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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A wave equation based Kirchhoff operator and its i
nverse - ten Kroode\, F (Shell International Explo
ration and Production)
DTSTART;TZID=Europe/London:20111215T153000
DTEND;TZID=Europe/London:20111215T160000
UID:TALK34979AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/34979
DESCRIPTION:In seismic imaging one tries to compute an image o
f the singularities in the earth's subsurface from
seismic data. Seismic data sets used in the explo
ration for oil and gas usually consist of a collec
tion of sources and receivers\, which are both pos
itioned at the surface of the earth. Since each re
ceiver records a time series\, the ideal seismic d
ata set is five dimensional: sources and receivers
both have two spatial coordinates and these four
spatial coordinates are complemented by one time v
ariable. \n\n Singularities in the earth give rise
to scattering of incident waves. The most common
situation is that of re\nflection against an inter
face of discontinuity. Refl\nected and incoming wa
ves are related via refl\nection coefficients\, wh
ich depend in general on two angles\, namely the a
ngle of incidence and the azimuth angle. Re\nflect
ion coefficients are therefore also dependent on f
ive variables\, namely three location variables an
d two angles.\n\n The classical Kirchhoff integral
can be seen as an operator mapping these angle-az
imuth dependent refl\nection coefficients to singl
y scattered data generated and recorded at the sur
face. It essentially depends on asymptotic quantit
ies which can be computed via ray tracing. For a k
nown velocity model\, seismic imaging comes down t
o nding a left inverse of the Kirchhoff operator.
\n\nIn this talk I will construct such a left inve
rse explicitly. The construction uses the well kno
wn concepts of subsurface offset and subsurface an
gle gathers and is completely implementable in a w
ave equation framework. Being able to perform such
true amplitude imaging in a wave equation based s
etting has signifficant advantages in truly comple
x geologies\, where an asymptotic approximation to
the wave equation does not suffice. The construct
ion also naturally leads to a reformulation of the
classical Kirchhoff operator into a wave equation
based variant\, which can be used e.g. for wave e
quation based least squares migration. Finally\, I
will discuss invertibility of the new Kirchhoff o
perator\, i.e. I will construct a right inverse as
well.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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