Microseisms and plate waves are two types of seismic waves that are generated by the interaction between the ocean surface gravity waves and the solid Earth, providing the primary seismic noise source on the Earth.

The source distribution of microseisms is important to study their generation mechanisms and in imaging Earth structures. Comparisons between different preprocessing methods to identify microseism source areas were made using Cascadia Initiative ocean bottom seismometer array data, where it was found that the total energy arriving from pelagic and coastal areas is similar. Moreover, pelagic-generated signals tend to be weaker but have a longer duration, in contrast to coastal-generated signals that tend to be stronger but have a shorter duration.

Ocean surface gravity waves interacting with Antarctic ice shelves affect their integrity and likely play a role in their evolution, critical for assessing long-term changes that will affect the rate of sea level rise. Long-period gravity-wave impacts excite plate waves in the ice shelves, which can expand pre-existing fractures and trigger iceberg calving. Flexural-gravity waves (<20 mHz) and extensional Lamb waves (20-100 mHz) were identified on both the Ross Ice Shelf and the Pine Island Glacier ice shelf. Considering the ubiquitous presence of storm activity in the Southern Ocean and the similar observations at both the Ross Ice Shelf and the Pine Island Glacier ice shelves, it is likely that most, if not all, West Antarctic ice shelves are subjected to similar gravity-wave excitation. The transfer of ocean wave energy to ice shelves was determined from the comparison of gravity wave forcing of the Ross Ice Shelf measured by an ocean bottom hydrophone near the ice shelf front with nearby broadband on-ice seismic observations. The relative impact of gravity wave forcing on the Ross Ice Shelf integrity is inferred from comparison of the Ross Ice Shelf response amplitudes in 0.001-0.04 Hz band and from the association of icequake activity with very-long-period (0.001-0.003 Hz) and swell (0.03-0.1 Hz) band responses.

In ocean acoustics and seismology, the Earth’s subsurface is imaged using acoustic and seismic waves. As they propagate through the ocean and solid earth, these waves obtain geophysical information. This information is recovered via optimization procedures which fit physical models to wavefield observations from sensor arrays. The estimation of geophysical model parameters from the observations, typically referred to as inverse problems, are challenging due to many issues, e.g. noisy and incomplete observations, as well as non-linear forward models.

In this dissertation, geophysical inversion methods are developed based on sparse model- ing and dictionary learning, an unsupervised machine learning method. These techniques employ more sophisticated model priors and latent representations than conventional methods, and obtain state-of-the-art performance in a variety of signal processing tasks. Sparse modeling assumes that signals can be reconstructed to acceptable accuracy using a small (sparse) number of vectors, called atoms, from a larger set of atoms, or dictionary. Sparsifying dictioniaries can be designed from generic functions such as wavelets, or can be learned directly from the data via dictionary learning. Provided sufficient signal examples exist, dictionary learning can learn sparsifying dictionaries which obtain better performance than generic dictionaries. Conventional methods, rely on smoothness and second order statistics (e.g. empirical orthogonal functions (EOFs)) to estimate geophysical structure. In contrast, sparse methods potentially permit the recovery of true smooth and discontinuous geophysical structures.

Ocean acoustic sound speed profile (SSP) estimation requires the inversion of acoustic fields using limited observations. A specific case of sparse modeling, called compressive sensing (CS) asserts that certain underdetermined problems can be solved in high resolution, provided their solutions are sparse. CS is used to estimate SSPs in a range-independent shallow ocean by inverting a non-linear acoustic propagation model. It is shown that SSPs can be estimated using CS to resolve fine-scale structure.

To provide constraints on their inversion, ocean sound speed profiles (SSPs) are modeled often using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimum-energy constraint on their coefficients, often yields low resolution SSP estimates. It is shown that dictionary learning, a form of unsupervised machine learning, can improve SSP resolution by generating a dictionary of shape functions for sparse modeling that optimally compress SSPs; both minimizing the reconstruction error and the number of coefficients. These learned dictionaries (LDs) are not constrained to be orthogonal and thus, fit the given signals such that each signal example is approximated using few LD entries. LDs describing SSP observations from the High Frequency ‘97 experiment and the South China Sea are generated using the K-SVD algorithm. These LDs better explain SSP variability and require fewer coefficients than EOFs, describing much of the variability with one coefficient. Thus, LDs improve the resolution of SSP estimates with negligible computational burden.

