Ergodic vs. Non-Ergodic Models in Ground Motion Modeling

1. Ergodic Models

An ergodic model assumes that spatial variability in ground motion is equivalent to temporal variability. In other words, it treats the variability of ground motions across different locations as if it represents the variability of ground motions at a single location over time. This assumption allows ground motion prediction equations (GMPEs) to be developed using global datasets from many earthquakes, ignoring site-specific effects.

Key Characteristics of Ergodic Models:

• Use a large dataset from various regions to develop a generalized ground motion model.
• Assume that ground motion variability at one site can be inferred from observations at other sites.
• Do not account for site-specific and path-specific effects, leading to increased uncertainty in ground motion predictions.
• Overestimate variability at a specific site since they include global variations.

Applications of Ergodic Models:

• Traditional ground motion prediction equations (GMPEs).
• Regional seismic hazard assessment.
• Probabilistic seismic hazard analysis (PSHA) for areas with limited local earthquake data.

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2. Non-Ergodic Models

A non-ergodic model does not make the assumption that spatial variability can substitute for temporal variability. Instead, it recognizes that each site and each path between a source and a site has unique, repeatable characteristics that affect ground motion. Non-ergodic models account for site-specific and path-specific effects, reducing uncertainty in seismic hazard analysis.

Key Characteristics of Non-Ergodic Models:

• Incorporate local geological and geophysical conditions that influence ground motion.
• Recognize that ground motion at a site is not a random sample from a global dataset but has systematic trends over time.
• Require region-specific or site-specific datasets for calibration.
• Reduce aleatory (random) uncertainty and increase epistemic (knowledge-based) uncertainty since the model relies on localized data.

Applications of Non-Ergodic Models:

• Site-specific seismic hazard analysis for critical infrastructure.
• Urban seismic hazard mapping, considering localized site effects.
• Advanced ground motion modeling, incorporating physics-based simulations and machine learning to refine predictions.

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Why Use Non-Ergodic Models?

Traditional ergodic models overestimate variability at a specific site because they include data from many locations, leading to conservative hazard estimates. In contrast, non-ergodic models provide more accurate site-specific predictions by incorporating long-term local seismic behavior, reducing uncertainty.

However, non-ergodic models require significant local data to be properly constrained, which can be a challenge in regions with limited seismic monitoring.

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Summary Table:

Feature	Ergodic Model	Non-Ergodic Model
Assumption	Spatial variability represents temporal variability	Recognizes site-specific and path-specific effects
Data Use	Large dataset from various locations	Site-specific or path-specific data
Uncertainty	Higher aleatory uncertainty	Reduced aleatory, higher epistemic uncertainty
Application	Regional seismic hazard analysis, GMPEs	Site-specific hazard analysis, infrastructure design
Advantage	Works with limited local data	More accurate ground motion predictions

In recent years, there has been a shift towards non-ergodic models for site-specific seismic hazard assessment, particularly for critical infrastructure projects. Advances in machine learning, physics-based simulations, and high-resolution seismic data have made non-ergodic models more viable for practical applications.