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Neural networks (NNs) enable precise modeling of complicated geophysical phenomena but can be sensitive to small input changes. In this work, we present a new method for analyzing this instability in NNs. We focus our analysis on adversarial examples, test‐time inputs with carefully crafted human‐imperceptible perturbations that expose the worst‐case instability in a model's predictions. Our stability analysis is based on a low‐rank expansion of NNs on a fixed input, and we apply our analysis to a NN model for tsunami early warning which takes geodetic measurements as the input and forecasts tsunami waveforms. The result is an improved description of local stability that explains adversarial examples generated by a standard gradient‐based algorithm, and allows the generation of other comparable examples. Our analysis can predict whether noise in the geodetic input will produce an unstable output, and identifies a potential approach to filtering the input that enable more robust forecasting 

In this study, we propose a scenario superposition method for real‐time tsunami wave prediction. In the offline phase, prior to actual tsunami occurrence, hypothetical tsunami scenarios are created, and their wave data are decomposed into spatial modes and scenario‐specific coefficients by the singular value decomposition. Then, once an actual tsunami event is observed, the proposed method executes an online phase, which is a novel contribution of this study. Specifically, the predicted waveform is represented by a linear combination of training scenarios consisting of precomputed tsunami simulation results. To make such a prediction, a set of weight parameters that allow for appropriate scenario superposition is identified by the Bayesian update process. At the same time, the probability distribution of the weight parameters is obtained as reference information regarding the reliability of the prediction. Then, the waveforms are predicted by superposition with the estimated weight parameters multiplied by the waveforms of the corresponding scenarios. To validate the performance and benefits of the proposed method, a series of synthetic experiments are performed for the Shikoku coastal region of Japan with the subduction zone of the Nankai Trough. All tsunami data are derived from numerical simulations and divided into a training data set used as scenario superposition components and a test data set for an unknown real event. The predicted waveforms at the synthetic gauges closest to the Shikoku Islands are compared to those obtained using our previous prediction method incorporating sequential Bayesian updating. 

We present an algorithm to solve the dispersive depth-averaged Serre--Green--Naghdi equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water equations. This has been implemented as a new component of the open source GeoClaw software that is widely used for modeling tsunamis, storm surge, and related hazards, improving its accuracy on shorter wavelength phenomena. We use a formulation that requires solving an elliptic system of equations at each time step, making the method implicit. The adaptive algorithm allows different time steps on different refinement levels and solves the implicit equations level by level. Computational examples are presented to illustrate the stability and accuracy on a radially symmetric test case and two realistic tsunami modeling problems, including a hypothetical asteroid impact creating a short wavelength tsunami for which dispersive terms are necessary. 

In Hawaiʻi, tsunamis are often described in orally transmitted legends (moʻolelo). This study examines sedimentary evidence of a possible local submarine landslide-generated tsunami, described in a legend from the south east coast of Maui which originated between the 15th Century CE and the first arrival of Europeans in 1778 CE. Physical evidence for a tsunami, found at the Nu’u Refuge, Maui, is primarily comprised of an extensive coral clast deposit (found 8.5 m above msl and 251 m inland from the shoreline) together with waterworn cobbles which form fracture-embedded wedge clasts in a local basalt escarpment (at up to 8 m above msl). U/Th dating of the coral clasts gives a maximum tsunami deposit age of 1671 CE for the event that may have inspired the local moʻolelo. This depositional sequence is used to characterize the nature of the assumed tsunami in terms of inundation distance, maximum wave runup and minimum flow velocities. A numerical model developed using GeoClaw matches well with the physical evidence. The data and modeling presented here suggest that locallygenerated tsunamis from submarine landslides warrant further research attention as sources of destructive high energy marine inundation events. 

We investigate the potential of using Global Navigation Satellite System (GNSS) observations to directly forecast full tsunami waveforms in real time. We train convolutional neural networks to use less than 9 min of GNSS data to forecast the full tsunami waveforms over 6 hr at select locations, and obtain accurate forecasts on a test data set. Our training and test data consists of synthetic earthquakes and associated GNSS data generated for the Cascadia Subduction Zone using the MudPy software, and corresponding tsunami waveforms in Puget Sound computed using GeoClaw. We use the same suite of synthetic earthquakes and waveforms as in earlier work where tsunami waveforms were used for forecasting, and provide a comparison. We also explore varying the number of GNSS stations, their locations, and their observation durations.