Physics-Constrained Deep Learning for Attenuation Compensation of Nonstationary Seismic Data

Because of the viscoelastic properties of the Earth, seismic waves experience attenuation during propagation, resulting in decreased amplitude and phase distortion, ultimately reducing resolution. The inverse Q filtering method is an important way to compensate for attenuation and consequently improve the resolution of seismic data. However, the compensatory capability and stability of the existing inverse Q filtering methods present a paradoxical relationship, ensuring compensation ability may diminish stability, and vice versa. In other words, the existing methods can hardly work in scenarios characterized by high levels of noise or significant attenuation (low Q values). In this article, a physics-constrained deep-learning-based attenuation compensation (PCDL-AC) method is proposed. Specifically, we first establish a time-domain attenuation model, which delineates the relation among a stationary seismic trace, the Q model, and the corresponding attenuated seismic trace. Then, we use this model as the physics law and propose a physics-constrained deep learning method for attenuation compensation in a semisupervised or even unsupervised manner. Benefiting from the noise-resistance ability of deep neural networks and the physics law, the proposed method can achieve stable and accurate compensation even when strong noise is present in data. In addition, this method significantly improves the efficiency of attenuation compensation since the application of deep learning is very efficient once it is trained. Both synthetic and field data experiments verify the effectiveness of the proposed method and demonstrate its advantages over common methods.