A 2D travel time tomography method is developed based on sparse modeling and dictionary learning. The method regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. Dictionary learning is used in the inversion method to adapt dictionaries to specific slowness maps. This patch regularization, called the local model, is integrated into the overall slowness map, called the global model. The local model considers small-scale variations using a sparsity constraint and the global model considers larger-scale features constrained using l2 regularization. This strategy in a locally-sparse travel time tomography (LST) approach enables simultaneous modeling of smooth and discontinuous slowness features. This is in contrast to conventional tomography methods, which constrain models to be exclusively smooth or discontinuous. We develop a maximum a posteriori formulation for LST and exploit the sparsity of slowness patches using dictionary learning. The LST approach compares favorably with smoothness and total variation regularization methods on densely, but irregularly sampled synthetic slowness maps.

Finally, the LST travel time tomography method is used to obtain high-resolution subsur- face geophysical structure in Long Beach, CA, from seismic noise recorded on a “large-N” array with 5200 geophones (∼ 13.5 million travel times). LST exploits the dense sampling obtained by ambient noise processing on large arrays by learning a dictionary of local, or small-scale, geophysical features directly from the data. Using LST, a high-resolution 1 Hz Rayleigh wave phase speed map of Long Beach is obtained. Among the geophysical features shown in the map, the important Silverado aquifer is well isolated relative to previous surface wave tomography studies. The results show promise for LST in obtaining detailed geophysical structure in travel time tomography studies.

Ambient seismic noise consists of emergent and impulsive signals containing distinguishing features from natural and anthropogenic activities. Developing techniques to identify and utilize specific cultural noise signals will benefit studies performing seismic imaging from continuous records. We examine time and frequency spectral features in urban cultural noise from a spatially dense seismic array located in Long Beach, California. The spectral features are used to develop self-supervised clustering models that differentiate cultural noise into separable classes of signal. We use 161 hours of seismic data from 5200 geophones that contain impulsive signals originating from human activity. The model uses convolutional autoencoders, a self-supervised machine learning technique, to learn latent features from spectrograms produced from the data. The latent space features are evaluated using a deep clustering algorithm to separate the noise signals into different classes. We evaluate the separation of data and analyze the classes to identify the likely sources of the signals present in the data. To interpret the model performance we examine the time-frequency domain features of the signals and the spatiotemporal evolution observed for each class. We demonstrate autoencoder feature extraction used with probabilistic clustering algorithms is a useful approach to characterize seismic noise and identify signals in the data with a low signal-to-noise ratio.

Passive acoustics, or the recording of pressure signals from uncontrolled sound sources, is a powerful tool for monitoring man-made and natural sounds in the ocean. Passive acoustics can be used to detect changes in physical processes within the environment, study behavior and movement of marine animals, or observe presence and motion of ocean vessels and vehicles. Advances in ocean instrumentation and data storage have improved the availability and quality of ambient noise recordings, but there is an ongoing effort to improve signal processing algorithms for extracting useful information from the ambient noise. This dissertation uses machine learning as a framework to address problems in underwater passive acoustic signal processing. Statistical learning has been used for decades, but machine learning has recently gained popularity due to the exponential growth of data and its ability to capitalize on these data with efficient GPU computation. The chapters within this dissertation cover two types of problems: characterization and classification of ambient noise, and localization of passive acoustic sources.

First, ambient noise in the eastern Arctic was studied from April to September 2013 using a vertical hydrophone array as it drifted from near the North Pole to north of Fram Strait. Median power spectral estimates and empirical probability density functions (PDFs) along the array transit show a change in the ambient noise levels corresponding to seismic survey airgun occurrence and received level at low frequencies and transient ice noises at high frequencies. Noise contributors were manually identified and included broadband and tonal ice noises, bowhead whale calling, seismic airgun surveys, and earthquake $T$ phases. The bowhead whale or whales detected were believed to belong to the endangered Spitsbergen population and were recorded when the array was as far north as 86$\degree$24'N. Then, ambient noise recorded in a Hawaiian coral reef was analyzed for classification of whale song and fish calls. Using automatically detected acoustic events, two clustering processes were proposed: clustering handpicked acoustic metrics using unsupervised methods, and deep embedded clustering (DEC) to learn latent features and clusters from fixed-length power spectrograms. When compared on simulated signals of fish calls and whale song, the unsupervised clustering methods were confounded by overlap in the handpicked features while DEC identified clusters with fish calls, whale song, and events with simultaneous fish calls and whale song. Both clustering approaches were applied to recordings from directional autonomous seafloor acoustic recorder (DASAR) sensors on a Hawaiian coral reef in February 2020. Next, source localization in ocean acoustics was posed as a machine learning problem in which data-driven methods learned source ranges or direction-of-arrival directly from observed acoustic data. The pressure received by a vertical linear array was preprocessed by constructing a normalized sample covariance matrix (SCM) and used as the input for three machine learning methods: feed-forward neural networks (FNN), support vector machines (SVM) and random forests (RF). The FNN, SVM, RF and conventional matched-field processing were applied to recordings from ships in the Noise09 experiment to demonstrate the potential of machine learning for underwater source localization. The source localization problem was extended by examining the relationship between conventional beamforming and linear supervised learning. Then, a nonlinear deep feedforward neural network (FNN) was developed for direction-of-arrival (DOA) estimation for two-source DOA and for $K$-source DOA, where $K$ is unknown. With multiple snapshots, $K$-source FNN achieved resolution and accuracy similar to Multiple Signal Classification (MUSIC) and SBL for an unknown number of sources. The practicality of the deep FNN model was demonstrated on ships in the Swellex96 experimental data.

