**R.
Minenko**^{1}**,
MSc****,
****E-mail:
maestozo.1_pavel@mail.ru;**

**P.
Minenko**^{1}**,
Dr. Sci. (Phys.-Math.), Prof.****;**

**Yu.
Mechnikov**^{2}**,
Engineer-Geologist**

**THE
PROBLEM OF FINDING MEANINGFUL SOLUTIONS TO LINEAR INVERSE PROBLEMS**

**OF
MAGNETOMETRY BY INTEGRATION OF INTERPRETIVE MODELS**

^{1
}**Krivorozhsky
National University****,
****54,
Gagarina Avenue, Krivoy Rog, 50086 Ukraine****,**

^{2
}**Krivoy
Rog Geophysical Department****,
****2
Geologichna Str., Krivoy Rog, 50001 Ukraine**

**The
aim of this work is the creation of methods for solving the inverse
problem of magnetometry in the conditions of uncertainty in the
spatial****
****distribution
of the magnetization of rocks. As a rule, the solution of the inverse
problem of magnetometry is ambiguous because of the inaccuracy of the****
****model
chosen, its displacement relative to the real masses, the degree of
discrepancy between the real physical parameter of rock with
specified initial****
****conditions.
Unlike gravity, the complexity of solving the inverse problem of
magnetometry due to the fact that the magnetic properties of rocks
are so****
****heterogeneous
that they simply cannot be reliably determined on samples from
outcrops or boreholes nor according to well logging data, i.e. the
micro****
****level
is not acceptable to the magnetic survey. The only method to
determine the magnetic properties at the macro level is the solution
of the inverse****
****problem.
However, comparing of the interpretation results does not seem
possible in a material sense. One can only solve the inverse problem
by****
****different
methods. It is desirable that these methods were varied and were
based on a grid-block interpretation models with different linearity.
For****
****example,
when using multi-layer models of the geological environment with
finite-height and semi-infinite blocks, we get totally different
results of****
****solving
the inverse problem. Since direct methods for solving the inverse
problem are developed very poorly, the decision has to be done by
optimized****
****iterative
methods which are much better designed. With the help of multi-layer
theoretical models it was found that for semi-infinite prisms the
definable****
****intensity
of magnetization decreases to a prism with increasing of the depth,
though in fact, it is constant in a geological massif. For multilayer
models****
****with
finite-height prisms the deeper is the prism in the model, the
greater is the intensity of magnetization, although, more accurately,
this is true only to****
****a
certain depth and even height of the prism. Such a set of rules might
result in deadlock the interpretation of magnetic anomalies by mesh
methods. In****
****nature,
however, vertical bodies can have falling or increasing intensity of
magnetization with depth, which further complicates the definition of
the****
****geological
situation. This article describes the methods we have developed that
speed up or slow down the processes of change of magnetization with****
****depth
in the solution of the inverse problem. A formula has been developed
concerning iterative corrections to the physical parameter. It takes
account****
****of
the depth of the block location in the interpretation model and
adjusts the distribution of the residuals of the field into blocks of
different depths to****
****recalculate
them in a correction to the intensity of magnetization of the block.
By use of several interpretative models with various clarifying
corrections,****
****stable
and meaningful solution of the inverse problem can be achieved.**

**Keywords:
gravimetry, inverse problem, iterative method, iterative correction,
optimization criterion, the correction for depth.**

**References****:**

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2. Minenko P.A., (2006). Isledovanie kristalicheskogo fundamenta lineynonelineynymi metodami magnitometrii i gravimetrii. Geoinformatika, 4, 41-45. (In Russian).

3. Minenko P.A., Minenko R.V., (2012). Uproshhennye algoritmy reshenija obratnyh zadach gravimetrii filtracionnymi metodami. Geoinformatika, 2(42), 27-29. (In Russian).

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