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Dispersion-curve inversion of Rayleigh waves to infer subsurface shear-wave velocity is a long-standing problem in seismology. Due to nonlinearity and ill-posedness, sophisticated regularization techniques are required to solve the problem for a stable velocity model. We have formulated the problem as a minimization problem with nonlinear operator constraint and then solve it by using an inexact augmented Lagrangian method, taking advantage of the Haney-Tsai Dix-type relation (a global linear approximation of the nonlinear forward operator). This replaces the original regularized nonlinear problem with iterative minimization of a more tractable regularized linear problem followed by a nonlinear update of the phase velocity (data) in which the update can be performed accurately with any forward modeling engine, for example, the finite-element method. The algorithm allows discretizing the medium with thin layers (for the finite-element method) and thus omitting the layer thicknesses from the unknowns and also allows incorporating arbitrary regularizations to shape the desired velocity model. In this research, we use total variation regularization to retrieve the shear-wave velocity model. We use two synthetic and two real data examples to illustrate the performance of the inversion algorithm with total variation regularization. We find that the method is fast and stable, and it converges to the solution of the original nonlinear problem.
Seismology, like many scientific fields, e.g., music information retrieval and speech signal pro- cessing, is experiencing exponential growth in the amount of data acquired by modern seismo- logical networks. In this thesis, I take advantage of the opportunities offered by "big data" and by the methods developed in the areas of music information retrieval and machine learning to predict better the ground motion generated by earthquakes and to study the properties of the surface layers of the Earth. In order to better predict seismic ground motions, I propose two approaches based on unsupervised deep learning methods, an autoencoder network and Generative Adversarial Networks. The autoencoder technique explores a massive amount of ground motion data, evaluates the required parameters, and generates synthetic ground motion data in the Fourier amplitude spectra (FAS) domain. This method is tested on two synthetic datasets and one real dataset. The application on the real dataset shows that the substantial information contained within the FAS data can be encoded to a four to the five-dimensional manifold. Consequently, only a few independent parameters are required for efficient ground motion prediction. I also propose a method based on Conditional Generative Adversarial Networks (CGAN) for simulating ground motion records in the time-frequency and time domains. CGAN generates the time-frequency domains based on the parameters: magnitude, distance, and shear wave velocities to 30 m depth (VS30). After generating the amplitude of the time-frequency domains using the CGAN model, instead of classical conventional methods that assume the amplitude spectra with a random phase spectrum, the phase of the time-frequency domains is recovered by minimizing the observed and reconstructed spectrograms. In the second part of this dissertation, I propose two methods for the monitoring and characterization of near-surface materials and site effect analyses. I implement an autocorrelation function and an interferometry method to monitor the velocity changes of near-surface materials resulting from the Kumamoto earthquake sequence (Japan, 2016). The observed seismic velocity changes during the strong shaking are due to the non-linear response of the near-surface materials. The results show that the velocity changes lasted for about two months after the Kumamoto mainshock. Furthermore, I used the velocity changes to evaluate the in-situ strain-stress relationship. I also propose a method for assessing the site proxy "VS30" using non-invasive analysis. In the proposed method, a dispersion curve of surface waves is inverted to estimate the shear wave velocity of the subsurface. This method is based on the Dix-like linear operators, which relate the shear wave velocity to the phase velocity. The proposed method is fast, efficient, and stable. All of the methods presented in this work can be used for processing "big data" in seismology and for the analysis of weak and strong ground motion data, to predict ground shaking, and to analyze site responses by considering potential time dependencies and nonlinearities.
In this article, we address the question of how observed ground-motion data can most effectively be modeled for engineering seismological purposes. Toward this goal, we use a data-driven method, based on a deep-learning autoencoder with a variable number of nodes in the bottleneck layer, to determine how many parameters are needed to reconstruct synthetic and observed ground-motion data in terms of their median values and scatter. The reconstruction error as a function of the number of nodes in the bottleneck is used as an indicator of the underlying dimensionality of ground-motion data, that is, the minimum number of predictor variables needed in a ground-motion model. Two synthetic and one observed datasets are studied to prove the performance of the proposed method. We find that mapping ground-motion data to a 2D manifold primarily captures magnitude and distance information and is suited for an approximate data reconstruction. The data reconstruction improves with an increasing number of bottleneck nodes of up to three and four, but it saturates if more nodes are added to the bottleneck.