  Seismic forward and inverse problems are significant research areas in
geophysics. However, the time burden of traditional numerical methods hinders
their applications in scenarios that require fast predictions. Machine
learning-based methods also have limitations as retraining is required for
every change in initial conditions. In this letter, we adopt deep operator
network (DeepONet) to solve forward and inverse problems based on the Eikonal
equation, respectively. DeepONet approximates the operator through two
sub-networks, branch net and trunk net, which offers good generalization and
flexibility. Different structures of DeepONets are proposed to respectively
learn the operators in forward and inverse problems. We train the networks on
different categories of datasets separately, so that they can deliver accurate
predictions with different initial conditions for the specific velocity model.
The numerical results demonstrate that DeepONet can not only predict the travel
time fields with different sources for different velocity models, but also
provide velocity models based on the observed travel time data.
