A neural network based global traveltime function (GlobeNN).

Global traveltime modeling is an essential component of modern seismological studies with a whole gamut of applications ranging from earthquake source localization to seismic velocity inversion. Emerging acquisition technologies like distributed acoustic sensing (DAS) promise a new era of seismological discovery by allowing a high-density of seismic observations. Conventional traveltime computation algorithms are unable to handle virtually millions of receivers made available by DAS arrays. Therefore, we develop GlobeNN-a neural network based traveltime function that can provide seismic traveltimes obtained from the cached realistic 3-D Earth model. We train a neural network to estimate the traveltime between any two points in the global mantle Earth model by imposing the validity of the eikonal equation through the loss function. The traveltime gradients in the loss function are computed efficiently using automatic differentiation, while the P-wave velocity is obtained from the vertically polarized P-wave velocity of the GLAD-M25 model. The network is trained using a random selection of source and receiver pairs from within the computational domain. Once trained, the neural network produces traveltimes rapidly at the global scale through a single evaluation of the network. As a byproduct of the training process, we obtain a neural network that learns the underlying velocity model and, therefore, can be used as an efficient storage mechanism for the huge 3-D Earth velocity model. These exciting features make our proposed neural network based global traveltime computation method an indispensable tool for the next generation of seismological advances.