  Full-waveform inversion problems are usually formulated as optimization
problems, where the forward-wave propagation operator $f$ maps the subsurface
velocity structures to seismic signals. The existing computational methods for
solving full-waveform inversion are not only computationally expensive, but
also yields low-resolution results because of the ill-posedness and cycle
skipping issues of full-waveform inversion. To resolve those issues, we employ
machine-learning techniques to solve the full-waveform inversion. Specifically,
we focus on applying the convolutional neural network~(CNN) to directly derive
the inversion operator $f^{-1}$ so that the velocity structure can be obtained
without knowing the forward operator $f$. We build a convolutional neural
network with an encoder-decoder structure to model the correspondence from
seismic data to subsurface velocity structures. Furthermore, we employ the
conditional random field~(CRF) on top of the CNN to generate structural
predictions by modeling the interactions between different locations on the
velocity model. Our numerical examples using synthetic seismic reflection data
show that the propose CNN-CRF model significantly improve the accuracy of the
velocity inversion while the computational time is reduced.
