Fault impedance and earthquake energy in the Fourier transform domain

The response of the elastic medium in which a fault is contained determines one relation between the slip function and the stress function on the fault. In the space-time domain, the slip and stress functions are related by a singular integral equation. If a Fourier transformation is performed over the two space dimensions on the fault and over time, the stress transform equals the slip rate transform times an impedance function. Using this impedance function, we may determine the energy radiated or stored in the elastic medium from either the slip or the stress transform.