Physics-informed Statistical Modeling of Earthquakes

**Physics-informed statistical modeling of earthquakes**:

- Réf
- **ABG-114606**
- Sujet de Thèse- 22/05/2023- Contrat doctoral- MINES ParisTech- Lieu de travail- Fontainebleau - Ile-de-France - France- Intitulé du sujet- Physics-informed statistical modeling of earthquakes- Champs scientifiques- Terre, univers, espace
- Numérique
- Science de la donnée (stockage, sécurité, mesure, analyse)

**Description du sujet**:
**Context**

Earthquakes correspond to the sudden reactivation of shear slip on pre-existing faults or fractures, releasing the elastic energy stored in the upper crust by tectonic plate motion. Stress is then redistributed, possibly triggering other earthquakes (King et. al, 1994). This cascade process results in swarms, or mainshock-aftershock sequences, that from time to time degenerate into catastrophic devastating events, as recently in Turkey (Melgar et al., 2023). However, it is today largely impossible to predict the evolution of such earthquake sequences.

One of the main challenges of seismic hazard assessment is to achieve a better physical understanding of what controls the nucleation and interaction of earthquakes on active faults. This can be done through two main approaches. In the first approach, earthquakes are seen as resulting from slip instabilities on active faults. In the simplest of such models, the slip behavior of the fault is modeled by a spring block system (or arrays of interacting spring blocks) loaded with a prescribed stress and charectrized by dynamic slip-dependent friction law (Burridge & Knopoff, 1967; Carlson et al., 1994; Dieterich, 1994). However, although successful in reproducing statistical properties of earthquake sequences, this approach largely simplifies mechanical interaction in an elastic medium. The second approach, on the other hand, consists in considering a fault as a frictional interface between continuous deformable solids. Initially developed for a single planar fault with homogeneous frictional properties (Rice, 1993), such models have later been extended to simulate the behavior of fault networks (Romanet, 2018; Ozawa & Ando, 2021), rough faults (Heimisson, 2020), or with heterogeneous friction (Dublanchet, 2019). The main outcome of these studies is that geometrical, or frictional heterogeneity needs to be considered to account for the observed earthquake complexity. However, the computational cost and the large number of unknown parameters generally hampers the use of such deterministic models to infer fault mechanical properties given earthquake observations.

Several studies attempt to incorporate physical considerations about earthquake nucleation and stress redistribution in ETAS models (Console, 2007), improving the physical interpretability of earthquake sequences. However, interaction kernels are generally inspired from the Dieterich model (Dieterich, 1994), which simplifies earthquake interaction, and does not predict earthquake magnitude. Here we propose to take advantage of more recent earthquake cycle model developments to propose a new physics-based formulation of ETAS model.

**Research goals of the thesis**

Seismic activity (the occurrence and magnitude of earthquakes) is generally modeled either with stochastic or deterministic (driven by physics) approaches. Although physics-based models allow realistic earthquake nucleation and interaction, their computational cost and the number of involved and unknown parameters prevent any practical use for earthquake hazard assessment. Stochastic models usually rely on a limited number of parameters, which allows tractable parameter inference and uncertainty quantification. Although congenial, stochastic models miss relevant features of earthquake triggering, resulting in unrealistic predictions.

This project aims at bridging the gap between statistical and mechanical approaches, by proposing new point process models for earthquake modeling, driven by physics-based models explaining the nucleation and interaction of earthquakes on a planar fault (asperity model). A refined formulation of the widely used ETAS model will be developed: the parameters of this model will be directly inherited from the asperity model (friction heterogeneity, stress state, loading rate), and their inference will be tackled using efficient Bayesian algorithms. The models developed will be tested against natural earthquake sequences, observed in several active regions worldwide (California, Italy, Corinth rift...), and also on earthquake swarms induced by the exploitation of georesources.

**References**
- Burridge, R., & Knopoff, L. "Model and theoretical seismicity." Bulletin of the seismological society of America, 57.3 (1967); 341-371.
- Carlson, J. M., Langer J. S., & Shaw, B. E. "Dynamics of earthquake faults." Reviews of Modern Physics 66.2 (1994): 657.
- Console, R., Murru, M., Catalli, F., & Falcone, G. "Real time forecasts through an earthquake clustering model constrained by the rate-and-