Publication Date:
2014-07-31
Description:
Short-period seismograms of earthquakes are complex especially beneath volcanoes, where the S wave mean free path is short and low velocity bodies composed of melt or fluid are expected in addition to random velocity inhomogeneities as scattering sources. Resonant scattering inherent in a low velocity body shows trap and release of waves with a delay time. Focusing of the delay time phenomenon, we have to consider seriously multiple resonant scattering processes. Since wave phases are complex in such a scattering medium, the radiative transfer theory has been often used to synthesize the variation of mean square (MS) amplitude of waves; however, resonant scattering has not been well adopted in the conventional radiative transfer theory. Here, as a simple mathematical model, we study the sequence of isotropic resonant scattering of a scalar wavelet by low velocity spheres at low frequencies, where the inside velocity is supposed to be low enough. We first derive the total scattering cross-section per time for each order of scattering as the convolution kernel representing the decaying scattering response. Then, for a random and uniform distribution of such identical resonant isotropic scatterers, we build the propagator of the MS amplitude by using causality, a geometrical spreading factor and the scattering loss. Using those propagators and convolution kernels, we formulate the radiative transfer equation for a spherically impulsive radiation from a point source. The synthesized MS amplitude time trace shows a dip just after the direct arrival and a delayed swelling, and then a decaying tail at large lapse times. The delayed swelling is a prominent effect of resonant scattering. The space distribution of synthesized MS amplitude shows a swelling near the source region in space, and it becomes a bell shape like a diffusion solution at large lapse times.
Keywords:
Seismology
Print ISSN:
0956-540X
Electronic ISSN:
1365-246X
Topics:
Geosciences
Published by
Oxford University Press
on behalf of
The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
