Physical Meaning of the Coda Envelopes

Abstract

This article shows a relatively complete solution for the coda envelopes in the time domain. The main theoretical basis is the energy transportation computation. After establishing the integral equation, the subsequential method of computation is used to find the solution. At this moment, the analytical solution for the multiple scattering in two-dimensional space has been obtained, whereas the solution for the three-dimensional space is only a fifth-order approximation which is from the digital computation. The solution shows that in the two-dimensional case the coda decay rate may reflect only the intrinsic absorption of the medium. In three-dimensional space the decay rate also reflects mainly the intrinsic absorption but with a certain percentage of scattering attenuation. This conclusion is to simplify matters: the receiver is set very close to the source. When the receiver is distant from the source, as the distance increases the scattering attenuation will effect the decay rate of codas more. Considering that intrinsic absorption is very sensitive to changes in temperature, microfractures and the content of fluid within the pores, coda Q should be a good detector of these changes. Therefore, the theoretical results show that precise analyses of coda envelopes and the discrimination of the different Q-factors are essential in detecting underground thermal-fluid activities that may be the precursor of imminent disasters.