Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography. The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results

Application of coupled-wave Wentzel-Kramers-Brillouin approximation to ground penetrating radar

This paper deals with bistatic subsurface probing of a horizontally layered dielectric half-space by means of ultra-wideband electromagnetic waves. In particular, the main objective of this work is to present a new method for the solution of the two-dimensional back-scattering problem arising when a pulsed electromagnetic signal impinges on a non-uniform dielectric half-space; this scenario is of interest for ground penetrating radar (GPR) applications. For the analytical description of the signal generated by the interaction of the emitted pulse with the environment, we developed and implemented a novel time-domain version of the coupled-wave Wentzel-Kramers-Brillouin approximation. We compared our solution with finite-difference time-domain (FDTD) results, achieving a very good agreement. We then applied the proposed technique to two case studies: in particular, our method was employed for the post-processing of experimental radargrams collected on Lake Chebarkul, in Russia, and for the simulation of GPR probing of the Moon surface, to detect smooth gradients of the dielectric permittivity in lunar regolith. The main conclusions resulting from our study are that our semi-analytical method is accurate, radically accelerates calculations compared to simpler mathematical formulations with a mostly numerical nature (such as the FDTD technique), and can be effectively used to aid the interpretation of GPR data. The method is capable to correctly predict the protracted return signals originated by smooth transition layers of the subsurface dielectric medium. The accuracy and numerical efficiency of our computational approach make promising its further development

Advanced BEM-based methodologies to identify and simulate wave fields in complex geostructures

To enhance the applicability of BEM for geomechanical modeling numerically optimized BEM models, hybrid FEM-BEM models, and parallel computation of seismic Full Waveform Inversion (FWI) in GPU are implemented. Inverse modeling of seismic wave propagation in inhomogeneous and heterogeneous half-plane is implemented in Boundary Element Method (BEM) using Particle Swarm Optimization (PSO). The Boundary Integral Equations (BIE) based on the fundamental solutions for homogeneous elastic isotropic continuum are modified by introducing mesh-dependent variables. The variables are optimized to obtain the site-specific impedance functions. The PSO-optimized BEM models have significantly improved the efficiency of BEM for seismic wave propagation in arbitrarily inhomogeneous and heterogeneous media. Similarly, a hybrid BEM-FEM approach is developed to evaluate the seismic response of a complex poroelastic soil region containing underground structures. The far-field semi-infinite geological region is modeled via BEM, while the near-field finite geological region is modeled via FEM. The BEM region is integrated into the global FEM system using an equivalent macro-finite-element. The model describes the entire wave path from the seismic source to the local site in a single hybrid model. Additionally, the computational efficiency of time domain FWI algorithm is enhanced by parallel computation in CPU and GPU

Seismic site effects in a deep alluvial basin: numerical analysis by the boundary element method

The main purpose of the paper is the numerical analysis of seismic site effects in Caracas (Venezuela). The analysis is performed considering the boundary element method in the frequency domain. A numerical model including a part of the local topography is considered, it involves a deep alluvial deposit on an elastic bedrock. The amplification of seismic motion (SH-waves, weak motion) is analyzed in terms of level, occurring frequency and location. In this specific site of Caracas, the amplification factor is found to reach a maximum value of 25. Site effects occur in the thickest part of the basin for low frequencies (below 1.0 Hz) and in two intermediate thinner areas for frequencies above 1.0 Hz. The influence of both incidence and shear wave velocities is also investigated. A comparison with microtremor recordings is presented afterwards. The results of both numerical and experimental approaches are in good agreement in terms of fundamental frequencies in the deepest part of the basin. The boundary element method appears to be a reliable and efficient approach for the analysis of seismic site effects

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.Comment: 25 pages, 10 Figure

Production of herbal shampoo from Madagascar periwinkle

Recently, the society interest in using herbal shampoos has increased significantly. Big companies have started to produce herbal shampoo to meet the market demands. However, most of these shampoos contain chemicals that could be harmful to human health. The main purpose of this study are to produce homemade herbal shampoo from Madagascar Periwinkle plant without harmful chemicals and have additional benefits to consumers. By using stem and leaf extract from the plant and cold press machine, we analysed the quantitative aspect of the extracts and use it as a main ingredient to produce homemade herbal shampoo. The extracts are then used as ingredients in production of the shampoo. Several tests were conducted to determine the performance of the shampoos. The Fourier Transform Infrared Spectroscopy (FTIR) analysis shows presence oh -OH groups and C=O bond to indicate the presence of vinca alkaloids. The performance tests result inconsistent to one extract only. This study provided an information to future researchers regarding the study of Madagascar Periwinkle and effectiveness of this plant in herbal shampoos production

Electromagnetic Waves in Contaminated Soils

Soil is a complex, potentially heterogeneous, lossy, and dispersive medium. Modeling the propagation and scattering of electromagnetic (EM) waves in soil is, hence, more challenging than in air or in other less complex media. This chapter will explain fundamentals of the numerical modeling of EM wave propagation and scattering in soil through solving Maxwell’s equations using a finite difference time domain (FDTD) method. The chapter will explain how: (i) the lossy and dispersive soil medium (in both dry and fully water-saturated conditions), (ii) a fourth phase (anomaly), (iii) two different types of transmitting antennae (a monopole and a dipole), and (iv) required absorbing boundary conditions can numerically be modeled. This is described through two examples that simulate the detection of DNAPL (dense nonaqueous-phase liquid) contamination in soil using Cross-well radar (CWR). CWR —otherwise known as cross-borehole GPR (ground penetrating radar)—modality was selected to eliminate the need for simulation of the roughness of the soil-air interface. The two examples demonstrate the scattering effect of a dielectric anomaly (representing a DNAPL pool) on the EM wave propagation through soil. The objective behind selecting these two examples is twofold: (i) explanation of the details and challenges of numerical modeling of EM wave propagation and scattering through soil for an actual problem (in this case, DNAPL detection), and (ii) demonstration of the feasibility of using EM waves for this actual detection problem