Kolmogorov-Arnold Networks for Semi-Supervised Impedance Inversion

Seismic impedance inversion plays a crucial role in obtaining underground physical properties and enhancing seismic exploration accuracy. In recent years, semi-supervised methods have significantly improved the efficiency and precision of impedance inversion. However, methods based on convolutional neural networks (CNNs) often struggle to effectively capture long-term dependencies in data, which can negatively impact the results of seismic acoustic impedance inversion for tasks with long-term characteristics. Therefore, this letter proposes a semi-supervised learning acoustic impedance inversion network that integrates the advanced deep learning techniques, including Kolmogorov-Arnold networks (KANs) and convolutional KAN. Through experimental comparisons of acoustic impedance fitting results, we demonstrate that KAN and convolutional KAN exhibit stronger fitting capabilities for long-term acoustic impedance data than traditional linear layers and CNN. This provides a novel method and strategy for establishing the mapping relationship between seismic data and wave impedance. Additionally, testing on the Marmousi2 model shows that the network incorporating these new deep learning methods improves the lateral continuity of the inversion profile and enhances the prediction accuracy in impedance inversion.