On the cause of 1/f‐power spectral scaling in borehole sonic logs

Abstract

Borehole logs provide in situ information about the scaling of fluctuations in the elastic properties of rock. A surprising finding has been the widespread 1/fβ‐type (0.5 < β < 1.5) scaling of borehole sonic log power spectra, yielding no clear correlation with geological age, type or history, raising questions about the reliability and origin of these findings. Ubiquitous fractures, for example, have been evoked as the most likely explanation of these results. Firstly, we show that the smoothing effects of the logging tool must be taken into account in order to obtain reliable values of β. We then investigate the scaling properties of lithology only in perfectly exposed metamorphic rock, by explicitly excluding fractures. We find clear 1/f scaling for reconstructed velocity data based solely on lithological variations. Although fractures are certainly important in contributing to 1/f fluctuations in borehole logs, intrinsic geology may also play a significant role.