Earthquakes induced by human activities present a unique set of challenges to the statistical modeller. Relative to tectonic earthquakes, the recorded number of induced earthquakes can be very small, while interventions to better record and prevent these earthquakes make the use of stationary models either statistically inefficient or inappropriate. On the other hand, the human activity causing seismicity is often well documented and can be a valuable resource that is not available in the tectonic setting.

This thesis focuses on how to model anthropogenic earthquakes while making best use of the limited available data. This research provides three main contributions to statistical seismology, each motivated by the induced earthquakes in the Groningen gas field.

Firstly, we consider the link between earthquake locations and gas extraction, using a state-of-the-art, physically-motivated model as our baseline. We investigate model simplifications to ensure parsimony of the baseline model and explore model extensions that assess the statistical evidence for additional physical characteristics that are not currently represented.

Secondly, we consider how to include developments to the earthquake detection network when modelling earthquake magnitudes. We develop a method for selecting a time-varying threshold above which the earthquake catalogue may be considered complete. This allows small magnitude events, unused by existing analyses, to contribute to our understanding of the largest events.

Finally, we turn our focus to aftershock activity and the Epidemic Type Aftershock Sequence (ETAS) model. The use of this model is widespread, but the conventional formulation represents a narrow model class with strong parameter dependence and assumes independent and identically distributed magnitudes. We introduce a reparameterisation and two extensions of the conventional ETAS model, along with efficient inference procedures, which alleviate these issues.