Propagation of Rayleighs waves in cracked media

Este trabajo está enfocado a la obtención de resultados numéricos que permitan la detección y caracterización de grietas sub-superficiales en sólidos mediante la incidencia de ondas elásticas de Rayleigh. Los resultados se obtienen a partir de ecuaciones integrales de frontera, que pertenecen al campo de la elastodinámica. Una vez que se aplican las condiciones de frontera se obtiene un sistema de ecuaciones integrales del tipo Fredholm de segunda especie y orden cero, el cual es resuelto mediante eliminación gaussiana. El método que se emplea para la discretización de dichas ecuaciones es conocido como «método indirecto de elementos frontera», el cual puede ser visto como una derivación del teorema clásico de Somigliana. A partir de los análisis realizados en el dominio de la frecuencia emergen picos de resonancia que permiten inferir la presencia de grietas mediante los cocientes espectrales. Se analizaron varios modelos de medios agrietados donde se pretende evidenciar la gran utilidad que presenta el uso de los cocientes espectrales para identificar grietas. Se estudiaron los efectos de la orientación y la localización de las grietas. Los resultados obtenidos presentan buena concordancia con los publicados previamente.This work is focused on the finding of numerical results for detection and characterization of sub-surface cracks in solids under the incidence of Rayleighs elastic waves. The results are obtained from boundary integral equations, which belong to the field of dynamics of elasticity. Once applied the boundary conditions, a system of Fredholms integral equations of second kind and zero order is obtained, which is solved using Gaussian elimination. The method that is used for the solution of such integral equations is known as the Indirect Boundary Element Method, which can be seen as a derivation of the Somiglianas classic theorem. On the basis of the analysis made in the frequency domain, resonance peaks emerge and allow us to infer the presence of cracks through the spectral ratios. Several models of cracked media were analyzed, where analyses reveal the great utility that displays the use of spectral ratios to identify cracks. We studied the effects of orientation and location of cracks. The results show good agreement with the previously published.Peer Reviewe

Multi-level fast multipole BEM for 3-D elastodynamics

To reduce computational complexity and memory requirement for 3-D elastodynamics using the boundary element method (BEM), a multi-level fast multipole BEM (FM-BEM) based on the diagonal form for the expansion of the elastodynamic fundamental solution is proposed and demonstrated on numerical examples involving single-region and multi-region configurations where the scattering of seismic waves by a topographical irregularity or a sediment-filled basin is examined

The scattering of SH waves by a finite crack with a superposition based diffraction technique

The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited -- We construct an approximate solution by the addition of independent diffracted terms -- We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge -- This building block is then used to compute the diffraction of the main incident waves -- The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached -- We propose a recipe to determine the number of required interactions as a function of frequency -- The solution derived with the superposition technique can be applied at low and high frequencie

Numerical simulation of ground rotations along 2D topographical profiles under the incidence of elastic plane waves

The surface displacement field along a topographical profile of an elastic half-space subjected to the incidence of elastic waves can be computed using different numerical methods. The method of fundamental solutions (MFS) is one of such techniques in which the diffracted field is constructed by means of a representation in terms of the Green’s functions for discrete forces located outside the domain of interest. From the enforcement of boundary conditions, such forces can be computed; thus, the ground motion can be calculated. One important advantage of MFS over boundary integral techniques is that singularities are avoided. The computation of ground motion rotations implies the application of the rotational operator to the displacement field. This can be done using either numerical derivatives or analytical expressions to compute the rotational Green’s tensor. We validate the method using exact analytical solutions in terms of both displacement and rotation, which are known for simple geometries. To demonstrate the accuracy for generic geometries, we compare results against those obtained using the spectral-element method. We compute surface rotations for incoming plane waves (P, SV, and Rayleigh) near a topographical profile. We point out the effects of topography on rotational ground motion in both frequency and time domains

Propagation of Rayleighs waves in cracked media

This work is focused on the finding of numerical results for detection and characterization of sub-surface cracks in solids under the incidence of Rayleighs elastic waves. The results are obtained from boundary integral equations, which belong to the field of dynamics of elasticity. Once applied the boundary conditions, a system of Fredholms integral equations of second kind and zero order is obtained, which is solved using Gaussian elimination. The method that is used for the solution of such integral equations is known as the Indirect Boundary Element Method, which can be seen as a derivation of the Somiglianas classic theorem. On the basis of the analysis made in the frequency domain, resonance peaks emerge and allow us to infer the presence of cracks through the spectral ratios. Several models of cracked media were analyzed, where analyses reveal the great utility that displays the use of spectral ratios to identify cracks. We studied the effects of orientation and location of cracks. The results show good agreement with the previously published

A generalized theory for full microtremor horizontal-to-vertical [H/V(z, f)] spectral ratio interpretation in offshore and onshore environments

Advances in the field of seismic interferometry have provided a basic theoretical interpretation to the full spectrum of the microtremor horizontal-to-vertical spectral ratio [H/V(f)]. The interpretation has been applied to ambient seismic noise data recorded both at the surface and at depth. The new algorithm, based on the diffuse wavefield assumption, has been used in inversion schemes to estimate seismic wave velocity profiles that are useful input information for engineering and exploration seismology both for earthquake hazard estimation and to characterize surficial sediments. However, until now, the developed algorithms are only suitable for on land environments with no offshore consideration. Here, the microtremor H/V(z, f) modelling is extended for applications to marine sedimentary environments for a 1-D layered medium. The layer propagator matrix formulation is used for the computation of the required Green's functions. Therefore, in the presence of a water layer on top, the propagator matrix for the uppermost layer is defined to account for the properties of the water column. As an application example we analyse eight simple canonical layered earth models. Frequencies ranging from 0.2 to 50 Hz are considered as they cover a broad wavelength interval and aid in practice to investigate subsurface structures in the depth range from a few meters to a few hundreds of meters. Results show a marginal variation of 8 per cent at most for the fundamental frequency when a water layer is present. The water layer leads to variations in H/V peak amplitude of up to 50 per cent atop the solid layers. © The Author(s) 2019

Seismic response of three-dimensional rockfill dams using the Indirect Boundary Element Method

The Indirect Boundary Element Method (IBEM) is used to compute the seismic response of a three-dimensional rockfill dam model. The IBEM is based on a single layer integral representation of elastic fields in terms of the full-space Green function, or fundamental solution of the equations of dynamic elasticity, and the associated force densities along the boundaries. The method has been applied to simulate the ground motion in several configurations of surface geology. Moreover, the IBEM has been used as benchmark to test other procedures. We compute the seismic response of a three-dimensional rockfill dam model placed within a canyon that constitutes an irregularity on the surface of an elastic half-space. The rockfill is also assumed elastic with hysteretic damping to account for energy dissipation. Various types of incident waves are considered to analyze the physical characteristics of the response: symmetries, amplifications, impulse response and the like. Computations are performed in the frequency domain and lead to time response using Fourier analysis. In the present implementation a symmetrical model is used to test symmetries. The boundaries of each region are discretized into boundary elements whose size depends on the shortest wavelength, typically, six boundary segments per wavelength. Usually, the seismic response of rockfill dams is simulated using either finite elements (FEM) or finite differences (FDM). In most applications, commercial tools that combine features of these methods are used to assess the seismic response of the system for a given motion at the base of model. However, in order to consider realistic excitation of seismic waves with different incidence angles and azimuth we explore the IBEM. © 2010 IOP Publishing Ltd