Browsing by Author "de Hoop, Maarten"

Now showing 1 - 7 of 7
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    Analysis of inverse boundary value problems for elastic waves
    (2018-04-13) Zhai, Jian; de Hoop, Maarten
    In seismology, people use waves generated by earthquakes, artificial explosions, or even "noises", to detect the Earth's interior structure. The waves traveling in rocks, which are the main components of Earth's crust and mantle, are elastic waves. A key problem in seismology is whether the interior structures of interest could be uniquely determined by the measurements people can collect. Since in most situations, people can only record the vibrations at the surface, such problems usually are formulated as inverse boundary value problems for the elastic wave equation. We study several inverse boundary value problems for the elastic wave equation and give some uniqueness and stability results for them.
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    Clustering earthquake signals and background noises in continuous seismic data with unsupervised deep learning
    (Springer Nature, 2020) Seydoux, Léonard; Balestriero, Randall; Poli, Piero; de Hoop, Maarten; Campillo, Michel; Baraniuk, Richard
    The continuously growing amount of seismic data collected worldwide is outpacing our abilities for analysis, since to date, such datasets have been analyzed in a human-expert-intensive, supervised fashion. Moreover, analyses that are conducted can be strongly biased by the standard models employed by seismologists. In response to both of these challenges, we develop a new unsupervised machine learning framework for detecting and clustering seismic signals in continuous seismic records. Our approach combines a deep scattering network and a Gaussian mixture model to cluster seismic signal segments and detect novel structures. To illustrate the power of the framework, we analyze seismic data acquired during the June 2017 Nuugaatsiaq, Greenland landslide. We demonstrate the blind detection and recovery of the repeating precursory seismicity that was recorded before the main landslide rupture, which suggests that our approach could lead to more informative forecasting of the seismic activity in seismogenic areas.
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    Conditional Injective Flows for Bayesian Imaging
    (IEEE, 2023) Khorashadizadeh, AmirEhsan; Kothari, Konik; Salsi, Leonardo; Harandi, Ali Aghababaei; de Hoop, Maarten; Dokmanić, Ivan
    Most deep learning models for computational imaging regress a single reconstructed image. In practice, however, ill-posedness, nonlinearity, model mismatch, and noise often conspire to make such point estimates misleading or insufficient. The Bayesian approach models images and (noisy) measurements as jointly distributed random vectors and aims to approximate the posterior distribution of unknowns. Recent variational inference methods based on conditional normalizing flows are a promising alternative to traditional MCMC methods, but they come with drawbacks: excessive memory and compute demands for moderate to high resolution images and underwhelming performance on hard nonlinear problems. In this work, we propose C-Trumpets—conditional injective flows specifically designed for imaging problems, which greatly diminish these challenges. Injectivity reduces memory footprint and training time while low-dimensional latent space together with architectural innovations like fixed-volume-change layers and skip-connection revnet layers, C-Trumpets outperform regular conditional flow models on a variety of imaging and image restoration tasks, including limited-view CT and nonlinear inverse scattering, with a lower compute and memory budget. C-Trumpets enable fast approximation of point estimates like MMSE or MAP as well as physically-meaningful uncertainty quantification.
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    High-Resolution Pacific Apparent Polar Wander Since the Paleocene: Evidence for Two Episodes of True Polar Wander and Two True Polar Stillstands
    (2022-08-11) Woodworth, Daniel; Gordon, Richard G; de Hoop, Maarten
    Paleomagnetic poles from the continents have long provided evidence for apparent polar wander (APW), the motion over geologic time of the spin axis relative to a continent or tectonic plate. In contrast, the APW paths of oceanic plates are much less developed, mainly because oceanic plates lack subaerially exposed surface, making conventional paleomagnetic approaches difficult or impossible. Herein two alternative approaches, skewness analysis of marine magnetic anomalies and paleo-spin axis estimation from the distribution of paleo-equatorial sediment bands, are developed and applied. With these approaches we determined a high-resolution APW path for the Pacific Plate from 56 Ma to 12 Ma. Combined with existing Pacific poles for 72 Ma to 58 Ma, our Pacific APW allows study of finer detail than is possible using conventional methods. We identify two tracks in the Pacific APW path, suggesting northward plate motion relative to the spin axis 72 Ma to 56 Ma and 46 Ma to 12 Ma. Surprisingly, there is no net apparent polar wander between 12 Ma and the present and during the gap between these tracks southward motion from 56 Ma to 46 Ma is indicated. When reconstructed into the reference frame of the Pacific hotspots, which has been used to approximate an absolute reference frame, the two Pacific APW tracks correspond to two stillstands in the motion of the paleo-spin axis at locations significantly different both from one another and the present spin axis. These locations are separated by spin axis motion from 56 to 46 Ma and 12 Ma to the present. We interpret these stillstands in paleo-spin axis motion relative to the Pacific hotspots as true polar stillstands and the intervals separating them, corresponding to anomalous Pacific APW, as episodes of true polar wander of 7° and 3°, respectively.
