# A Cox Rate-and-State Model for Monitoring Seismic Hazard in the Groningen Gas Field

## TL;DR

This paper introduces a modified rate-and-state model to better monitor seismic risks in the Groningen gas field by accounting for measurement noise and gas production data.

## Contribution

The novel contribution is incorporating gas production volumes and measurement noise into a Cox rate-and-state model for seismic hazard monitoring.

## Key findings

- The modified model accounts for noise in pore pressure measurements.
- A parallel Metropolis-adjusted Langevin algorithm is used to sample the conditional distribution for hazard monitoring.

## Abstract

To monitor the seismic hazard in the Groningen gas field, this paper modifies the rate-and-state model that relates changes in pore pressure to induced seismic hazard by allowing for noise in pore pressure measurements and by explicitly taking into account gas production volumes. The first and second-moment structures of the resulting Cox process are analysed, an unbiased estimating equation approach for the unknown model parameters is proposed and the conditional distribution of the driving random measure is derived. A parallel Metropolis-adjusted Langevin algorithm is used for sampling from the conditional distribution and to monitor the hazard.