On low-frequency oscillations of a plate on elastic half-space

Krauklis, P. V.; Molotkov, L. A.

doi:10.1016/0021-8928(63)90084-4

Cited by 6 publications

(5 citation statements)

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“…We assume quasi-static elastic response of the fracture walls. Quasi-static elasticity is justified as we are interested in the long-wavelength limit where crack wave phase velocity is much smaller than elastic wave speeds in the solid (Krauklis, 1962;Staecker & Wang, 1973;Ferrazzini & Aki, 1987;Korneev, 2008;Lipovsky & Dunham, 2015), making seismic wave radiation and elastodynamic stress transfer negligible. Fluid properties are assumed to be homogeneous in the crack.…”

Section: Governing Equations In the Crackmentioning

confidence: 99%

“…In a series of two papers, we investigate the resonance of waves in a coupled conduit-reservoir system in general (Part 1, the current paper) and then apply that to interpret the VLP observations from Kilauea Volcano (Part 2, Liang et al, 2020). A fluid-filled crack supports crack waves with phase velocities much lower than the fluid sound wave speed (Krauklis, 1962;Staecker & Wang, 1973;Chouet, 1986;Ferrazzini & Aki, 1987;Korneev, 2008;Lipovsky & Dunham, 2015;Liang et al, 2017) Figure 1. (a) Coupled conduit-crack system: a cylindrical conduit is connected to a tabular crack at the bottom and to a lava lake at the top.…”

Section: Introductionmentioning

confidence: 99%

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Magma Oscillations in a Conduit‐Reservoir System, Application to Very Long Period (VLP) Seismicity at Basaltic Volcanoes: 1. Theory

2020

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Very long period (VLP, 2-100 s) seismic signals at basaltic volcanoes like Kilauea, Hawai'i, and Mount Erebus, Antarctica are likely from resonant oscillations of magma within the shallow plumbing system. The system consists of conduits connected to cracks (dikes and sills) or reservoirs of other shapes. A quantitative understanding of wave propagation and resonance in a coupled conduit-crack system is required to interpret observations. In this work, we idealize the system as an axisymmetric conduit coupled to a tabular crack, accounting for fluid inertia, compressibility, and viscosity, buoyancy, and crack wall elasticity. We perform time domain simulations and eigenmode analyses of the governing equations, linearized about a rest state. The fundamental mode or conduit-reservoir mode reflects the balance of conduit magma inertia with buoyancy (and, for small cracks, crack wall elasticity). Magma oscillates in an effectively incompressible manner within the conduit, deflating and inflating the crack, which couples to the surrounding solid to produce observable surface displacements. For sufficiently low viscosity magmas, viscous effects are confined to boundary layers. Shorter period modes are primarily reverberating crack waves with negligible coupling to the conduit. Finally, we introduce an approximate reduced model for the conduit-reservoir mode, which can also handle more general reservoir geometries (e.g., spherical chambers). The reduced model connects the observable VLP period and quality factor to two uniquely constrained parameters: the inviscid oscillation period T 0 and the viscous diffusion time vis across the conduit radius. Our models can be extended to study the seismic response of more complex magmatic systems.

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Section: Governing Equations In the Crackmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magma Oscillations in a Conduit‐Reservoir System, Application to Very Long Period (VLP) Seismicity at Basaltic Volcanoes: 1. Theory

2020

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“…A great deal of information has now accumulated concerning the properties of the phase curves for various relations between the parameters of the layer and the medium (see, e~., [6][7][8][9][10])o For a layer on a half space (with sliding contact), Krauklis and Molotkov [11] derived the long-wave asymptote of the perturbations and proved that in this case two waves are propagated -the Rayleigh wave for the half space, and the longitudinal wave in the free plate. Nevertheless, despite the rather large number of publications on this interesting problem, certain features of wave propagation in stratified structures have not yet been studied.…”

