Posted by Hani Alzahrani

Convolutional RNNs combine the advantages of CNNs (including a significant reduction in required memory) that have made them successful in a wide range of applications, while simultaneously benefiting from including hidden-state feature maps to propagate information from the initial to the final input.  We use a sequence-to-sequence convolutional LSTM (ConvLSTM) neural network architecture that follows the logic of multi-scale FWI. The input sequences to the ConvLSTM network consist of frequency-domain seismic data ordered by frequency from lowest available to highest usable or chosen, while the corresponding output sequences are frequency-dependent smoothed velocity models (Figure 1).

Figure 1: Convolutional LSTM process seismic data in the frequency domain incrementally from the lowest available to the highest.

Training this network with geologically realistic velocity model allows it to recover highly accurate models when the testing data is generated using the same engine that generated the training data. However, it fails to produce accurate models when the testing data comes from a different distribution. To overcome this problem, we use hybrid training data that consists of geologically realistic models as well as purely geometric velocity models (Figure 2).

Figure 2. The two types of velocity models constituting the hybrid training data.

These purely geometric models, that are not restricted to following a specific geologic structure, greatly improve the network generalization. We test this network using overlapping subsets from the BP 2004 benchmark model. Seismic data are synthesized for each subset. The synthesized data are then injected into two networks; one is trained using geological-only training models, the other using a combination of geological and geometric models. We then place each subset back in it its location on the BP model, take the average in overlapping areas and apply a 2D Gaussian smoothing operator to smooth out discontinuities at the subset boundaries. Figure 3 shows the improved accuracy in the recovered models when using a hybrid training data.

Figure 3. Recovered velocity subsets for the two types of training data.

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