Modeling Non-Ergodic Path Effects Using Conditional Generative Model for Fourier Amplitude Spectra

2025-12-22

AI Summary

Existing non-ergodic ground motion models (GMMs) rely on Gaussian processes (GPs) with pre-specified covariance functions, suffering from computational intractability and poor scalability for large-scale predictions. To address this, we propose CGM-FAS, the first conditional generative model for non-ergodic path-effect modeling—introducing a conditional variational autoencoder (CVAE) that uses geographic coordinates as conditioning variables to learn, end-to-end, the joint spatial–frequency correlations of Fourier amplitude spectra (FAS), thereby eliminating dependence on hand-crafted covariance structures. CGM-FAS integrates geospatial embeddings with a multi-frequency joint generation mechanism. Evaluated on the San Francisco Bay Area dataset, it achieves prediction accuracy comparable to state-of-the-art GPs. A single inference pass generates FAS path corrections for 10,000 sites across 1,000 frequencies in under 10 seconds, consuming only several gigabytes of memory—demonstrating substantial gains in computational efficiency and scalability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Recent developments in non-ergodic ground-motion models (GMMs) explicitly model systematic spatial variations in source, site, and path effects, reducing standard deviation to 30-40% of ergodic models and enabling more accurate site-specific seismic hazard analysis. Current non-ergodic GMMs rely on Gaussian Process (GP) methods with prescribed correlation functions and thus have computational limitations for large-scale predictions. This study proposes a deep-learning approach called Conditional Generative Modeling for Fourier Amplitude Spectra (CGM-FAS) as an alternative to GP-based methods for modeling non-ergodic path effects in Fourier Amplitude Spectra (FAS). CGM-FAS uses a Conditional Variational Autoencoder architecture to learn spatial patterns and interfrequency correlation directly from data by using geographical coordinates of earthquakes and stations as conditional variables. Using San Francisco Bay Area earthquake data, we compare CGM-FAS against a recent GP-based GMM for the region and demonstrate consistent predictions of non-ergodic path effects. Additionally, CGM-FAS offers advantages compared to GP-based approaches in learning spatial patterns without prescribed correlation functions, capturing interfrequency correlations, and enabling rapid predictions, generating maps for 10,000 sites across 1,000 frequencies within 10 seconds using a few GB of memory. CGM-FAS hyperparameters can be tuned to ensure generated path effects exhibit variability consistent with the GP-based empirical GMM. This work demonstrates a promising direction for efficient non-ergodic ground-motion prediction across multiple frequencies and large spatial domains.

Problem

• Modeling non-ergodic path effects in Fourier Amplitude Spectra
• Overcoming computational limitations of Gaussian Process methods
• Enabling efficient large-scale seismic hazard predictions

Innovation

• Uses Conditional Variational Autoencoder for spatial pattern learning
• Learns from earthquake and station coordinates without preset correlations
• Enables rapid multi-frequency predictions across large spatial domains