The application of non-periodic homogenization of elastic equation

It is a problem that in the case of heterogeneity scales much smaller than the minimum wavefield length and complicated mesh of discontinuity for spectra element method. The purpose of this paper is to understand and to build the effective medium through upscaling rules and equations allowing to average the small scales of the original medium without losing the accuracy of the wavefield computation. Traditional normal modes method was used to get the eigenfrequencies and eigenfunctions and the results show that this method is correct and practicable. Relations among the eigenfrequencies and eigenfunctions of fundamental spheroidal modes, seismograms and homogenization parameters and order were analyzed. This has been extended to SEM1D and it will lay a foundation for the homogenization of CSEM in the next work.