Abstract:
Typical three-dimensional inverse problems of magnetic prospecting are considered,
namely: determination of the vector density of magnetic dipoles in the studied area of the
earth's crust from the components of the vector (and/or gradient tensor) of magnetic
induction measured on the surface. These problems, being, as a rule, ill-posed, can be
solved by standard regularization methods. However, for such a solution on sufficiently
detailed grids, significant computing resources (computing clusters, supercomputers, etc.)
are required to solve the problem in minutes. The article proposes a new "fast" regularizing
algorithm for solving such three-dimensional problems, which makes it possible to obtain
their approximate solution on a personal computer of average performance in tens of
seconds or in a few minutes. In addition, the approach used allows us to calculate an aposteriori error estimate of the found solution in a comparable time, and this makes it
possible to evaluate the quality of the solution when interpreting the results. Algorithms
for solving the inverse problem and a-posteriori error estimation for found solutions are
tested in solving model inverse problems and used in the processing of experimental data.
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