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confidence: 99%

Propagation of harmonic waves in a plane layer in contact with an elastic medium

Abdukadyrov¹,

Stepanenko²

1979

Soviet Mining Science

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To identify signals passing through solid rock, generated by powerful sources of vibration, in various aspects of practical geodynamics and in solving questions of protection of engineering structures (buildings, pipelines, tunnels, etc.) from seismic waves and pulsed loads, it is very useful to have information on the fundamental properties of the propagation of elastic waves in inhomogeneous and stratified media, composites, and compound structures and systems.One of the simplest models of a compound (stratified) medium is an inffmitely long layer in contact with elastic media. As some limiting cases of this model we can consider the following, a) The media adjoining the upper and lower surfaces of the layer have the same physical characteristics; b) one medium is absent (the corresponding surface of the layer is free from stresses); c) either the layer or one of the media has zero shear strength (an ideal compressible liquid); d) an elastic layer is immersed in a liquid; e) a layer is compressed between absolutely rigid bodies.The problems also differ in the conditions of contact between the layer and the medium-rigid contact (stresses and displacements equal); sliding contact (no shear resistance in the plane of contact); and various types of elastic contact (we have in mind the presence of a linear elastic bond between the layer and the medium).A fairly extensive bibliography has now accumulated on the existence and description of various types of free waves propagated in a system. This work was begun by Bromwich [1] and Love [2], who discussed longwave and short-wave approximations respectively (since the only linear dimension here is the thickness of the layer, the wavelength is referred to it). Among investigations of the dynamic of stratified media, Brekhovskikh [3] gives the dispersion characteristics of the first few modes of a plane homogeneous layer with surfaces free from stresses. Further investigations were devoted to the properties of the dispersion equations and the construction of the phase curves for various wave modes (a fairly complete survey of this work can be found in [4]).in the USSR, various methods of solving dynamic problems of this type have been successfully developed by the Lenin_grad school (G. I. Petrashen', L. A. Molotkov, K. I. Ogurtsov, G. I. Marchuk, E. I. Shemyakin, and others). In a monograph, describes completed investigations of a number of fundamental aspects of the theory of wave propagation in strata, describes the conditions of existence of various groups of waves (mainly surface waves) in relation to the parameters of the strata, and studies wave perturbations in each particular case. He gives references up to 1960.With the advent of high-speed computers, solution of the dispersion equations became a purely technical problem. A great deal of information has now accumulated concerning the properties of the phase curves for various relations between the parameters of the layer and the medium (see, e~., [6][7][8][9][10])o For a layer on a half space (with sliding cont...

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“…Since its first discovery by Krauklis (1962), crack waves have been studied analytically (Aki et al, 1977;Ferrazzini & Aki, 1987;Korneev, 2008;Lipovsky & Dunham, 2015), experimentally (Cao et al, 2021;Nakagawa et al, 2016;Tang & Cheng, 1988), and numerically by various methods (e.g., Chouet, 1986;Frehner & Schmalholz, 2010;Jin et al, 2022;Liang et al, 2020;O'Reilly et al, 2017;Shauer et al, 2021;Yamamoto & Kawakatsu, 2008). Analytically derived dispersion relations are useful for understanding the propagation behavior but are meant for an infinitely long crack and do not account for the restriction of the finite crack tip.…”

Section: Introductionmentioning

confidence: 99%

“…Slow guided waves that propagate along fluid-filled cracks, named crack waves or Krauklis waves, can be used for inferring the geometries of subsurface cracks and the fluid properties in a wide range of geological settings (Chouet, 1986;Ferrazzini & Aki, 1987;Korneev, 2008;Krauklis, 1962;Lipovsky & Dunham, 2015;Paillet & White, 1982;Tang & Cheng, 1989). In volcanology, crack wave resonances along magma or gasfilled sills and dikes have been used for interpreting long period (LP, 0.5-2 s) and VLP (2-100 s) seismic signals at many volcanos, including Mount Redoubt (Chouet et al, 1994), Aso (Kawakatsu et al, 2000;Niu & Song, 2020), Galeras (Cruz & Chouet, 1997), Asama (Fujita & Ida, 2003), Kusatsi-Shirane (Kumagai et al, 2003;Nakano & Kumagai, 2005), Etna (Lokmer et al, 2008), and Erebus (Aster, 2019).…”

Section: Introductionmentioning

confidence: 99%

Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

Liang,

Peng,

Ampuero

et al. 2024

JGR Solid Earth

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Fluid‐filled cracks sustain a slow guided wave (Krauklis wave or crack wave) whose resonant frequencies are widely used for interpreting long period (LP) and very long period (VLP) seismic signals at active volcanoes. Significant efforts have been made to model this process using analytical developments along an infinite crack or numerical methods on simple crack geometries. In this work, we develop an efficient hybrid numerical method for computing resonant frequencies of complex‐shaped fluid‐filled cracks and networks of cracks and apply it to explain the ratio of spectral peaks in the VLP signals from the Fani Maoré submarine volcano that formed in Mayotte in 2018. By coupling triangular boundary elements and the finite volume method, we successfully handle complex geometries and achieve computational efficiency by discretizing solely the crack surfaces. The resonant frequencies are directly determined through eigenvalue analysis. After proper verification, we systematically analyze the resonant frequencies of rectangular and elliptical cracks, quantifying the effect of aspect ratio and crack stiffness. We then discuss theoretically the contribution of fluid viscosity and seismic radiation to energy dissipation. Finally, we obtain a crack geometry that successfully explains the characteristic ratio between the first two modes of the VLP seismic signals from the Fani Maoré submarine volcano in Mayotte. Our work not only reveals rich eigenmodes in complex‐shaped cracks but also contributes to illuminating the subsurface plumbing system of active volcanoes. The developed model is readily applicable to crack wave resonances in other geological settings, such as glacier hydrology and hydrocarbon reservoirs.

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On low-frequency oscillations of a plate on elastic half-space

Cited by 6 publications

References 0 publications

Magma Oscillations in a Conduit‐Reservoir System, Application to Very Long Period (VLP) Seismicity at Basaltic Volcanoes: 1. Theory

Magma Oscillations in a Conduit‐Reservoir System, Application to Very Long Period (VLP) Seismicity at Basaltic Volcanoes: 1. Theory

Propagation of harmonic waves in a plane layer in contact with an elastic medium

Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

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