Fractal Fracture Scattering Origin of S-Wave Coda: Spectral Evidence from Recordings at 2.5 km

Peter Leary, & Rachel E. Abercrombie

Published 1994, SCEC Contribution #112

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 corner frequencies fo ≈ 20-30 Hz coda spectra decay by power-law exponent n ≈ −2.3±0.1 while the source shear-wave spectra decay by cubic power-law (mean power-law exponent n ≈ −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 ≈ f 0.7±0.1. The distribution of acoustic reflectivity deduced from the Cajon Pass well log has a power-law density ≈ ν0.6 at the relevant spatial frequencies ν. The agreement between the temporal and spatial frequency power-law exponents may be explained by first order scattering in fractal fracture-heterogeneous material.

Citation
Leary, P., & Abercrombie, R. E. (1994). Fractal Fracture Scattering Origin of S-Wave Coda: Spectral Evidence from Recordings at 2.5 km. Geophysical Research Letters, 21(16), 1683-1686.