Spectrum sensing is essential for enabling optimal spectrum usage and ensuring data security, especially with the proliferation of IoT devices. Spectrum sensing involves detecting and characterizing intentional RF emissions called overt, and unintentional RF emissions called emanations. The thesis focuses on two pivotal aspects of spectrum sensing: characterization of overt specifically modulation classification and characterization of emanations.

Three distinct works are presented on modulation classification. DL has been successfully used recently. The focus, however, has been model-centric, with attempts to improve performance on the standard synthetic dataset RML16. The quality of the training dataset impacts model performance on real data. A hybrid approach is taken by leveraging wireless domain knowledge to improve dataset quality. The first two works respectively leverage domain knowledge of wireless channel conditions and SNR to improve dataset quality. Over-the-air (OTA) data captured using USRP radios are used in these works.

In the first work, studies are done to understand the performance impact due to the disparity of probability distribution between training and test data within the context of channel conditions. This is studied for OTA data collected in channels emulating LOS, NLOS, and AWGN. In the second work, signal processing advances in blind SNR estimation are leveraged to improve DL performance on modulation classification. A training methodology is introduced that partitions OTA data into subsets of different SNR levels. For the third work, shortcomings such as errors and ad-hoc choice of parameters are identified in RML16. A new realistic benchmark dataset RML22 is provided with the errors corrected and the choice of parameters justified. Thorough mathematical derivations are provided for the wireless models used to generate data. Performance impact due to artifacts and model parameterization is studied using the RML22 data generation framework.

For the second paradigm of detection and characterization of emanations, an HW agnostic solution is proposed. Prior work focussed on profiling specific HW but scalability led to the need for a HW-agnostic solution. Emanations are detected by scanning for the signature of harmonics from leakages of clock signals. A signal processing algorithm is provided to remove artifacts and estimate the pitch of harmonics that characterizes the emanation. IQ data is collected from the source of emanations placed inside a sanitized shield room using Signal Hound SDR. Results for anomaly detection using emanation patterns are presented for the use cases compromising data security: damaged electronic peripherals, and illegal copying of data to external storage devices.

The dynamics of many natural phenomena are described by partial differential equations (PDEs). With the rise in computing resources, machine learning methods for PDE recovery directly from observations are emerging. Unlike traditional PDE derivation, a machine learning method requires less mathematical prowess and is widely applicable to various dynamical systems. This dissertation uses two machine learning methods, sparse modeling and physics informed neural networks, to address PDE recovery issues: (1) identifying unknown PDE terms; (2) recovering PDE coefficients from noisy, partial observations. We tackle both spatially-independent and spatially-dependent PDEs, with the latter's recovery elucidating the spatial variations of medium material properties, essential for modern industrial applications.

First, sparse modeling methods are used to identify unknown PDEs. A dictionary with redundant hypothetical PDE terms is computed numerically from observations, and then sparse modeling approaches extract some of the terms from this dictionary to form the identified PDE. For spatially-dependent PDE identification, a dictionary is computed from the observations at each location, and then sparse regression is used to extract active terms from the dictionary to be the PDE terms at this location. The methods are validated on both synthetic datasets and real laser measurements of structural vibrations.

Next, a deep learning method spatially dependent physics informed neural network (SD-PINN) is used to recover spatially-dependent PDEs from noisy and partial observations. The spatially-dependent PDE coefficients for each term at all locations in the region of interest (ROI) are modeled as a low-rank coefficient matrix. The low-rank assumption is from the fact that the physical property of the material at one location is impacted by its surroundings, which results in decreased degrees of freedom for the entries in the coefficient matrix. The coefficient matrix is rewritten as a product of a small number of eigenvalues and eigenvectors, where ``small" refers to the rank of the coefficient matrix. Remarkably, these eigenvalues and eigenvectors contain fewer unknowns than the coefficient matrix itself. Given only noisy observations from a subset of locations within ROI, SD-PINN can efficiently recover these eigenvalues and eigenvectors and thus reconstruct the coefficient matrix, which encapsulates the PDE coefficients for all locations.

