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SUMMARY:C5 - Coherent interferometric imaging in random media I - Borcea\,
  L (Rice)
DTSTART:20110728T084500Z
DTEND:20110728T093000Z
UID:TALK32171@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:I will describe the mathematical problem of imaging remote sou
 rces or reflectors in heterogeneous (cluttered) media with passive and act
 ive arrays of sensors. Because the inhomogeneities in the medium are not k
 nown and cannot be estimated\, we model the uncertainty about the clutter 
 with spatial random perturbations of the wave speed. The goal of the lectu
 res is to carry out analytically a comparative study of the resolution and
  signal-to-noise ratio (SNR) of two array imaging methods: the widely used
  Kirchhoff migration (KM) and coherent interferometry (CINT). By noise in 
 the images we mean fluctuations that are due to the random medium.\n\nKirc
 hhoff migration and its variants are widely used in seismic inversion\, ra
 dar and elsewhere. It forms\nimages by superposing the wave fields receive
 d at the array\, delayed by the travel times from the array sensors to the
  imaging points. KM works well in smooth and known media\, where there is 
 no wave scattering and the travel times can be estimated accurately. It al
 so works well with data that has additive\, uncorrelated measurement noise
 \, provided the array is large\, because the noise is averaged out by the 
 summation over the many sensors. KM images in clutter are unreliable and d
 ifficult to interpret because of the significant wave distortion by the in
 homogeneities. The distortion is very different from additive\, uncorrelat
 ed noise\, and it cannot be reduced by simply summing over the sensors in 
 the array. CINT images efficiently in clutter at ranges that do not exceed
  one or two transport mean free paths. Beyond such ranges the problem beco
 mes much more difficult\, specially in the case of active arrays\, because
  the clutter backscatter overwhelms the echoes from the reflectors that we
  wish to image. Coherent imaging in such media may work only after pre-pro
 cessing the data with filters of clutter backscatter.\n\nThe CINT method f
 orms images by superposing time delayed\, local cross-correlations of the 
 wave fields received at the array. The local cross correlations are comput
 ed in appropriate time windows and over limited array sensor offsets. It h
 as been shown with analysis and verified with numerical simulations that t
 he time and offset thresholding in the computation of the cross-correlatio
 ns is essential in CINT\, because it introduces a smoothing that is necess
 ary to achieve statistical stability\, at the expense of some loss in reso
 lution. By statistical stability we mean negligibly small fluctuations in 
 the CINT image even when cumulative fluctuation effects in the random medi
 um are not small.\n
LOCATION:Seminar Room 1\, Newton Institute
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