INVERSION OF SYNTHETIC APERTUR,E R,ADAR (SAR) - MSpace ...

4.2 Review of Born fnversion Application
Boln irversion is a rvave equation invelsion procedure tltlough a Boln (first)
approxirnation (Boll [12]). To illustrate the Born invelsion approach, a
seisuric velocity inversion example is to l¡e clescril¡ed il this section. The
acoustic rvave propagating into the Ealth's sul¡sulface is cliscussecl belolv.
Vectol variables are denotecl by bold type ancl the clornain of Fourier'
transform is denotecl by the corresponcling argument.
The equation governilg simple rvave propagation for a point soulce in an
inhonogeneous medium is
/ t
â2\
(v'_ -o* ) U(r,r.;t): á(r - r'.)á(¿) (4.1)
\ D¿\t) cJL¿ /
whele U(r,ro;t) is a total wavefielcl, o(r) is the local acoustic velocity, ro
and t'are lespectively the source and observation positions, ancl ô(.) is a
Dirac clelta function. If the subsulface velocity variatiol is small cornparecl
with a refelence velocity, the velocity u(r) can be clefine