Some Mathematical Aspects of Earthquake Research

  • Date: 02/26/2008

David W. Eaton (University of Calgary)


Calgary Place Tower (Shell)


An earthquake is the motion produced when stress within the Earth builds up over a long period of time until it exceeds the strength of the rock, which then fails by breaking along a fault. Although catastrophic earthquakes are rare, earthquakes occur frequently in seismogenic regions of the planet and represent one of the most deadly natural hazards. The modern view of earthquakes as cyclical phenomena first appeared in the 1908 Lawson report, commissioned following the Great San Francisco earthquake of 1906. Although earthquakes are complex multi-scale phenomena, we now have much better models for earthquake nucleation and rupture processes, associated phenomena such as tsunamis, and tools with which earthquakes can be carefully studied from both deterministic and statistical points of view.
This presentation will provide a brief overview of selected aspects of earthquake phenomena. We will begin by considering the evolution of magnitude scales used to quantify earthquakes, some of which saturate for the very largest events (e.g., the 26 December 2004 Sumatra-Andaman earthquake), and show how these have led to more complete tensor descriptions of earthquake sources. Recent methods used to image earthquake ground motion include spectacular results from satellite-based Interferometric Synthetic Aperture Radar (InSAR). The development of magnitude scales quickly led to the observation that earthquakes exhibit a power-law distribution, known as the Gutenberg-Richter magnitude-recurrence relation. The radiation of elastic-wave energy from earthquakes produces a variety of wave phenomena with which Earth’s interior has been studied for the past century. Small induced events (microseismicity), similar in nature to natural earthquakes, can be measured and sometimes exploited in petroleum and mining applications. Finally, although new models of stress transfer between faults provide tantalizing hints that earthquake forecasting may be achievable, earthquake prediction remains an elusive goal of seismology.

Other Information: 

PIMS is presenting a series of lectures at the Calgary Place Tower 1 in downtown Calgary. These lectures, given by experts from the PIMS Universities, will focus on mathematical techniques and applications relevant to the oil and gas industry and will demonstrate the utility and beauty of applied mathematics. The talks are aimed at a general audience. Attendance may qualify for APEGGA Professional Development Hours.