Representations of the radiated energy in earthquakes

Abstract

We investigate the representation of the radiated energy, E_R, in earthquakes. In seismology E_R is estimated from either far-field seismic waves or the stress and displacement on the fault plane. Although E_R 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 E_R in a simplified practice in seismology, it is correctly included in the expression of E_R in standard seismological practice. Using the representation theorem, we can express E_R 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 E_R is estimated by summation of the local energy flux on the fault plane does not yield a correct estimate.

Files

Additional details