Imaging and modeling of seismic transitions: a site 
Percolation model for upper-mantle discontinuities

Felix Herrman
December 10, 2004

ABSTRACT

In this talk I will give an overview of the imaging, characterization 
and modeling techniques that are being developed in my research group. 
First,  I will show that curvelet frames  (new generation of non-separable
 wavelets) juxtaposed with non-linear thresholding and constrained 
optimization can be used to improve seismic imaging and inversion. 
Then, I will introduce an novel representation for seismic transitions,
 parameterized by scale exponents expressing the sharpness of seismic 
transitions. This parameterization allows me to distinguish between 
zero- and first-order discontinuities and anything in between.   
I will conclude by introducing a site Percolation model with a critical 
point that coincides with the transition.  As the mineralogical mixture 
passes through the critical point, a fractional order singularity 
(discontinuity with an order between zero and one) is created which 
explains the  waveforms of converted phases at the discontinuity. 
Examples for the 410 using receiver functions are shown.