Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments

We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.Civil, Architectural, and Environmental Engineerin

Spectral element modeling of three dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core

This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling approximation in order to fully account for the effects of self-gravitation. In particular, the perturbation of the gravity field outside the Earth is handled by a projection of the spectral element solution onto the basis of spherical harmonics. Second, we propose a new formulation inside the fluid which allows to account for an arbitrary density stratification. It is based upon a decomposition of the displacement into two scalar potentials, and results in a fully explicit fluid-solid coupling strategy. The implementation of the method is carefully detailed and its accuracy is demonstrated through a series of benchmark tests.Comment: Sent to Geophysical Journal International on July 29, 200

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

Spectral-Element and Adjoint Methods in Seismology

We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem

Modelling Seismic Wave Propagation for Geophysical Imaging

International audienceThe Earth is an heterogeneous complex media from the mineral composition scale (10−6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Günther et al., 2006; Rücker et al., 2006), diffusive methods (Cognon, 1971; Druskin & Knizhnerman, 1988; Goldman & Stover, 1983; Hohmann, 1988; Kuo & Cho, 1980; Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968; Bolt & Smith, 1976; Dablain, 1986; Kelly et al., 1976; Levander, 1988; Marfurt, 1984; Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields

Seismic Waves

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni

Application of full-waveform inversion to shallow-seismic Rayleigh waves on 2D structures

The main objective of this work is the application of 2D elastic full-waveform inversion (FWI) to recorded shallow-seismic Rayleigh waves on 2D structures. The thesis is focused on methodological improvements in preparation for shallow-seismic applications, investigations of line-source implementation in order to consider 3D wave propagation effects in a 2D FWI and applications to field data recorded at the southern rim of the Taunus which is a significantly 2D-heterogeneous structure