Green's function model for time‐reversal focusing of elastic surface waves.

2008 ◽  
Vol 124 (4) ◽  
pp. 2514-2514
Author(s):  
Evgenia A. Zabolotskaya ◽  
Yurii A. Ilinskii ◽  
Mark F. Hamilton
Keyword(s):  
Green’S Function ◽  
Surface Waves ◽  
Green's Function ◽  
Time Reversal ◽  
Function Model ◽  
Elastic Surface

An orthonormality relation for elastic body waves

1968 ◽  
Vol 58 (6) ◽  
pp. 1949-1954
Author(s):  
L. E. Alsop
Keyword(s):  
Green’S Function ◽  
Surface Waves ◽  
Elastic Body ◽  
Half Space ◽  
Green's Function ◽  
Body Waves ◽  
P Wave ◽  
Wave Incident ◽  
Elastic Surface

ABSTRACT Herrera's orthonormality relation for elastic surface waves is generalized for elastic body waves. As an example, the normalization of a P-wave incident on the surface of a half space is considered. The Green's function for body waves and surface waves is obtained.

scholarly journals Unified double- and single-sided homogeneous Green’s function representations

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160162 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Time Reversal ◽  
Wave Theory ◽  
Boundary Integral ◽  
Open Boundary ◽  
Quantum Mechanical ◽  
Holographic Imaging ◽  
Scattering Time

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.

The Search of Diffusive Properties in Ambient Seismic Noise

2021 ◽  
Author(s):  
José Piña-Flores ◽  
Martín Cárdenas-Soto ◽  
Antonio García-Jerez ◽  
Michel Campillo ◽  
Francisco J. Sánchez-Sesma
Keyword(s):  
Green’S Function ◽  
Surface Waves ◽  
Green's Function ◽  
Seismic Noise ◽  
Elastic Field ◽  
Spectral Ratio ◽  
Ambient Seismic Noise ◽  
Data Sets ◽  
Original Experiment ◽  
Imaging Theory

ABSTRACT Ambient seismic noise (ASN) is becoming of interest for geophysical exploration and engineering seismology, because it is possible to exploit its potential for imaging. Theory asserts that the Green’s function can be retrieved from correlations within a diffuse field. Surface waves are the most conspicuous part of Green’s function in layered media. Thus, the velocities of surface waves can be obtained from ASN if the wavefield is diffuse. There is widespread interest in the conditions of emergence and properties of diffuse fields. In the applications, useful approximations of the Green’s function can be obtained from cross correlations of recorded motions of ASN. An elastic field is diffuse if the background illumination is azimuthally uniform and equipartitioned. It happens with the coda waves in earthquakes and has been verified in carefully planned experiments. For one of these data sets, the 1999 Chilpancingo (Mexico) experiment, there are some records of earthquake pre-events that undoubtedly are composed of ASN, so that the processing for coda can be tested on them. We decompose the ASN energies and study their equilibration. The scheme is inspired by the original experiment and uses the ASN recorded in an L-shaped array that allows the computation of spatial derivatives. It requires care in establishing the appropriate ranges for measuring parameters. In this search for robust indicators of diffusivity, we are led to establish that under certain circumstances, the S and P energy equilibration is a process that anticipates the diffusion regime (not necessarily isotropy), which justifies the use of horizontal-to-vertical spectral ratio in the context of diffuse-field theory.

scholarly journals A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

2016 ◽  
Vol 205 (1) ◽  
pp. 531-535 ◽  
Author(s):  
Kees Wapenaar ◽  
Jan Thorbecke ◽  
Joost van der Neut
Keyword(s):  
Green’S Function ◽  
Inverse Scattering ◽  
Green's Function ◽  
Time Reversal ◽  
Boundary Integral ◽  
Open Surface ◽  
Function Representation ◽  
Holographic Imaging ◽  
Scattering Time ◽  
Time Reversal Acoustics

Abstract Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

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