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7Section 6
INVERSE PROBLEMS
On the stability of determining the position and shape of local acoustic inhomogeneities when solving
an inverse problem using the BaL algorithm
A. B. Bakushinsky1,2, A. S. Leonov3
1Research Center Computer Science and Control of RAS, Institute for Systems Analysis
2Mari State University
3National Nuclear Research University 'MEPHI', Moscow
Email: asleonov@mephi.ru
DOI 10.24412/cl-35065-2021-1-01-87
In [1], the so-called BAL algorithm is proposed for stable solvng of the 3D scalar inverse problem of acous-
tic sounding of an inhomogeneous medium. The data for the solution is the complex amplitude of the wave
field measured in a layer outside the region of inhomogeneities. The inverse problem is reduced to solving 1D
Fredholm integral equations of the first kind, to the subsequent calculation of the complex amplitude in the
region of inhomogeneity, and then to finding the required sound velocity field in this region. The algorithm
allows solving the 3D inverse problem on a PC of average performance for sufficiently fine 3D grids in tens of
seconds. Now we present the numerical study of the stability of determining the position and shape of local
inhomogeneities using the BAL algorithm in the case of many such inclusions with different geometries.
This work was supported by the Russian Science Foundation (project 20-11-20085) (first author) and the Programm
of Competitiveness Increase of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute);
contract no. 02.a03.21.0005, 27.08.2013 (second author).
References
1. Bakushinskii, A.B., Leonov, A.S. Numerical solution of an inverse multifrequency problem in scalar acoustics.
Comput. Math. and Math. Phys. 2020. V.60. P. 987�999.
Algorithm for inversion of resistivity logging-while-drilling data in 2D pixel-based model
A. V. Bondarenko, D. Yu. Kushnir, N. N. Velker and G. V. Dyatlov
Baker Hughes
Email: alexey.bondarenko@bakerhughes.com
DOI 10.24412/cl-35065-2021-1-01-88
Multi-frequency and multi-component extra-deep azimuthal resistivity measurements with depth of in-
vestigation a few tens of meters provide advanced possibilities for mapping of complex reservoir structures.
Inversion of the induction measurements set becomes an important technical problem. We present a regular-
ized Levenberg � Marquardt algorithm for inversion of resistivity measurements in a 2D environment model
with pixel-based resistivity distribution. The cornerstone of the approach is an efficient parallel algorithm for
computation of resistivity tool signals and its derivatives with respect to the pixel conductivities using volume
integral equation method. Numerical tests of the suggested approach demonstrate its feasibility for near real
time inversion.
