Energy Budget of Earthquakes and Seismic Efficiency

Abstract

An earthquake is a rupture process occurring in Earth's interior under tectonic stresses caused primarily by plate motion. During an earthquake, the stress on a fault changes in a complex fashion, and the potential energy (strain energy and gravitational energy) stored in Earth is released as seismic waves. The ratio of the released seismic wave energy to the potential energy is the seismic efficiency which is determined by how the stress changes as a function of time during seismic rupture. A traditional method to investigate the stress variation on the fault plane is to determine the rupture pattern and slip function on a fault plane by inversion of observed seismograms. The stress can be inferred from the slip function. However, a fault plane is mechanically heterogeneous and the rupture pattern is very complex in both space and time. As a result, it is not possible to determine every detail of the rupture pattern. Another approach to this problem is to examine the energy budget of earthquakes and the efficiency. The amount of radiated energy increases with the slip velocity, which is proportional to the driving stress. Thus, by measuring the total radiated energy, we can obtain useful information about the state of stress during seismic faulting. In this approach, we do not determine the details of slip function at every point on the fault but, instead, determine the total energy radiated from the entire fault. This is somewhat similar to determining thermodynamic parameters (pressure, temperature, etc.) of a system without determining the motion of individual molecules in it. We will take the latter approach to investigate the physical processes associated with earthquakes.