Wideband source localization is an important problem in signal processing, and it has wide-range applications in underwater acoustics, indoor speaker localization, teleconferencing, and etc. Over the past few decades, there are significant amount of methods proposed for the wideband source localization. However, it still remains a challenging problem. This dissertation tackles the wideband source localization from data-driven and model-based perspectives.

For the data-driven part, a novel deep learning framework for the sound source localization (SSL) was proposed. SSL is to estimate the locations of the sound sources based on the received signal from the microphone array. SSL in the reverberant environment can be challenging due to the multipath artifacts in the received signals. To tackle with this challenge, a deep learning framework based on multi-task learning and image translation (MTIT) network is proposed. MTIT utilizes the encoder-decoder structure and it consists of one encoder and two decoders. The encoder aims to obtain a compressed representation of the input while the two decoders focus on two tasks in parallel. One decoder focuses on mitigating the multipath caused by reverberation and the other decoder predicts the source location. Due to the explicit dereverberation module and the shared encoder (representation), the proposed localization framework can achieve superior performance and can generalize to the unseen data in the reverberant environment compared to the existing baseline methods.

For the model-based part, gridless direction-of-arrival (DOA) estimation based on atomic norm minimization (ANM) for the multi-frequency signal was studied. ANM was formulated to an equivalent computationally feasible semi-definite program (SDP) problem. The dual certificate condition is given to certify the optimality. A fast algorithm implementation is given and the dual problem of the SDP is considered. The method is further generalized to the non-uniform array and non-uniform frequency case. Extensive theoretical analysis and numerical experiments demonstrate the superior performance of the proposed method compared to sparse Bayesian learning, the existing grid-based multi-frequency DOA estimation method.

Refractivity is an important atmospheric parameter which determines the propagation speed of electromagnetic (EM) waves traveling through the lower troposphere. The vertical refractivity profile of the atmosphere dictates how much the wave front of a radio wave will bend away from the straight-line path from its transmitter. The standard atmospheric refractivity profile over a terrestrial path is well known, experiences little fluctuation, and causes radio waves to curve towards the Earth. This effectively increases the `radio horizon' for non-optical frequencies. Over a marine channel however, the refractivity profile of the atmosphere is highly variable and can form spurious natural waveguides known as `ducts,' which allow for abnormally long range propagation and other anomalous effects. As a result, it is desirable to be able to track the refractivity profile of the atmosphere over marine channels to better predict and exploit the propagation paths of EM waves.

Currently, the state of the art in atmospheric refractivity research involves inference of the atmospheric refractivity profile from observations of the propagation loss of narrowband signals transmitted from a known location. Though this method has found some success, it is limited by the fact that there are often many refractivity profiles resulting in the same observed propagation loss. Thus, it is often impossible to know for certain the atmospheric refractivity profile using propagation loss alone.

In this dissertation, it is suggested that additional information about atmospheric refractivity can be found by measuring the direction of arrival (DOA) of a wave front in addition to its propagation loss. The topic of DOA estimation is discussed in depth, from classical techniques to the development of new super-resolution algorithms. The construction of a passive receiver array and first long term measurements of the DOA of an over the horizon signal propagating through a marine channel are detailed. These measurements show that the time series of DOA information is not well correlated with the time series of propagation loss information, implying that wave front DOA could be used to infer additional information about the atmospheric refractivity profile.

[1] This paper addresses the problem of estimating the lower atmospheric refractivity ( M profile) under nonstandard propagation conditions frequently encountered in low-altitude maritime radar applications. This is done by statistically estimating the duct strength (range- and height-dependent atmospheric index of refraction) from the sea surface reflected radar clutter. These environmental statistics can then be used to predict the radar performance. In previous work, genetic algorithms (GA) and Markov chain Monte Carlo (MCMC) samplers were used to calculate the atmospheric refractivity from returned radar clutter. Although GA is fast and estimates the maximum a posteriori ( MAP) solution well, it poorly calculates the multidimensional integrals required to obtain the means, variances, and underlying posterior probability distribution functions of the estimated parameters. More accurate distributions and integral calculations can be obtained using MCMC samplers, such as the Metropolis-Hastings and Gibbs sampling (GS) algorithms. Their drawback is that they require a large number of samples relative to the global optimization techniques such as GA and become impractical with an increasing number of unknowns. A hybrid GA-MCMC method based on the nearest neighborhood algorithm is implemented in this paper. It is an improved GA method which improves integral calculation accuracy through hybridization with a MCMC sampler. Since the number of forward models is determined by GA, it requires fewer forward model samples than a MCMC, enabling inversion of atmospheric models with a larger number of unknowns.