Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation: Extended Materials

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables and denoising). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the Full Waveform Inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method is efficient for the challenging reconstruction of media with salt-domes. We employ the method in two and three-dimensional experiments and show that the eigenvector representation compensates for the lack of low frequency information, it eventually serves us to extract guidelines for the implementation of the method.Comment: 45 pages, 37 figure

Poroelastic Modelling of Wavefields in Heterogeneous Media. Poroelastische Modellierung von Wellenfeldern in Heterogenen Medien

Numerical modelling of seismic waves in heterogeneous, porous reservoir rocks is an important tool in the field of reservoir engineering. A new 2-D velocity-stress finite-differences scheme is presented that allows to simulate waves and coupled diffusion processes within poroelastic media as described by Biot theory. The presented numerical methods allow to further develop rock physics theories of wave-induced fluid flow and contribute to the interpretation of new laboratory experiments

Verification of an ADER-DG method for complex dynamic rupture problems

We present results of thorough benchmarking of an arbitrary high-order derivative discontinuous Galerkin (ADER-DG) method on unstructured meshes for advanced earthquake dynamic rupture problems. We verify the method by comparison to well-established numerical methods in a series of verification exercises, including dipping and branching fault geometries, heterogeneous initial conditions, bimaterial interfaces and several rate-and-state friction laws. We show that the combination of meshing flexibility and high-order accuracy of the ADER-DG method makes it a competitive tool to study earthquake dynamics in geometrically complicated setups

Seismological forward and inverse modelling for upper mantle seismic anisotropy studies

Seismic anisotropy is the dependence of seismic wave velocity on the propagation direction and it is mainly generated by strain-induced lattice preferred orientation (LPO) of intrinsically anisotropic minerals. Despite previous studies have demonstrated that neglecting anisotropy introduces notable imaging artifacts, most tomographic methods rely on the assumption of isotropy, interpreting fast and slow velocity anomalies as related to seismically isotropic sources (e.g., temperature anomalies, presence of a liquid phase, etc). In this Thesis we carried out numerical simulations aiming at improving strain-induced fabric estimates and predicting realistic elastic properties in 2-D and 3-D synthetic domains. We generated synthetic datasets with forward waveform modelling and explored different inverse methodologies (e.g., P- and S-wave travel time tomography, automatic partitioned waveform inversion of surface waves) both with real and synthetic data. Among the results, we present ani-NEWTON21, the first 3D anisotropic teleseismic P-wave tomography revealing upper mantle structures and dynamics beneath the Central Mediterranean. By performing synthetic seismic data inversions we tested how ray density, data quality and regularization (i.e., damping and smoothing factors) influence the tomographic image. Finally, from the comparison of purely isotropic and anisotropic tests, we observed that the first-order effect of including anisotropy in the inversion is to reduce the magnitude of isotropic anomalies, more significantly for low-velocity zones relative to high-velocity zones. The research activities described in this Thesis altogether provide important insights for predicting and isolating seismic anisotropy, and for obtaining more reliable and physically consistent imaging of the Earth’s internal structure.Seismic anisotropy is the dependence of seismic wave velocity on the propagation direction and it is mainly generated by strain-induced lattice preferred orientation (LPO) of intrinsically anisotropic minerals. Despite previous studies have demonstrated that neglecting anisotropy introduces notable imaging artifacts, most tomographic methods rely on the assumption of isotropy, interpreting fast and slow velocity anomalies as related to seismically isotropic sources (e.g., temperature anomalies, presence of a liquid phase, etc). In this Thesis we carried out numerical simulations aiming at improving strain-induced fabric estimates and predicting realistic elastic properties in 2-D and 3-D synthetic domains. We generated synthetic datasets with forward waveform modelling and explored different inverse methodologies (e.g., P- and S-wave travel time tomography, automatic partitioned waveform inversion of surface waves) both with real and synthetic data. Among the results, we present ani-NEWTON21, the first 3D anisotropic teleseismic P-wave tomography revealing upper mantle structures and dynamics beneath the Central Mediterranean. By performing synthetic seismic data inversions we tested how ray density, data quality and regularization (i.e., damping and smoothing factors) influence the tomographic image. Finally, from the comparison of purely isotropic and anisotropic tests, we observed that the first-order effect of including anisotropy in the inversion is to reduce the magnitude of isotropic anomalies, more significantly for low-velocity zones relative to high-velocity zones. The research activities described in this Thesis altogether provide important insights for predicting and isolating seismic anisotropy, and for obtaining more reliable and physically consistent imaging of the Earth’s internal structure

Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications

In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation derived from the Dyson equation under the first-order smoothing approximation. The model establishes accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovicic discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.Comment: 70 pages, 42 figure

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Three-dimensional inversion of transient-electromagnetic data: A comparative study

Inversion of transient-electromagnetic (TEM) data arising from galvanic types of sources is approached by two different methods. Both methods reconstruct the subsurface three-dimensional (3D) electrical conductivity properties directly in the time-domain. A principal difference is given by the scale of the inversion problems to be solved. The first approach represents a small-scale 3D inversion and is based upon well-known tools. It uses a stabilized unconstrained least-squares inversion algorithm in combination with an existing 3D forward modeling solver and is customized to invert for 3D earth models with a limited model complexity. The limitation to only as many model unknowns as typical for classical least-squares problems involves arbitrary and rather unconventional types of model parameters. The inversion scheme has mainly been developed for the purpose of refining a priori known 3D underground structures by means of an inversion. Therefore, a priori information is an important requirement to design a model such that its limited degrees of freedom describe the structures of interest. The inversion is successfully applied to data from a long-offset TEM survey at the active volcano Merapi in Central Java (Indonesia). Despite the restriction of a low model complexity, the scheme offers some versatility as it can be adapted easily to various kinds of model structures. The interpretation of the resistivity images obtained by the inversion have substantially advanced the structural knowledge about the volcano. The second part of this work presents a theoretically more elaborate scheme. It employs imaging techniques originally developed for seismic wavefields. Large-scale 3D problems arising from the inversion for finely parameterized and arbitrarily complicated earth models are addressed by the method. The algorithm uses a conjugate-gradient search for the minimum of an error functional, where the gradient information is obtained via migration or backpropagation of the differences between the data observations and predictions back into the model in reverse time. Treatment for electric field and time derivative of the magnetic field data is given for the specification of the cost functional gradients. The inversion algorithm is successfully applied to a synthetic TEM data set over a conductive anomaly embedded in a half-space. The example involves a total number of more than 376000 model unknowns. The realization of migration techniques for diffusive EM fields involves the backpropagation of a residual field. The residual field excitation originates from the actual receiver positions and is continued during the simulated time range of the measurements. An explicit finite-difference time-stepping scheme is developed in advance of the imaging scheme in order to accomplish both the forward simulation and backpropagation of 3D EM fields. The solution uses a staggered grid and a modified version of the DuFort-Frankel stabilization method and is capable of simulating non-causal fields due to galvanic types of sources. Its parallel implementation allows for reasonable computation times, which are inherently high for explicit time-stepping schemes