Core Concepts
Rate-and-state models analyze seismic hazard based on pore pressure changes.
Abstract
The content discusses the moments of Cox rate-and-state models in predicting seismic hazards. It covers the modification of pore pressure measurements affected by noise, providing explicit expressions for the first and second moments of the state variable. The article explores correlations between pressure changes and seismic activity, deriving approximate moments of the rate variable using the delta method. It also delves into stochastic rate-and-state models with added noise to pore pressure, presenting detailed mathematical derivations and simulations to validate approximations.
- Introduction:
- Importance of studying induced earthquakes from fluid extraction/injection.
- Shift in public opinion due to earthquakes at Groningen gas field.
- Rate-and-State Model:
- Inverse relationship between earthquake intensity and state variable.
- Euler difference equation for state variable evolution.
- Cox Rate-and-State Models:
- Definition of Cox process with driving random measure.
- Incorporating stochastic processes into state variables with Gaussian white noise.
- Moments Analysis:
- Derivation of first and second-moment properties for the state variable.
- Conditions for positive and negative correlation based on pressure changes.
- Approximate Moments:
- Using delta method to approximate moments of the rate variable based on tractable moments of the state variable.
- Simulation Examples:
- Comparison of theoretical approximations with population estimates through simulated examples.
- Conclusion:
- Modification of rate-and-state model to account for measurement errors in pore pressure.
- Acknowledgements and References provided.
Stats
Years 1995–2001: 179.81, 177.39, 174.86, 172.20, 169.42, 166.50, 163.48
Years 2002–2008: 160.32, 157.05, 153.65, 150.13, 146.49, 142.72, 138.82