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    Microlocal Analysis of Hyperbolic Equations with Memory and Applications
    (2019-04-24) Cocola, Jorio; de Hoop, Maarten
    This thesis introduces a framework for extending microlocal analysis to hyperbolic equations with memory. These equations describe wave motion in attenuating and dispersive media and have been widely employed in various domain of science, spanning from global seismology to medical imaging. Although mathematical problems in these domains have been successfully studied with microlocal analysis, its application to hyperbolic equation with memory has somewhat lagged behind. This thesis proposes to bridge that gap. In the first part, I construct parametrices for first order hyperbolic initial value problems with a zero order memory term. These parametrices are then used to prove a propagation of singularities theorem and to explain the arising of stationary singularities. I then discuss an open problem on the diagonalization of second order wave equations with memory. Finally, in the last part, I leverage the analysis developed in the previous chapters to extend time reversal methods (TR) for these types of wave equations. The presence of the memory term, precludes the time reversibility of wave propagation creating an obstruction in the naive employment of TR methods. I derive and analyze a microlocal “boundary compensation method” that allows overcoming this issue and that, coupled with a reverse-time continuation from the boundary, is applied to solve an inverse source problem.
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    Physics-based machine learning for classifying, forecasting, and blindly locating seismic events
    (2022-12-02) Jasperson, Hope; de Hoop, Maarten
    The use of machine learning (ML) in seismology has skyrocketed within the past several years. However, studies often use generic networks that do not incorporate the physics of the specific task. Failure to use existing knowledge makes these problems more difficult and artificially reduces accuracy. Here, we focus on several problems from the seismic data processing pipeline and build networks that are specific to each problem and are grounded in physics. First, we present a method using unsupervised classification and an attention network to forecast labquakes using acoustic emission (AE) waveform features. We analyzed the temporal evolution of AEs generated throughout several hundred laboratory earthquake cycles and used a Conscience Self-Organizing Map (CSOM) to perform topologically ordered vector quantization based on waveform properties. The resulting map was used to interactively cluster AEs. We examined the clusters over time to identify those with predictive ability. Finally, we used a variety of LSTM and attention-based networks to test the predictive power of the AE clusters. By tracking cumulative waveform features over the seismic cycle, the network is able to forecast the time-to-failure (TTF) of lab earthquakes. Our results show that analyzing the data to isolate predictive signals and using a more sophisticated network architecture are key to robustly forecasting labquakes. Next, we tackled phase association by framing it as a combinatorial optimization problem and using reinforcement learning (RL). By leveraging the latent structure of typical problem instances, RL works even for problems that are computationally hard in the worst case. RL usually relies on domain-specific heuristics crafted over years of research. For many relevant problems, however, finely-tuned heuristics do not exist. We propose Generalized Optimizer for Unsupervised Deep Assignment (GOUDA), an unsupervised framework for seismic phase association. In place of a heuristic, GOUDA uses a deep consensus network to learn the latent structure of the data - the wave speed model - which is used to calculate rewards. We show on synthetic data of varying complexity that GOUDA effectively solves the association problem while simultaneously recovering an accurate 3D wave speed model and earthquake locations. Since this is achieved with minimal a priori information, GOUDA is the first-of-a-kind tool suitable for ab initio seismic imaging and phase association.
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    REVISITING THE COMPUTATION OF NORMAL MODES IN SNREI MODELS OF PLANETS - close eigenfrequencies
    (2018-02-21) Ye, Jingchen; de Hoop, Maarten
    We develop a robust algorithm to compute seismic normal modes in a spherically symmetric, non-rotating Earth. A well-known problem is the cross-contamination of modes near "intersections" of dispersion curves for separate waveguides. Our novel computational approach completely avoids artificial degeneracies by guaranteeing orthonormality among the eigenfunctions. We extend Buland’s work, and reformulate the Sturm-Liouville problem as a generalized eigenvalue problem with the Rayleigh-Ritz Galerkin method. A special projection operator incorporating the gravity terms proposed by de Hoop and a displacement/pressure formulation are utilized in the fluid outer core to project out the essential spectrum. Moreover, the weak variational form enables us to achieve high accuracy across the solid-fluid boundary, especially for Stoneley modes, which have exponentially decaying behavior. We also employ the mixed finite element technique to avoid spurious pressure modes arising from discretization schemes and a numerical inf-sup test is performed following Bathe’s work. In addition, the self-gravitation terms are reformulated to avoid computations outside the Earth, thanks to the domain decomposition technique. Our package enables us to study the physical properties of intersection points of waveguides. According to Okal's classification theory, the group velocities should be continuous within a branch of the same mode family. However, we have found that there will be a small “bump” near intersection points, which is consistent with Miropol'sky’s observation. In fact, we can loosely regard Earth’s surface and the CMB as independent waveguides. For those modes that are far from the intersection points, their eigenfunctions are localized in the corresponding waveguides. However, those that are close to intersections will have physical features of both waveguides, which means they cannot be classified in either family. Our results improve on Okal’s classification, demonstrating that dispersion curves from independent waveguides should be considered to break at intersection points. Moreover, intersection points have close relations with Stoneley-related modes observed from earthquakes data, which casts light on studying deep Earth's structures.