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A Generic Model for Seismic Velocity Fluctuations Based on Evidence From Sonic Logs Klaus Holliger 1 (+41-1-633-26-59; holliger@geo.phys.ethz.ch) John A Goff 2 (goff@utig.ig.utexas.edu) 1Institute of Geophysics, ETH-Hoenggerberg, Zurich CH-8093, Switzerland 2University of Texas Institute for Geophysics, Spicewood Springs Road, Building 600, Austin, TX 78759, United States Sonic logs are detailed measurements of the in situ seismic velocity along borehole walls. Power spectra of sonic log velocity fluctuations typically decay as the reciprocal of the spatial frequency, regardless of the petrological composition, geologic age, and tectonic history of the probed lithological column. The origins of this surprisingly uniform scaling of the upper crustal seismic structure remain enigmatic. We present a generic model that evaluates the respective roles played by petrological variability as well as by brittle faulting in determining the scaling laws evidenced by upper crustal sonic log velocity fluctuations. The model is based on current knowledge of the structure and scaling properties of upper crustal petrological variability and brittle faults. Based on evidence from nuclear logs and core records the petrological effects on velocity fluctuations are modeled as a random superposition of rectangular impulses of variable length. The probability distributions of the amplitude and length of this random impulse sequence are Gaussian and hyperbolic, respectively. Brittle faults are surrounded by a halo of micro-cracks and the resulting velocity perturbation is assumed to be proportional to the crack density. The thickness of this micro-crack halo is proportional to the length of the fault and the density of micro-cracks within the halo decreases logarithmically with increasing distance from the fault zone. This yields Brownian power spectra for the velocity perturbations induced both by a single petrological heterogeneity and by a single brittle fault zone. The cumulative power spectrum is then obtained by superposing these Brownian power spectra weighted according to the hyperbolic frequency-size scaling relationship of petrological variabilities and brittle faults. This model indicates that the uniform scaling of upper crustal velocity fluctuations is linked to the correspondingly uniform scaling properties of petrological heterogeneities and fault structures. Given the generic nature of the proposed model and assuming that the basic nature of petrological variability does not change fundamentally, seismic scaling properties similar to those observed in upper crustal sonic logs may be expected to prevail throughout the earth. |
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