  Seismic full-waveform inversion (FWI), which applies iterative methods to
estimate high-resolution subsurface detail from seismograms, is a powerful
imaging technique in exploration geophysics. In recent years the computational
cost of FWI has grown exponentially due to the increasing size and resolution
of seismic data. Moreover, it is a non-convex problem, and can become stuck in
a local minima due to the limited accuracy of the initial velocity maps, the
absence of low frequencies in the measurements, the presence of noise, and the
approximate modeling of the wave-physics complexity. To overcome these
computational issues, we develop a multiscale data-driven FWI method based on
the fully convolutional network (FCN). In preparing the training data, we first
develop a real-time style transform method to create a large set of physically
realistic subsurface velocity maps from natural images. We then develop two
convolutional neural networks with encoder-decoder structure to reconstruct the
low- and high-frequency components of the subsurface velocity maps,
respectively. To validate the performance of our new data-driven inversion
method and the effectiveness of the synthesized training set, we compare it
with conventional physics-based waveform inversion approaches using both
synthetic and field data. These numerical results demonstrate that, once our
model is fully trained, it can significantly reduce the computation time, and
yield more accurate subsurface velocity map in comparison with conventional
FWI.
