5:15 PM - 6:45 PM
[STT38-P05] Event Detection and Classification from Seismic Waveform Data Based on Optimal Transport Theory
Keywords:optimal transportation, low-frequency tremor, k-nearest neighbor, event classification, entropy regularized optimal transport, sliced-Wasserstein distance
Low-frequency tremors, discovered by Obara (2002), occur at a deeper or shallower zone than the seismogenic zone on the plate boundary. A remarkable characteristic of these tremors is that low-frequency and small-amplitude oscillations last from several seconds to several hours. Analyzing the low-frequency tremors, which are expected to relate to plate-boundary earthquakes (Obara and Kato 2016), is vital in seismology. Since the low-frequency tremors in seismic waveform data are difficult to distinguish from local noises, detection algorithms well-accepted in seismology have not yet been established.
In this study, we applied the optimal transport theory to detect seismic events, including low-frequency tremors, in given seismic waveform data. The distance between two given waveforms for the events detection is calculated by the following two steps: (1) a cost matrix is calculated based on a weighted sum of the squared difference in amplitudes of the transported waveforms and the squared difference in their time indices, and then (2) the solution of the optimal transport problem based on the cost matrix is found. As a specific distance, we adopted the Time-Adaptive Optimal Transport (TAOT) (Zhang et al., 2020). Using this distance, we classify events (earthquake/tremor/noise) in seismic waveform data using the k-nearest neighbor (k-NN) method (Cover and Hart 1967). The k-NN uses dictionary data whose labels are known in advance. It determines the top k dictionary data with the highest similarity to the test data whose labels are to be predicted and predicts the most common label among them as the label of the test data. To reduce the computation time, we developed the Sliced-TAOT algorithm, which applies the concept of sliced Wasserstein distance, rapidly computable for the optimal transport distance, to the TAOT.
We investigated the properties of TAOT/Sliced-TAOT as indicators of distances between two waveforms through numerical experiments using artificial data and validations using the Hi-net data at the Tohoku region, Japan. The results indicate that they retain the properties of such as noise robustness and shift robustness. Then we investigated the performance of the proposed algorithm of seismic event detection using the k-NN and TAOT/sliced-TAOT by applying them to the Hi-net data. The results showed that the distances and classification algorithm are appropriately designed to detect low-frequency tremors.
In this study, we applied the optimal transport theory to detect seismic events, including low-frequency tremors, in given seismic waveform data. The distance between two given waveforms for the events detection is calculated by the following two steps: (1) a cost matrix is calculated based on a weighted sum of the squared difference in amplitudes of the transported waveforms and the squared difference in their time indices, and then (2) the solution of the optimal transport problem based on the cost matrix is found. As a specific distance, we adopted the Time-Adaptive Optimal Transport (TAOT) (Zhang et al., 2020). Using this distance, we classify events (earthquake/tremor/noise) in seismic waveform data using the k-nearest neighbor (k-NN) method (Cover and Hart 1967). The k-NN uses dictionary data whose labels are known in advance. It determines the top k dictionary data with the highest similarity to the test data whose labels are to be predicted and predicts the most common label among them as the label of the test data. To reduce the computation time, we developed the Sliced-TAOT algorithm, which applies the concept of sliced Wasserstein distance, rapidly computable for the optimal transport distance, to the TAOT.
We investigated the properties of TAOT/Sliced-TAOT as indicators of distances between two waveforms through numerical experiments using artificial data and validations using the Hi-net data at the Tohoku region, Japan. The results indicate that they retain the properties of such as noise robustness and shift robustness. Then we investigated the performance of the proposed algorithm of seismic event detection using the k-NN and TAOT/sliced-TAOT by applying them to the Hi-net data. The results showed that the distances and classification algorithm are appropriately designed to detect low-frequency tremors.