New 2.5D finite element GILD Born modeling using new magnetic integral equation
Ganquan Xie 1), Jianhua Li 1) and Wang Tieqi 2)
1) Earth Sciences Division, Lawrence Berkeley National Laboratory, USA.
e-mail: g_xie@lbl.gov
2) Hunan Province Electric Power Test and Research Institute, China.
Abstract
In this paper, we developed a 2.5D finite element GILD Born electromagnetic (EM) modeling using a new
magnetic integral equation. The 2.5D problem is that the EM source is in 3D and the electric parameter is
only distributed in 2D. Because there are many 2D data configuration site, the 2.5D EM modeling and
nonlinear inversion can be useful to interpret the field data in the geophysical oil exploration and
environmental characterization. There are many papers described the EM modeling using the electric field.
Habashy, Oristaglio, and de Hoop (1994) developed a nonlinear reconstruction of 2D permittivity and conductivity. Ellis
(1995) developed a joint 3D EM inversion. Li et al. (1995) developed a new 3D cubic-hole element using boundary
integral equation. Newman (1995) developed a crosswell EM inversion using integral and differential equations. In 1995,
Xie and Li create a new 3D/2.5D integral equation using the magnetic field. The EM physical principle is that when the
conductivity and permittivity are discontinuous and the magnetic permeability is continuous, then the magnetic field is
continuous. Therefore, the new magnetic integral equation is conveniences for finite element modeling. The 2.5D finite
element GILD Born modeling consists of the following parts:
(1) Suppose that the conductivity and
permittivity vary only on the (x,z) plane, using Fourier transformation , the spatial magnetic filed ,and
the electric field will be transformed into the ky domain magnetic field and electric filed. The New 2.5D magnetic integral equation is
(1)
(2) finding a finite element solution of (1) on a coarse mesh, , using first order element sample
function, (3) upon substituting the into the right hand of (1) and using the second element
sample function. The is the finite element Born approximation of (1). The numerical tests shown that
the solution has reasonable accuracy and save lot of time. The new finite element Born approximation
can be used to the data simulation and 2.5D EM inversion. (4) Born approximation of (1) in SI and
finite element magnetic differential equation in SII assemble into the GILD-Born EM modeling.
The original abstract contains mathematical expressions that can not be transformed into HTML.
raeg98@tansa.kumst.kyoto-u.ac.jp
Last modified: Mon Sep 21 09:24:29 1998