Among the biggest challenges we face in utilizing neural networks trained on waveform (i.e., seismic, electromagnetic, or ultrasound) data is its application to real data. The requirement for accurate labels often forces us to train our networks using synthetic data, where labels are readily available. However, synthetic data often fail to capture the reality of the field/real experiment, and we end up with poor performance of the trained neural networks (NNs) at the inference stage. This is because synthetic data lack many of the realistic features embedded in real data, including an accurate waveform source signature, realistic noise, and accurate reflectivity. In other words, the real data set is far from being a sample from the distribution of the synthetic training set. Thus, we describe a novel approach to enhance our supervised neural network (NN) 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 section are not crucial to the prediction, like classification, or can be corrected after the prediction, like velocity model building using a well, we suggest a series of linear operations on the input to the network data so that the training and application data have similar distributions. This is accomplished by applying two operations on the input data to the NN, whether the input is from the synthetic or real data subset domain: (1) The crosscorrelation of the input data section (i.e., shot gather, seismic image, etc.) with a fixed-location reference trace from the input data section. (2) The convolution of the resulting data with the mean (or a random sample) of the autocorrelated sections from the other subset domain. In the training stage, the input data are from the synthetic subset domain and the auto-corrected (we crosscorrelate each trace with itself) sections are from the real subset domain, and the random selection of sections from the real data is implemented at every epoch of the training. 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 on active seismic data for predicting low frequencies are used to demonstrate the power of this approach in improving the applicability of our trained NNs to real data.
