As aforementioned, this assumption is almost necessary to differentiate the invariance mechanismfromthevariantones.

Training specific deep learning models for particular tasks is common across various domains within seismology. However, this approach encounters two limitations: inadequate labeled data for certain tasks and limited generalization across regions. To address these challenges, we develop SeisCLIP, a seismology foundation model trained through contrastive learning from multi-modal data. It consists of a transformer encoder for extracting crucial features from time-frequency seismic spectrum and an MLP encoder for integrating the phase and source information of the same event. These encoders are jointly pre-trained on a vast dataset and the spectrum encoder is subsequently fine-tuned on smaller datasets for various downstream tasks. Notably, SeisCLIP's performance surpasses that of baseline methods in event classification, localization, and focal mechanism analysis tasks, employing distinct datasets from different regions. In conclusion, SeisCLIP holds significant potential as a foundational model in the field of seismology, paving the way for innovative directions in foundation-model-based seismology research.

Current supervised learning can learn spurious correlation during the data-fitting process, imposing issues regarding interpretability, out-of-distribution (OOD) generalization, and robustness. To avoid spurious correlation, we propose a Latent Causal Invariance Model (LaCIM) which pursues causal prediction. Specifically, we introduce latent variables that are separated into (a) output-causative factors and (b) others that are spuriously correlated to the output via confounders, to model the underlying causal factors. We further assume the generating mechanisms from latent space to observed data to be causally invariant. We give the identifiable claim of such invariance, particularly the disentanglement of output-causative factors from others, as a theoretical guarantee for precise inference and avoiding spurious correlation. We propose a Variational-Bayesian-based method for estimation and to optimize over the latent space for prediction. The utility of our approach is verified by improved interpretability, prediction power on various OOD scenarios (including healthcare) and robustness on security.