  Deep learning techniques have been used to build velocity models (VMs) for
seismic traveltime tomography and have shown encouraging performance in recent
years. However, they need to generate labeled samples (i.e., pairs of input and
label) to train the deep neural network (NN) with end-to-end learning, and the
real labels for field data inversion are usually missing or very expensive.
Some traditional tomographic methods can be implemented quickly, but their
effectiveness is often limited by prior assumptions. To avoid generating and/or
collecting labeled samples, we propose a novel method by integrating deep
learning and dictionary learning to enhance the VMs with low resolution by
using the traditional tomography-least square method (LSQR). We first design a
type of shallow and simple NN to reduce computational cost followed by
proposing a two-step strategy to enhance the VMs with low resolution: (1)
Warming up. An initial dictionary is trained from the estimation by LSQR
through dictionary learning method; (2) Dictionary optimization. The initial
dictionary obtained in the warming-up step will be optimized by the NN, and
then it will be used to reconstruct high-resolution VMs with the reference
slowness and the estimation by LSQR. Furthermore, we design a loss function to
minimize traveltime misfit to ensure that NN training is label-free, and the
optimized dictionary can be obtained after each epoch of NN training. We
demonstrate the effectiveness of the proposed method through the numerical
tests on both synthetic and field data.
