Statistical properties of induced earthquakes

Induced seismicity is a central issue in the development of subsurface energy technologies in the kingdom and around the world. It is basically the earthquakes caused by human activities that involve extracting or injecting fluids into the subsurface and modifying subsurface stresses around pre-existing faults. Examples include subsurface wastewater injection, reservoir impoundment in the vicinity of large dams, development of mining, geothermal or hydrocarbon resources, and in geologic carbon sequestration. While most of the induced earthquakes are fortunately too small to be felt, some can go up to magnitude 5—large enough to be felt and to cause damage to buildings. Quantifying the statistical properties of induced seismicity is essential to successful management and mitigation of the seismic risk associated with subsurface energy technologies. A fundamental statistical relationship in seismology is the Gutenberg-Ricter frequency-magnitude relation. It describes the frequency of earthquakes as a function of their magnitude. It is usually expressed as: log10 N = a - b M, where N is the number of earthquakes with magnitude ≥ M, a is a constant that represents the total seismicity rate in a given region and time period, b is the b-value, typically around 1 for natural earthquakes, which characterizes the relative likelihood of small versus large earthquakes, and M is the earthquake magnitude. The b-value associated with induced earthquakes is a subject of ongoing debate and uncertainty.

A widely used model in the statistical study of earthquakes is the Burridge-Knopoff model (1967). It is a mechanical model in earthquake physics used to simulate and understand the dynamics of fault slip and earthquake generation. Carlson & Langer (1989) performed the first study of the statistical properties of the B-K model, paying attention to the magnitude distribution of natural earthquake events and its dependence on friction parameters. They used a velocity-weakening friction, and were able to produce a frequency-magnitude plot with a b-value around 1. In this project, the student is expected to: (1) review the derivation of the Burridge-Knopoff model (1967), (2) reproduce the results for the frequency-magnitude relation in Carlson & Langer (1989), and (3) explore ways to extend it to induced earthquakes. A preliminary code will be provided as a starting point.