Among the biggest challenges we face in utilizing neural networks trained on waveform data (i.e., seismic, electromagnetic, or ultrasound) is its application to real data. The requirement for accurate labels forces us to develop solutions using synthetic data, where labels are readily available. However, synthetic data often do not capture the reality of the field/real experiment, and we end up with poor performance of the trained neural network (NN) at the inference stage. We describe a novel approach to enhance supervised training on synthetic data with real data features (domain adaptation). Specifically, for tasks in which the absolute values of the vertical axis (time or depth) of the input data are not crucial, like classification, or can be corrected afterward, like velocity model building using a well-log, we suggest a series of linear operations on the input so the training and application data have similar distributions. This is accomplished by applying two operations on the input data to the NN model: 1) The crosscorrelation of the input data (i.e., shot gather, seismic image, etc.) with a fixed reference trace from the same dataset. 2) The convolution of the resulting data with the mean (or a random sample) of the autocorrelated data from another domain. In the training stage, the input data are from the synthetic domain and the auto-correlated data are from the real domain, and random samples from real data are drawn at every training epoch. In the inference/application stage, the input data are from the real subset domain and the mean of the autocorrelated sections are from the synthetic data subset domain. Example applications on passive seismic data for microseismic event source location determination and active seismic data for predicting low frequencies are used to demonstrate the power of this approach in improving the applicability of trained models to real data.
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