Link between Systematic Deviation between First-break Velocity & Phase Velocity and Heterogeneities in Rocks

Elastic wave velocities in rocks are classically measured by two methods, namely first-break picking (detection of the onset arrival of the wave and measurement of the first-break velocity Vfb) and phase spectrum method (exploitation of the frequency dependence of the signal phase and measurement of the phase velocity Vphase). Here we propose a method to exploit the deviation between Vfb and Vphase for characterizing rock heterogeneity size. For this we adapt existing asymptotic wave theories in random elastic media in order to deal with viscoelastic media, such as rocks. The adapted theory gives the heterogeneity size as a function of the deviation between the two previous velocities, of pathlength, and of the estimated standard deviation of the velocity fluctuations. The heterogeneity sizes deduced from ultrasound in two heterogeneous rocks compare rather well with independent observations on the same samples using X-ray tomodensitometry. In parallel we check the asymptotic result with finite difference (FD) simulations. The agreement is rather satisfactory, however the systematic increase of the deviation between VFB and Vphase with pathlength predicted by asymptotic theory is observed only at small offsets. Frequency effects, not taken into account by asymptotic theory, could be the cause of disagreement at large offsets.