fixed amount, i. e. carry out measurements with a gap h
Z
equal to h
Z1
and h
Z2
, when
h
Z1
-h
Z2
= const at any point of the scan. Then, a multiple solution of the direct problem
is performed by numerical methods in two parameters so that a two-dimensional array
of data is obtained.
Thus, in the construction of approximation curves, a family of characteristics is
obtained when the values of one parameter (ε) are plotted along the ordinate axis, and
the family is constructed according to another parameter (h
Z
). After this, it is necessary
to carry out a so-called two-parameter approximation. Firstly, the entire family of
curves is approximated using the same formula in terms of the parameter plotted along
the ordinate axis. As a result, we obtain a set of approximation coefficients, each of
which depends to a certain extent on the second parameter on which the family was
built. Each of the coefficients is also approximated by the second parameter and these
analytic dependencies are substituted into the first formula. A single analytic formula
appears that depends on two parameters at once. Then, based on this formula, we
construct a system of equations of the form:
3
0
1
(h,)
(h)
(A(h)exp(
))
(h)
Z
Z
i
Z
i
iZ
f
y
f
t
=
−
=
+
,
(1)
3
0
1
(h
h,)
(h
h)
(A(h
h)exp(
))
(h
h)
Z
Z
Z
Z
i
Z
Z
i
i
Z
Z
f
y
f
t
=
−
+
=
+
+
+
+
,
(2)
Where y
0
, t
1 ... 3
, A
1 ... 3
are coefficients that depend, in the main, on the gap, whose
dependences have the following general form:
()
1exp(
(
0))
L
fx
k
x
x
=
+
−−
,
(3)
A further solution is reduced to solving a system of equations consisting of two
equations with two unknowns at each scan point, which is not difficult even in the case
of cumbersome summary equations.
The resulting error of signal recovery, expressed as a percentage, and the
corresponding summary signal, over which the naturalization was performed is shown
in Figure 5.
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