# PRAGUE CENTRE OF
MATHEMATICAL
GEOPHYSICS,
METEOROLOGY, AND THEIR
APPLICATIONS

(MAGMA)

### Blind deconvolution and its seismological applications

Olivier Sebe, Universite Joseph Fourier, Grenoble, France

Prague, Nov 26, 2004
For around twenty years, the signal processing community has developed,
for digital communication, different methods of blind deconvolution making
it possible to retrieve the unknown convolutive components of one known
signal. In this work, we study the way to apply these blind deconvolution
technics to seismology in order to estimate the source function or the
site effects from only a small numbers of surface seismic records. Based
on the theory of coda wave and on a minimum phase deconvolution method, we
develop an original algorithm for coda waves. We first apply it to the
records of the Kursk's underwater explosion (12/08/2000). After showing
that such an explosion is roughly a minimum phase source, we estimate,
from the obtained minimum phase source function of the Kursk, the depth
and the power of the explosion. We then apply this method to the
Rambervillers's earthquake (22/02/2003, Ml=5.4). From the estimated
minimum phase source time function, we retrieve not only the duration and
the seismic moment but also the site effect at recording stations located
several kilometers away from one another. In order to release the minimum
phase assumption, we use a higher order statistic blind deconvolution on
the stationnarized coda signal. From the multi-station stacked
tricorrelation, we obtain a source time function consistent with the
source function estimated after deconvolution by empirical Green function,
which is in agreement with the minimum phase seismic source function.
These first results show that these methods seem to be very powerful, and
they should be applied on a set of records of different events from
different stations through global inversion scheme.

Keywords: Seismology, blind deconvolution, higher order statistics,
tricorrelation, minimum phase, stationnarization, coda waves, source time
function, site effects.

Last edited Dec 3, 2004