FAULT SCALING AND 1 F NOISE SCALING OF SEISMIC VELOCITY FLUCTUATIONS IN THE UPPER CRYSTALLINE CRUST/

Sonic logs are detailed measurements of the in situ seismic velocity a long borehole walls. Power spectra of sonic logs typically decay appro ximately as the reciprocal of spatial frequency f, regardless of the c hemical composition, geologic age, and tectonic history of the probed lithologies. Data sequences of this type are fractal or scale-invarian t. The origins of this uniform lif scaling of seismic structure are no t clear, particularly in low-porosity crystalline rocks, but faults, f ractures, and cracks are considered to be important. Fault structures also follow fractal scaling laws and have significant effects on seism ic velocity. This paper presents a quantitative model that evaluates t he role played by faults in determining the scaling laws of seismic ve locity fluctuations. The model is based on current knowledge of the st ructure and scaling properties of brittle faults and of associated reg ions of microcracking. By approximating the relationship between crack density and velocity variation as linear, this model yields a Brownia n power spectrum (proportional to 1/f(2)) for velocity perturbations a cross a single fault zone in a medium of otherwise constant velocity. The power spectrum of velocity fluctuations induced by a population of faults is then obtained by superposing the corresponding Brownian pow er spectra weighted according to the observed frequency-size scaling r elationship of brittle faults. The results of this study indicate that the uniform 1/f scaling of velocity fluctuations in crystalline rocks seems to be linked to the correspondingly uniform scaling properties of fault structures.