Inversion of Electromagnetic Induction Log in Anisotropic Media using an Adjoint Integral Equation Method
D.H. Saputera (University of Bergen)
M. Jakobsen (University of Bergen)
N. Jahani (NORCE Norwegian Research Centre AS)
K.W.A. van Dongen (TU Delft - ImPhys/Van Dongen goup, TU Delft - ImPhys/Medical Imaging)
S. Alyaev (NORCE Norwegian Research Centre AS)
K. S. Eikrem (NORCE Norwegian Research Centre AS)
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Abstract
Inversion of electromagnetic induction log while drilling provides structural information around borehole for geosteering decision process. Imaging a complex three-dimensional (3D) anisotropic formation is very challenging due to the significant cost of the forward solver. To overcome this challenge, we have developed an inversion algorithm using an adjoint Integral Equation Method for logging while drilling scenarios in anisotropic media with several inexpensive approaches in this study. We use a quasi-Newton method with L-BFGS algorithm and implement a matrix-free adjoint Integral Equation method for efficient update of inverted model parameters. In addition, we propose the use of limited number of iterations for solving the adjoint equation as an approximation to the gradient for a faster computation time. To regularize the inverted models, we adopt the use of multiplicative regularization and weighted L2 total variation. Additionally, we impose priori information in our formulations, such as 2D parameterization and the range of conductivity values. We show a numerical example of logging while drilling inversion on a 2.5D faulted anisotropic formation. Numerical experiments show that our inversion workflow shows a good structural agreement of the inverted model within the sensitive range of the tool.