We have worked on modelling 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). The parallel fractures in the experimental sample had a spacing of 3 mm. We have five acquisition setups, P-wave propagation perpendicular to and then parallel to the fractures, and S-wave propagation perpendicular to the fractures, SH-wave and SV-wave propagation parallel to the fractures. 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 1.19μs. On the other hand, waveforms for the EM model were very different from the other two models and in some cases it is not even similar in arrival time, with time differences of more than 33μs. In one case though, for the SH-wave case which has the least interaction with the fractures, all three models for fracture representation agree very well and also match the experimental data with a correlation coefficient ≥0.94. In this case, where all model waveforms match each other, the frequency content of the experiment is the same as the three models based on Fourier analysis (see Figure below). This leads to the conclusion that there is a threshold frequency for each acquisition case where the models will start to perform the same below a certain frequency and will match each other. 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 1~MHz with higher amplitudes concentrated below 0.5~MHz. We use a low-pass filter on the waveforms with a cutoff 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.
