New 3D parallel SGILD modeling and inversion Page: 8 of 20
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Xie et al, LBNL 42252, New Parallel SGILD Modeling and Inversion, September 1, 1998
The new SGILD parallel modeling and nonlinear inversion algorithm is de-
signed to overcome the shortcomings of the conventional inversion. The advan-
tages of the SGILD algorithm are: (1) Supposing the parameters and measured
data are random variable, the new statistical moments acoustic and magnetic
integral and differential equation will be together used to assess the poste-
rior probability using Bayes theorem; (2) It uses new exact moments global
boundary integral equations and local differential equations in the domain that
reduces the numerical boundary noises and improves accuracy of the modeling
and inversion; (3) Using a new moment global integral and local differential
decomposition in inversion that decompose the ill-posed full matrix into 4'
small sparse matrices and a smaller full matrix, greatly improved the ill-posed
condition, and reduced computation time and storage requirements; (4) The
SGILD is a high performance parallel multiple hierarchy algorithm with paral-
lel efficiency of 90 %; (5) it minimized data communication between processors
that is suitable for the MPP T3E; (6) The moments of the parameters can
be used to construct a confidence interval of the parameter. (7) the SGILD
parallel algorithm can be widely useful to solve stochastic elliptic, parabolic,
and hyperbolic modeling and inversion. The algorithm can be used for elastic
wave, electromagnetic, and flow modeling and inversion, that will be a ben-
efit for developing a new coupled GEO-HYDRO imaging. The new coupled
stochastic modeling and high resolution imaging software will be useful for
the prediction of oil, gas, coal, and geothermal energy reservoirs in geophysi-
cal exploration. This paper is constructed as follows: In section 1 we describe
the stochastic acoustic equation and derive new moment Galerkin equations
and boundary integral equations for forward modeling. The stochastic acoustic
equations for nonlinear inversion are described in section 2, we derive the new
moment volume integral equation and variation Garlerkin equations, translate
the posterior probability optimization into a stochastic nonlinear regularizing
optimization, and describe a Gauss-Newton annealing iteration. In section 4
we present the new parallel SGILD modeling and inversion algorithm using
the global integral and local differential equations. Applications are described
in section 5. Finally, we describe conclusions in section 6.
2 Stochastic acoustic equation for forward modeling
2.1 Stochastic differential equation
--- '- +- a O-- +- '.-' +w u= S(r,r,) (1)
whe ry ay 8z is aoz) (
where 0. is the acoustic impedance, u is an acoustic wave function, w is the
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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/m1/8/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.