Multiscaling nature of sonic velocities and lithology in the upper crystalline crust: evidence from the KTB Main Borehole

The observed scaling of sonic logs is generally described using a monofractal model (fractional Brownian motion with Hurst exponent typically between 0.1 and 0.2, or fractional Lévy motion); even though such a description recognizes the existence of the self-similarity of the logs, it offers only a limited account of the actual symmetry, as it misses the displayed heterogeneous fractality. Intermittency of the velocity increments is here observed, and calls for the use of a multifractal description. We quantify such a multifractality in the case of the P-wave sonic log recorded at the KTB Main Borehole. We also show that the associated lithology, inferred from the gamma log, has a multifractal distribution as well, though characterized by a stronger intermittency. It can be expected that the multifractality of the sonic log is partially induced by the lithology, though the observed discrepancy in the degree of intermittency between the two logs indicates that the scaling symmetry of the seismic velocity is probably due to many different contributions. Such statistics for both sonic and gamma logs have important implications on our understanding of wave propagation and rock strength and permeability in the crystalline crust, as they show the crust to be more heterogeneous than is usually modeled.