGR Solid Earth

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Slip during large crustal earthquakes continues for extended periods of time on spatially extensive fault planes. High-frequency body waves from other parts of the fault system thus impinge on patches of the fault that are still actively sliding. Intuitively, the material within sliding fault planes does not rheologically distinguish between the low-frequency stresses driving the gross earthquake and highfrequency dynamic stresses from impinging body waves. Nonlinear interaction occurs, interrogating the rheology of the fault plane. High-frequency S waves nonlinearly produce additional inelastic slip ΔS on the sliding fault. The ratio of this slip to the elastic displacement (ΔS/ΔS E ), where ΔS E is the elastic displacement, depends on the slip-reflection number, (∂V/∂τ)ρβ, where ∂V/∂τ is the derivative of sliding velocity with respect to shear traction, ρ is density, and β is S-wave velocity. The sliding fault transmits and weakly reflects S waves for small values ≪2 of the parameter; it weakly transmits and strongly reflects for high values ≫2. It is relevant to evaluate ∂V/∂τ at the long-period slip velocity V 0 and shear traction τ 0 of the gross earthquake. The ratio is then ΔS/ΔS E = ρβV 0 Φ/τ 0 , where Φ ≡ (∂V/∂τ)(τ 0 /V 0 ) is measure of the nonlinearity the fault rheology. For example, the parameter Φ at high-frequency impinging S waves is the ratio μ 0 /a of the coefficient of friction to the rate parameter a ≈ 0.01 for rate and state friction. Weak sliding faults (low τ 0 and high V 0 ) strongly reflect impinging S waves. During waning slip, dynamic stresses from S waves antithetical to the gross slip direction and compressional P waves may heterogeneously lock the fault.

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“…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%

Three-dimensional edge waves in plates

Zernov

Kaplunov

2007

Proc. R. Soc. A.

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This paper describes the propagation of three-dimensional symmetric waves localized near the traction-free edge of a semi-infinite elastic plate with either traction-free or fixed faces. For both types of boundary conditions, we present a variational proof of the existence of the low-order edge waves. In addition, for a plate with traction-free faces and zero Poisson ratio, the fundamental edge wave is described by a simple explicit formula, and the first-order edge wave is proved to exist. Qualitative variational predictions are compared with numerical results, which are obtained using expansions in threedimensional Rayleigh-Lamb and shear modes. It is also demonstrated numerically that for any non-zero Poisson ratio in a plate with traction-free faces, the eigenfrequencies related to the first-order wave are complex valued.

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Rayleigh waves guided by topography

Cited by 22 publications

References 16 publications

Surface waves guided by topography in an anisotropic elastic half-space

Surface waves guided by topography in an anisotropic elastic half-space

Nonlinear Interaction of High‐Frequency Seismic Waves With Sliding Fault Planes

Three-dimensional edge waves in plates

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