BiLSTM-Based Low-Frequency Extrapolation: Generalizing from Synthetic Training to Field Airgun Data

Low-frequency (LF) components are critical for resolving deep structures and mitigating cycle skipping in full-waveform inversion (FWI). However, seismic surveys often lack sufficient LF content below 4 Hz due to source and receiver limitations. We propose and evaluate a data-driven method for LF extrapolation using Bidirectional Long Short-Term Memory (BiLSTM) networks trained exclusively on synthetic data. The model learns to reconstruct missing LF content from conventional airgun data by observing how high-frequency traces relate to their low-frequency-rich counterparts. The training dataset comprises 100,000 synthetic traces generated by convolving randomized reflectivity series with estimated airgun and tuned pulse source (TPS) signatures. Additive noise is introduced before and after convolution to simulate acquisition variability and unmodeled effects. The network is trained to map airgun-band inputs to TPS-band outputs using a hybrid loss function combining time-domain mean squared error with a frequency-domain regularization term, encouraging spectral recovery below 4 Hz. To assess generalization, we apply the trained model to a real field dataset acquired with dual-source acquisition (airgun and TPS). Despite no exposure to real data during training, the BiLSTM predicts low-frequency components that closely match the TPS ground truth. Spectral analysis shows significant enhancement below 4 Hz, and a 3 Hz low-pass filter reveals strong event alignment between the model output and TPS recordings (Figure). These results demonstrate the potential of synthetic training pipelines and recurrent architectures to enrich legacy seismic datasets and support LF-sensitive applications like FWI. The method offers a lightweight, field-deployable tool requiring no changes to acquisition hardware.