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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, November 16, 1999}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Paul Segall}
\centerline{\sl Geophysics Department}
\centerline{\sl Stanford University}
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\centerline{\bf Space-Time Inversion for Earthquake and Volcanic Sources}
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Abstract: 
The past five years has witnessed a tremendous expansion in
technologies for monitoring deformation of the earth's crust.  Arrays of
Global Positioning System (GPS) receivers measure changes in three
dimensional position with sub-centimeter precision.   Interferometric
Synthetic Aperture Radar (SAR) allows continuous mapping of the scalar
range change in the radar line of site.  Borehole tilt and strain meters
measure local strain changes with precision of part per billion over some
frequency band. These data can be used to invert for spatial and temporal
variations in slip on earthquake faults and dilation of magma filled
conduits.  Previously, space-time inversions had been hampered by poor
spatial coverage, low signal to noise ratios, contaminating non-tectonic
motions and our lack of knowledge of the temporal character of aseismic
motions.  

I will discuss methods to estimate quasi-static fault slip as a function of
space and time using data from dense geodetic networks.  The method
combines linear inverse theory with time domain, Kalman filtering, and
allows for non-parametric descriptions of slip velocity.  A state-space
model for the full geodetic network is adopted, so that all data from a
given epoch are analyzed together.  This allows the filter to distinguish
between non-steady fault slip and local noise processes.  I will illustrate
the method with data from a seismic swarm off the coast of Japan in 1997.
Using GPS, tilt, and leveling data we are able to image the growth of a
magma filled crack in space and time.  Although spatial resolution is
limited, we 
are able to infer that the crack expanded at a maximum rate of 2 million
cubic meters per day,  and propagated upward with time.  Such methods could
lead to improved eruption forecasting.  Further work is needed to treat
spatially coherent errors including seasonal effects, to determine
confidence intervals in quantities of interest, and perhaps to include
non-linear constraints and time dependent kernels. 


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