Sergey Fomel

Lexing Ying, Sergey Fomel

We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to decompose the summation domain of into simpler components in a multiscale way. Existing fast algorithms are then applied to each component to obtain optimal complexity. The algorithm in 1D is exact and takes $O(N\log^2 N)$ steps. Our solution in 2D is an approximate but accurate algorithm that takes $O(N^2 \log^2 N)$ steps. In both cases, the complexities are almost linear in terms of the degree of freedom. We provide numerical results on several test examples.

Hanlin Sheng, Xinming Wu, Hang Gao et al.

Foundation models, as a mainstream technology in artificial intelligence, have demonstrated immense potential across various domains in recent years, particularly in handling complex tasks and multimodal data. In the field of geophysics, although the application of foundation models is gradually expanding, there is currently a lack of comprehensive reviews discussing the full workflow of integrating foundation models with geophysical data. To address this gap, this paper presents a complete framework that systematically explores the entire process of developing foundation models in conjunction with geophysical data. From data collection and preprocessing to model architecture selection, pre-training strategies, and model deployment, we provide a detailed analysis of the key techniques and methodologies at each stage. In particular, considering the diversity, complexity, and physical consistency constraints of geophysical data, we discuss targeted solutions to address these challenges. Furthermore, we discuss how to leverage the transfer learning capabilities of foundation models to reduce reliance on labeled data, enhance computational efficiency, and incorporate physical constraints into model training, thereby improving physical consistency and interpretability. Through a comprehensive summary and analysis of the current technological landscape, this paper not only fills the gap in the geophysics domain regarding a full-process review of foundation models but also offers valuable practical guidance for their application in geophysical data analysis, driving innovation and advancement in the field.