Project I10: Point process modelling of induced seismicity

Timescale: Oct. 2021 – Sept. 2024

Supervisors:

PD Sebastian Hainzl, GFZ Potsdam

Prof. Matthias Holschneider University of Potsdam

apl. Prof. Gert Zöller, University of Potsdam

Description

Natural seismicity is usually governed by some universal characteristics, e.g. exponentially distributed magnitudes with slope parameter around unity (Gutenberg-Richter law), and power-law decaying aftershocks (Omori law). Man-made seismicity, e.g. induced earthquakes resulting from fluid injection or gas production, often shows different characteristics. Moreover, fluid migration results in many cases in diffusive seismicity patterns in space and time without the well-known temporal clustering characteristics. While the traditional point process models based on Poisson processes or the Epidemic-Type-Aftershock-Sequences (ETAS) model are designed overall for natural seismicity, modelling approaches for earthquakes with strongly deviating characteristics are missing.

The first step in I10 will be the statistical analysis of various catalogues from man-made earthquakes (geothermal and fracking sites, gas fields, mines etc.) using families of potential distributions and parameter estimation techniques. Suitable pattern recognition techniques will help to quantify the spatio-temporal evolution of diffusive seismicity. Then appropriate point process models will be compared and extended in order to reproduce the main characteristics. Sophisticated processes of Cox and Levy type will also be considered for this aim. Non-stationarity can be modelled by extending the change-point methods from project I2 to more gradual changes. If specific distributions can be approximated sufficiently by normal distributions, tools of data assimilation and reproducing kernel Hilbert spaces might be applied.

We expect to obtain point process models which are suitable to describe seismicity that deviates from the typical Gutenberg-Richter- and Omori-type earthquakes. This will provide a better understanding of the underlying processes and the related hazard.

Dedicated Regional Cluster: no specific cluster

Related PhD-projects: I2 (first cohort, Bernhard Fiedler) and I6 (second cohort, Shubham Sharma): I10 aims to continue the projects I2 and I6.

Responsibilities: The PhD project “Point process modelling of induced seismicity” deals with model design for induced and triggered seismicity, which can have fundamentally different characteristics in comparison with natural seismicity. Potential models include stochastic point processes of Hawks type, like the “Epidemic Type Aftershock Sequences” (ETAS) model, Gauss process models, as well as physics-based seismicity models, e.g. related to rate-and-state dependent dynamics. The goal is the characterization of observed spatiotemporal seismicity, e.g. migration patterns, and the identification of potential driving mechanisms. A main focus will be the proper statistical treatment and uncertainty assessment, preferably in a Bayesian framework.

Requirements: We are seeking applications from highly motivated candidates with excellent Master’s degree in mathematics, geosciences, physics or a related discipline. Programming skills (preferably Python) are mandatory. Fluency in the English language (speaking and writing) as well as the willingness to work in an interdisciplinary team are expected.