A Numerical Study of Lamb's Problem*

Kuhn, M. J.

doi:10.1111/j.1365-2478.1985.tb01355.x

Cited by 14 publications

(4 citation statements)

References 15 publications

(11 reference statements)

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“…If the source is placed near a seismic discontinuity such as the free surface an inhomogeneous P wave can be transformed into a homogeneous S wave by the reflection. Such wave types are intermediate in character between surface and body waves and are referred to as non‐geometric waves because they are linked to a complex incidence angle and it is not possible to associate them with a geometrical ray path (Kuhn 1985).…”

Section: Introductionmentioning

confidence: 99%

“…We refer to this wave as ¯P S to emphasize its affinity to the geometric PS phase. It should, however, be noted that there are different notations for this phase in literature, including ‘¯ P ‐pulse′ (Gilbert & Laster 1962; Gilbert et al 1962; Chapman 1972) and ‘ U ‐pulse′ (Kuhn 1985). To date we are aware of only a few tentative observations of this particular non‐geometric wave (Leet 1949; Kisslinger 1959).…”

Section: Introductionmentioning

confidence: 99%

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The non-geometric¯P Swave in high-resolution seismic data: observations and modelling

Roth¹,

Holliger²

2000

Geophys. J. Int.

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Summary In data from a high‐resolution seismic survey conducted over a near‐surface environment consisting of homogeneous soft clay, we consistently observe a distinct seismic phase arriving between the direct compressional wave and the Rayleigh wave. This phase is characterized by high amplitudes at near offsets and a phase velocity corresponding to about twice the shear wave velocity. Based on analytical and numerical analyses, this signal could be unambiguously identified as a non‐geometric wave, which is excited if the source is located near the Earth’s surface and the Poisson’s ratio in the vicinity of the source is unusually high. To date there are only a few speculative observations of this particular non‐geometric seismic wave phenomenon. However, given the commonly very high Poisson’s ratio of surficial materials, we expect this phase to be present, albeit unidentified, in many near‐surface seismic surveys. The presence of this non‐geometric wave increases the complexity of the seismic record, and failure to identify it may result in misinterpretations, particularly of high‐resolution seismic reflection data as well as of shear wave and surface wave data. Potential applications of this seismic phase may arise from its high sensitivity to the shear wave velocity in the immediate source region.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The non-geometric¯P Swave in high-resolution seismic data: observations and modelling

Roth¹,

Holliger²

2000

Geophys. J. Int.

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“…This test can also be used to check the generation of coupled phases, head waves and Rayleigh waves at a free surface by implementing explosive source inside an homogeneous medium (sometimes called Garvin's (1956) problem). Kuhn (1985) studied the modelling of elastic wave propagation at various positions of the receivers for two kinds of sources, a buried compressional source and a vertically directed load on the surface. When spherical waves interact with a free surface boundary of a half‐space, the incident waves are divided into three major types of waves: reflected waves from the boundary, head waves travelling with a body wave speed and Rayleigh waves decaying exponentially with depth.…”

Section: Elastic Wave Propagationmentioning

confidence: 99%

A wavelet-based method for simulation of two-dimensional elastic wave propagation

Hong¹

2002

Geophysical Journal International

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S U M M A R YA wavelet-based method is introduced for the modelling of elastic wave propagation in 2-D media. The spatial derivative operators in the elastic wave equations are treated through wavelet transforms in a physical domain. The resulting second-order differential equations for time evolution are then solved via a system of first-order differential equations using a displacement-velocity formulation. With the combined aid of a semi-group representation and spatial differentiation using wavelets, a uniform numerical accuracy of spatial differentiation can be maintained across the domain. Absorbing boundary conditions are considered implicitly by including attenuation terms in the governing equations and the traction-free boundary condition at a free surface is implemented by introducing equivalent forces in the semi-group scheme. The method is illustrated by application to SH and P-SV waves for several models and some numerical results are compared with analytical solutions. The wavelet-based method achieves a good numerical simulation and shows an applicability for an elastic-wave study.

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“…Lamb () studied the propagation of a transient disturbance due to a point force in a half space. Afterwards, many studies have been carried out (Nakano ; Sakai ; Cagniard ; De Hoop ; Chapman ; Johnson ; Kuhn ). These studies constitute an important aspect of seismology for which a fixed seismic source is involved.…”

Section: Introductionmentioning

confidence: 99%

Green's function for three‐dimensional elastic wave equation with a moving point source on the free surface with applications

Chen,

Cao

2020

Geophysical Prospecting

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A B S T R A C THigh-speed train seismology has come into being recently. This new kind of seismology uses a high-speed train as a repeatable moving seismic source. Therefore, Green's function for a moving source is needed to make theoretical studies of the high-speed train seismology. Green's function for three-dimensional elastic wave equation with a moving point source on the free surface is derived. It involves a line integral of the Green's function for a fixed point source with different positions and corresponding time delays. We give a rigorous mathematical proof of this Green's function. According to the principle of linear superposition, we have also obtained the Green's function for a group of moving sources which can be regarded as a model of a traveling highspeed train. Based on a temporal convolution, an analytical formula for other moving sources is also given. In terms of a moving Gaussian source, we deal with the issue of numerical calculations of the analytical formula. Applications to modelling of a traveling high-speed train are presented. We have considered both the land case and the bridge case for a traveling high-speed train. The theoretical seismograms show different waveform features for these two cases.

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A Numerical Study of Lamb's Problem*

Cited by 14 publications

References 15 publications

The non-geometric¯P Swave in high-resolution seismic data: observations and modelling

The non-geometric¯P Swave in high-resolution seismic data: observations and modelling

A wavelet-based method for simulation of two-dimensional elastic wave propagation

Green's function for three‐dimensional elastic wave equation with a moving point source on the free surface with applications

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