Representations of the radiated energy in earthquakes

Abstract

We investigate the representation of the radiated energy, ER, in earthquakes. In seismology ER is estimated from either far-field seismic waves or the stress and displacement on the fault plane. Although ER comes from the entire volume of the Earth, it can be expressed as an integral over the fault plane. However, the integrand cannot be given a simple physical meaning such as the radiated energy density on the fault plane. The stress on the fault plane changes rapidly during a seismic rupture. Although the energy radiated by this process is not included in the estimate of ER in a simplified practice in seismology, it is correctly included in the expression of ER in standard seismological practice. Using the representation theorem, we can express ER as a surface integral over the fault plane, with the integrand containing the slip function on the fault plane. However, the integrand at a point depends not only on the slip function at the point but also on the slip functions everywhere on the fault plane. Thus, the simple method in which ER is estimated by summation of the local energy flux on the fault plane does not yield a correct estimate. © 2005 RAS.