Separating High-Frequency Source and Site Effects Using
Very Small Earthquakes

Glenn P. Biasi and Kenneth D. Smith, University of Nevada
Reno Seismological Laboratory, Reno, NV, 89557
glenn@seismo.unr.edu ken@seismo.unr.edu

Virtually all analyses to separate earthquake source
spectral shapes from observed data assume that displacement
spectra roll off proportional to frequency squared $\omega
^ {-2}$ above a corner frequency related to the source
dimension.  When the source spectra are assumed to follow
the $\omega ^ {-2}$ model, deviations can only be measured
relative to this model.  For example, the $\kappa$
parameter proposed by Anderson and Hough (1984), interprets
the residual slope from the $\omega ^ {-2}$ model in terms
of path and site attenuation.

We present a simple method to measure site effects directly
from the displacement spectra of small earthquakes below
their corner frequencies.  Below the corner frequency, the
source displacement spectra are flat, so after geometric
correction, any residual slope below the corner is due to
attenuation and site effects.  Once the site effects are
known, they can be removed from the spectra of larger
events, leaving only the desired source spectra.  We apply
this approach to three-component aftershock recordings from
the Little Skull Mountain earthquake (M 5.6, 6/28/92).
This data set includes on-scale recordings of aftershocks
as large as M 4.5, and well-recorded events of M 0 and
smaller.  By assuming an $\omega ^ {-2}$ model above the
corner frequencies of the larger events, $\kappa$ estimates
average 0.012 for the stations considered.  This compares
with an average of 0.030 at the same sites using small
event displacement spectra below their corner-frequency.
Scattering may play some role in individual spectra, but
seems unlikely to explain the average differences we
observe.  Site attenuation must affect both measurements
equally.  The difference in $\kappa$ values implies that
for the small- to moderate-sized earthquakes considered,
significant excess high-frequency energy was radiated
beyond that in the $\omega ^ {-2}$ model.  Partial
stress-drop and composite-source models offer potential
explanations for the observed slower spectral decay.
Small-event displacement spectra thus provide an
independent means of estimating site effects, and allow
source spectra to be directly estimated for larger and more
important events.