Evidence that non-linear elasticity contributes to the seismic coda
SUMMARY

Different factors might affect the propagation of seismic waves producing scattering, including heterogeneities and non-linear elasticity. A key difference between these two factors is the dependence of the strength of the scattered waves on the strength of the incident wave, being linear for the former and non-linear for the latter. A detailed study of the TIPTEQ data, where about a hundred explosions were recorded on 180 three-component stations in the distance range of approximately 0–100 km, shows that this dependence is non-linear. Data were analysed in the following way: (i) the envelope of bandpass filtered data between 10 and 40 Hz was obtained for a large number of stations from different distance ranges and charge sizes of shots, (ii) for these distances we modelled the envelope considering the non-linear elasticity. The shapes of the theoretical and observed envelopes were in general very similar. A scale factor for each case was obtained considering the best fit of its complete envelope and (iii) since this scale factor depends mainly on the size of the explosion, we computed the ratio (R) of the scale factor (sf) for different sizes of explosions at the same distance. Finally, varying the distance between 0 and 50 km and (iv) we computed the power (p) of the dependence of the ratio (R) on the ratio of the charge sizes []. For the complete data set we obtain a value of p= 2.5 ± 0.9, which is clearly greater than 1. This shows that non-linear elasticity is an important factor in the contribution to seismic wave scattering in the frequency range of 10–40 Hz.