  We simulate the response of acoustic seismic waves in horizontally layered
media using a deep neural network. In contrast to traditional finite-difference
modelling techniques our network is able to directly approximate the recorded
seismic response at multiple receiver locations in a single inference step,
without needing to iteratively model the seismic wavefield through time. This
results in an order of magnitude reduction in simulation time from the order of
1 s for FD modelling to the order of 0.1 s using our approach. Such a speed
improvement could lead to real-time seismic simulation applications and benefit
seismic inversion algorithms based on forward modelling, such as full waveform
inversion. Our proof of concept deep neural network is trained using 50,000
synthetic examples of seismic waves propagating through different 2D
horizontally layered velocity models. We discuss how our approach could be
extended to arbitrary velocity models. Our deep neural network design is
inspired by the WaveNet architecture used for speech synthesis. We also
investigate using deep neural networks for simulating the full seismic
wavefield and for carrying out seismic inversion directly.
