How do waveforms from the Explicit fracture, the Effective medium, and the Localised Effective Medium models, compare within different frequency bands?

ABSTRACT: We have worked on modeling seismic wave propagation in a laboratory experiment with multiple parallel fractures, using three different approaches for implementing fractures. The first approach is an explicit implementation (EX) of the displacement discontinuity with explicit fracture surfaces. The second is the effective medium (EM) where the fractures are mapped into the properties of the material creating a transversely isotropic material. The third is a hybrid of the two methods with a localised effective medium (LEM). In previous work we observed that the explicit and the LEM model waveforms match one another with correlations between 87% to 97% and with time shifts of 0.07 to 1.19 μs. In this study we filter the waveforms in order to define this threshold value where the model waveforms match each other and link this threshold frequency with the fracture spacing. From the Fourier analysis we can see that the waveforms have a bandwidth up to 1000 kHz with higher amplitudes concentrated below 500 kHz. We use a low-pass filter on the waveforms with a cut-off frequency based on the results of the Fourier analysis for each case. We conclude then that filtering the high frequency content of the waveforms, the EM model starts approaching the other two models when the wavelength is at least ten times larger than the fracture spacing.