Attribute-constrained unsupervised ground-roll suppression via mid-band amplitude–phase fidelity and wavefield orthogonalization

Abstract Ground roll (GR) is a high-amplitude coherent noise to be attenuated during data processing. Supervised deep neural networks (DNNs) typically rely on labeled training data and often exhibit limited interpretability. To improve network interpretability for GR suppression and avoid any dependence on labeled data, we propose an unsupervised deep neural network (UDNN) based on attribute constraints (ACs) with the mid-band amplitude–phase fidelity and wavefield orthogonalization. GR predominantly contaminates the low-frequency effective signal, and the low- and mid-frequency effective components in the original data exhibit a frequency band similarity. Accordingly, we employ the mid-frequency component to reconstruct the low–mid-frequency effective signal. However, the conventional pixelwise amplitude consistency loss term for DNNs is highly susceptible to overfitting, often leaving substantial residual GR in the suppression result. To address this issue, we use the AC loss function by adding a mid-band amplitude–phase fidelity loss term and a wavefield orthogonalization loss term. The AC loss function enforces the physically constraints on output data in terms of amplitude, frequency, and phase. Under this loss function, an encoder–decoder convolutional network adaptively calibrates the amplitude, frequency, and phase of the mid-band effective component into the low–mid-band signal, thereby enabling thorough separation of GR noise. Superior noise-suppression and signal-fidelity performance are consistently observed in both time-domain sections and frequency–wavenumber spectra. The proposed method outperforms the synchrosqueezed generalized phase-shifted S-transform method, the supervised deep learning method, and UDNN variants trained using either single loss terms or two loss terms.