BACKGROUND: This PhD is funded through the ‘RISE’ project as part of the Horizon 2020 program: Towards operational forecasting of earthquakes and early warning capacity for more resilient societies. Operational earthquake forecasting is the development of time evolving forecasts to quantify and communicate changing seismic hazard , for example during aftershock sequences. This project will adapt a fully Bayesian, cutting-edge spatio-temporal modeling approach to model time-dependent seismicity. This approach, called inlabru (http://inlabru.org) [2,3], has been developed primarily on ecological datasets [e.g. 4,5] but it is now ripe for application to earthquake seismicity. Your work will contribute to the success of this €8M project which contains 24 collaborating institutions across 12 countries.
PROJECT SUMMARY: On short time scales of days and weeks, earthquake sequences show clustering in space and time, as illustrated by the aftershocks triggered by large events. Statistical descriptions of clustering explain many features observed in seismicity catalogues, and they can be used to construct forecasts that indicate how earthquake probabilities change over the short term. Properly applied, short-term forecasts have operational utility; for example, in anticipating aftershocks that follow large earthquakes. Although the value of long-term forecasts for ensuring seismic safety is clear, the interpretation of short-term forecasts is problematic, because earthquake probabilities may vary over orders of magnitude but typically remain low in an absolute sense (< 1% per day).
In this project you will develop a new operational earthquake model rooted in a novel Bayesian statistical approach using Nested Laplace Approximations for improved performance compared with Markov Chain Monte Carlo methods. This innovation has led to the application of more realistic and flexible spatio-temporal models than was previously possible. Theoretical advances in statistical modelling will be required in key two areas; to model self-exciting clustering and to address uncertainty derived from imperfect observations. The framework will generate, evaluate, optimize and discriminate earthquake forecasts based on robust statistical modelling, with full quantification of uncertainty.
These methods are implemented within the open source software inlabru which is written in R. This has the advantage that it utilizes existing R libraries for loading and manipulating diverse spatial datatypes including points, polygons and fields in a natural way, making it feasible to incorporate a variety of prior geological and geophysical information.
Dr Mark Naylor is a physicist and statistical seismologist with expertise in natural hazards, statistical seismology and uncertainty.
Prof Finn Lindgren is Chair in Statistics at the University of Edinburgh and one of the main theoretical and software developers behind inlabru.
Prof Ian Main is Chair of seismology and Rock physics at the University of Edinburgh and has a long-term interest in the population dynamics of earthquakes and its application in earthquake hazard and operational forecasting.
REQUIREMENTS: This project would suit a statistician, mathematician, physicist, geophysicist or similar with good numeracy and computational skills. You will be interested in the development of cutting edge spatio-temporal modelling theory and implementation within software to address a real-world problem. This requires a balance of mathematical and coding competencies.
For more details and a link to the application see: https://www.ed.ac.uk/geosciences/postgraduate/phd/programmes-supervisors/physical-sciences/phd-projects/project/301
 Jordan, T., Y. Chen, P. Gasparini, R. Madariaga, I. Main, W. Marzocchi, G. Papadopoulos, G. Sobolev, K. Yamaoka & J. Zschau (2011). Operational earthquake forecasting: State of Knowledge and Guidelines for Utilization. Annals Of Geophysics, 54(4), 361-391. doi:10.4401/ag-5350
 Bakka et al. (2018), Spatial Modelling with R-INLA: A review [https://arxiv.org/pdf/1802.06350.pdf]
 Zuur et al, (2017) Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA, by Highland Statistics
 Python, A, Illian, JB, Jones-Todd, C, & Blangiardo, M (2016). A Bayesian approach to modelling fine-scale spatial dynamics of non-state terrorism: world study, 2002-2013, JRSS A, https://doi.org/10.1111/rssa.12384.
 Yuan, Y.; Bachl, F. E.; Lindgren, F.; Borchers, D. L.; Illian, JB; Buckland, S. T.; Rue, H.; Gerrodette, T., (2017) Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales, Annals of Applied Statistics, 11(4):2270– 2297.