CapsPhase: Capsule Neural Network for Seismic Phase Classification and Picking

We develop a capsule neural network (CapsPhase) for seismic data classification and picking. CapsPhase consists of several layers, e.g., convolutional, primary capsule, and digit capsule layer. The convolutional layer extracts the significant features from the seismic data, while the primary capsule combines the extracted features into several vector representations named capsules. Afterward, the primary capsule is connected to the digit capsule layer using a dynamic routing strategy to obtain the vector representation of each output class, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> -wave, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -wave, and noise class. CapsPhase is trained using 90% of the Southern California seismic dataset, which contains 4.5 million 4 s-three-component seismograms, and is validated and tested using the remaining 10%. Accordingly, the training accuracy reaches 98.70%, while the validation accuracy is 98.67% and the testing accuracy is 98.66%. Furthermore, the CapsPhase is tested using 300 000 earthquake waveforms recorded worldwide from the STanford EArthquake Dataset (STEAD). Accordingly, the precision, recall, and F1-score of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> -picks corresponding to the CapsPhase reach 94.50%, 99.86%, and 97.10%, respectively, whereas the precision, recall, and F1-score of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -picks corresponding to the CapsPhase are 88.05%, 99.87%, and 93.60%, respectively. In addition, CapsPhase is evaluated using the Japanese seismic data and is compared to benchmark methods, e.g., short-time average/long-time average (STA/LTA), generalized phase detection (GPD), and CapsNet methods. As a result, CapsPhase reaches F1-scores of 99.10% and 98.64% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> -wave and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -wave arrival times, respectively, and outperforms the benchmark methods. The results show that the CapsPhase has the ability to pick the arrival times accurately despite the existence of strong background noise, e.g., the signal-to-noise-ratio (SNR) can be as low as −4.97 dB. Besides, the CapsPhase detects the arrival time when the earthquake has a small local magnitude, e.g., as low as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.1~M_{L}$ </tex-math></inline-formula> . In addition, we find that the proposed algorithm has the ability to train using a small dataset, which is valuable for regions that have limited training data.