FRACTAL FRACTURE SCATTERING ORIGIN OF S-WAVE CODA - SPECTRAL EVIDENCE FROM RECORDINGS AT 2.5 KM

Local earthquake seismograms recorded at a depth of 2.5 Km in the Cajon Pass borehole near the San Andreas fault, southern California, yield body-wave and coda-wave amplitude spectra at frequencies between 10 and 200 Hz without interference from either near-surface attenuation or surface waves. The coda-wave spectra resemble the shear-wave source spectra except that above the comer frequencies f(o) almost-equal-to 20-30 Hz coda spectra decay by power-law exponent n almost-equal-to -2.3+/-0.1 while the source shear-wave spectra decay by cubic power-law (mean power-law exponent n almost-equal-to -3.1+/-0.1). Assuming a cubic source power-law spectral decay, the high frequency power-law enrichment of coda amplitudes relative to source amplitudes implies a power-law distribution of scatterers that increases with frequency as almost-equal-to f0.7+/-0.1. The distribution of acoustic reflectivity deduced from the Cajon Pass well log has a power-law density almost-equal-to nu0.6 at the relevant spatial frequencies nu. The agreement between the temporal and spatial frequency power-law exponents may be explained by first order scattering in fractal fracture-heterogeneous material.