Hybrid TDOA/AOA Hypocenter Localization Using the Constrained Least Squares Method with Deep Learning P-Onset Picking

In this study, we propose a hypocenter localization algorithm that uses the time difference of arrival (TDOA) and angle of arrival (AOA) as a hybrid model. The hypocenter measurements are detected by the accelerator sensors of the four separate observatories that are closest to the origin of an earthquake. The measurements are calibrated by the proposed deep learning P-onset picking system with short-time Fourier transform (STFT) signal analysis because the accurate detection of Primary waves (P-waves) is limited by seismic environmental noise. The revised measurements are used to calculate the precise distances between the observatories and hypocenters. The proposed hybrid TDOA/AOA is represented by a linear matrix equation that includes the unknowns of the precise distances, coordinates, and arrival angles to the observatories. We estimate a hypocenter using the constrained least squares method (CLS) under the constraints of the TDOA/AOA. The objective function with the constraints is optimized using the Lagrange function, and the asymptotic optimum is obtained by specifying the optimal Lagrange multipliers. Simulations show the performance of the proposed hypocenter localization method.