Seismic waves and dispersion relations

The propagation of plane waves in a homogeneous medium with a finite relaxation kernel is described by the Volterra integro-differential equation. However, it is shown that the case most common in seismology cannot be described using the Volterra equation due to the inadequately general formulation of the initial problem. A full description of attenuating waves is possible by examining complex oscillations in a homogeneous medium with an imaginary relaxation kernel which in a special case can degenerate into the Dirac Delta Function. Proceeding of this basis, the required solution is found in Fourier transform space. A numerical estimate of C sub true can be obtained on the basis of stipulated x, n(omega) and v(omega) using a discrete Fourier transform.