New 3D parallel SGILD modeling and inversion Page: 10 of 20
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Xie et al, LBNL 42252, New Parallel SGILD Modeling and Inversion, September 1, 1998
Auo (r) = Bub (r) + ab aGb (r', n uo (r') ds
b< > Gb (r', r) ds, (7)
FMI(< a >, C, C,, uo, ) = 0,
FMI (< a >, C., C., uo, ) = 0,
FMI (< Or >, < u2 >, 1, CQ, ) = 0, (8)
FMI (< a >, Cw, asuo, ) = ACu. (r', R) - a Cu, (r', fit) ds
acu (n' )Gb (r', r) ds + *j Cao(r) Gb (r', r) ds, (9)
We use the Galerkin finite element method to discretize the forward moment
Galerkin equations (3) and (4), and the collocation finite element method to
discretize the boundary integral equations (7) and (8),see  . The discrete
equations (3) and (7), (4) and (8) will be coupled as a complete equation
system. The SGILD modeling algorithm will be used to solve the equations
from the domain to the boundary, in parallel  .
3 Stochastic acoustic equations for nonlinear inversion
In this section, we describe the new stochastic acoustic volume integral equa-
tions and differential equations for nonlinear inversion.
3.1 Stochastic acoustic volume integral equation
Ud(r) = ub (r) + J (a - ab)VGb (r, r) Vu (r) dr, (10)
Because the measured data u, and the acoustic impedance, a, are assumed
to be random variables, the equation (10) becomes a stochastic first type
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Xie, G.; Li, J. & Majer, E. New 3D parallel SGILD modeling and inversion, article, September 1, 1998; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc710929/m1/10/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.