Firstly, I will mainly talk about our recent applications of deep learning for seismic data denoising and velocity inversion. Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse time migration and other high-resolution seismic imaging techniques. We have investigated a novel method based on the deep fully convolutional neural network (FCN) for velocity model building (VMB) directly from raw seismograms. One key characteristic of the data-driven method is that it can automatically extract multi-layer useful features from the seismic traces for VMB without human-curated activities.

Then, I will simply report our recent development on frequency domain pooling based DL method. Our spectrum pooling is constructed by the Hartley transform, and performs dimensionality reduction by truncating the feature maps in the frequency domain. Compared with the spectral pooling implemented by Fourier transform, our spectrum pooling requires much less computation since we do not need extra operation to ensure the output of spectral pooling is real except for transforming, spectrum cropping and padding. On the MNIST dataset, we empirically show that embedding our spectrum pooling in some existing convolutional neural networks (CNNs), by replacing its original pooling layers, is able to improve classification accuracy.

Finally, I will mention our next work on using the Wasserstein distance as the loss function of deep learning for the geophysical inverse problem. The Wasserstein distance does not only compare objects point by point, as standard Lp metrics, but instead quantifies how the mass is moved. This makes optimal transport natural for quantifying uncertainty and modeling deformations.