Rayleigh-wave scattering by shallow cracks using the indirect boundary element method

Ávila-Carrera, R.; Rodríguez-Castellanos, Alejandro; Sánchez-Sesma, F. J.; Ortíz-Alemán, C.

doi:10.1088/1742-2132/6/3/002

Cited by 16 publications

(8 citation statements)

References 29 publications

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“…where p i (x 2 ) (i = 1, 2) is defined in Equation 13, and A inc represents the complex amplitude of the incident wave. We use the far-field form of half-space Green's functions (12), and substitute them into Equation (17), and obtain the reflected wave of the same wave number ξ 0 , as shown by Equation (19):…”

Section: Formulation Of Inverse Reconstructionmentioning

confidence: 99%

“…Their early works include Wong [9] and Kawase's [10] applications of discrete wavenumber BEM for calculation of scattered Rayleigh wave fields in frequency domains. Sanchez-Sesma et al [11] and Ávila-Carrera et al [12] used indirect BEM to solve similar problems. For half-space problems, there have been two main modeling patterns: (i) analyzing and meshing the flaw surface only, with usage of half-space Green's functions, in which the interface boundary conditions are satisfied automatically; (ii) analyzing and meshing the flaw surface and the whole interface, with usage of full-space Green's functions.…”

Section: Introductionmentioning

confidence: 99%

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Forward and Inverse Studies on Scattering of Rayleigh Wave at Surface Flaws

Wang

Qian

2018

Applied Sciences

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The Rayleigh wave has been frequently applied in geological seismic inspection and ultrasonic non-destructive testing, due to its low attenuation and dispersion. A thorough and effective utilization of Rayleigh wave requires better understanding of its scattering phenomenon. The paper analyzes the scattering of Rayleigh wave at the canyon-shaped flaws on the surface, both in forward and inverse aspects. Firstly, we suggest a modified boundary element method (BEM) incorporating the far-field displacement patterns into the traditional BEM equation set. Results show that the modified BEM is an efficient and accurate approach for calculating far-field reflection coefficients. Secondly, we propose an inverse reconstruction procedure for the flaw shape using reflection coefficients of Rayleigh wave. By theoretical deduction, it can be proved that the objective function of flaw depth d(x 1) is approximately expressed as an inverse Fourier transform of reflection coefficients in wavenumber domain. Numerical examples are given by substituting the reflection coefficients obtained from the forward analysis into the inversion algorithm, and good agreements are shown between the reconstructed flaw images and the geometric characteristics of the actual flaws.

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Section: Formulation Of Inverse Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Forward and Inverse Studies on Scattering of Rayleigh Wave at Surface Flaws

Wang

Qian

2018

Applied Sciences

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“…Moreover, we present results for layered models using IBEM. Additional details on the discretization scheme can be consulted in [35][36][37][38]. Work related to fluid-solid interfaces using IBEM was also presented in [39], in which general aspects of wave propagation in fluid-solid media were pointed out.…”

Section: Boundary Conditions From the Configuration Depicted Inmentioning

confidence: 99%

Diffraction of Elastic Waves in Fluid-Layered Solid Interfaces by an Integral Formulation

Basaldúa-Sánchez

Samayoa

Rodríguez-Sánchez

et al. 2013

Journal of Applied Mathematics

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In the present communication, scattering of elastic waves in fluid-layered solid interfaces is studied. The indirect boundary element method is used to deal with this wave propagation phenomenon in 2D fluid-layered solid models. The source is represented by Hankel’s function of second kind and this is always applied in the fluid. Our method is an approximate boundary integral technique which is based upon an integral representation for scattered elastic waves using single-layer boundary sources. This approach is typically called indirect because the sources’ strengths are calculated as an intermediate step. In addition, this formulation is regarded as a realization of Huygens’ principle. The results are presented in frequency and time domains. Various aspects related to the different wave types that emerge from this kind of problems are emphasized. A near interface pulse generates changes in the pressure field and can be registered by receivers located in the fluid. In order to show the accuracy of our method, we validated the results with those obtained by the discrete wave number applied to a fluid-solid interface joining two half-spaces, one fluid and the other an elastic solid.

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“…Therefore, some areas of knowledge such as engineering, seismology and geophysics have had a considerable interest in studying scattered wave fields caused by sub-surface cracks over the past century (Mendelsohn et al, 1980;Brind and Achenbach, 1981;Achenbach and Brind, 1981). However, recent works indicate that the study of modifications in the wave propagation phenomena caused by cracks and fractures is still an important issue in physical sciences (Yang et al, 2008;Dineva et al, 2006, Rodríguez-Castellanos et al, 2007and Ávila-Carrera et. al., 2009.…”

Section: Introductionmentioning

confidence: 99%

“…Descriptions of different wave-crack interactions for shallow parallel-crack patterns might be meaningful to several engineering and seismology areas. It is likely that specialists working on evaluation of seismic field amplifications for earthquake site response, interpretation of full waveforms in borehole sonic logs (Ávila-Carrera et al, 2011) or deviations of seismic energy in exploration of hydrocarbon reservoirs could be interested in the results of this numerical research.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of multiple scattering of P and SV waves caused by near-surface parallel cracks

Ávila-Carrera

Rodríguez-Castellanos

Valle-Molina

et al. 2016

GeofInt

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Scattering and diffraction of P and SV waves caused by parallel oriented cracks located near to a free surface are investigated in this work. The Indirect Boundary Element Method (IBEM) was applied for studying the wave propagation phenomena in a half-plane model that contain the cracks. Various incidence angles of P and SV waves are considered. Sometime before it has been reported that a near free-surface crack generates scattered surface waves whose amplitude spectra show conspicuous resonance peaks. Such effect has been attributed to local resonances originated in a virtual layer between the shallowest crack and the free surface. For our case of two parallel crack system, where cracks are located at different depths, the amplitude spectra show additional peaks, which can be associated with the presence of the second crack. Given similar sizes between these two cracks, the characteristic resonance frequency observed at the free surface corresponds mainly to the equivalent layer formed by the shallowest crack and the free surface. However, when the deepest crack becomes sufficiently large with respect to the shallow crack, two resonance characteristic frequency peaks appear in the measured spectra at the free surface. Some examples including a three crack system are also illustrated in our work. The identification and characterization of the seismic response for the scattered field generated by the second and third crack has been an intricate task and, the time domain interpretation of traces becomes quite complicated. The results in this paper have been validated against some other reported from classic papers. In order to show the seismic response and multiple scattering effects due to the presence of systems of cracks, calculations in frequency and time domain are provided.

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Rayleigh-wave scattering by shallow cracks using the indirect boundary element method

Cited by 16 publications

References 29 publications

Forward and Inverse Studies on Scattering of Rayleigh Wave at Surface Flaws

Forward and Inverse Studies on Scattering of Rayleigh Wave at Surface Flaws

Diffraction of Elastic Waves in Fluid-Layered Solid Interfaces by an Integral Formulation

Numerical simulation of multiple scattering of P and SV waves caused by near-surface parallel cracks

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