PROBLEMS OF GEOCOSMOS

Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
ε i
20
1E-4 1E-3 1E-2 1E-1 1E+0
10
20
x = 47 km
1E-4 1E-3 1E-2 1E-1 1E+0
10
20
10
x = 37 km
1E-4 1E-3 1E-2 1E-1 1E+0
8
8
8
x
fHz
f Hz
= 60 km
Fig. 3. The frequency responses of the ρa sensitivities to variations in the resistivities
of the structure elements for three points of the profile AA: x = 37, 45, 60 km
i = 8, 10, 20, 30 – the numbers of the structure elements and its resistivities in Ω m
The results of the method testing at these points for two variants of changes in the resistivities of three
deeps elements are given in Table 1. The matrices of the coefficients aij were calculated for these points. It
should be noted that the matrix A is the characteristic of the given point placed on the surface of the given
structure. It can be calculated once for all if geoelectric structure is studied well enough to perform numerical
modeling. Owing to that the conversion of apparent resistivity changes into relative changes in rock
resistivity can be easily produced.
In Table 1 ρi1 and ρi2 are the resistivities of the ith structure element at two different moments; (ρi2/ρi1)r
– the real relative changes in the resistivities of the ith element; (ρi2/ρi1)c – the values calculated using the
tested method; δ% – the relative error of (ρi2/ρi1)c; ”noise” – the errors introduced into the apparent
resistivities ρa1 and ρa2; εi max – the maximal value of the function εi(Tj) at the present points. To construct the
columns of free terms of system of linear equations bj = lg cj = lg (ρa2/ρa1), the values ρa1 and ρa2 are
calculated for the sets of given values ρi1 and ρi2 for the optimal interval of periods Tj using the program by
Vardaniants. To make the model problem even more realistic, the errors typical of the accuracy of the
present-day MTS studies (3-5 %) are introduced into the values ρa1 and ρa2. As can be seen from Table 1 the
variations in the resistivity of 20th element are determined rather roughly at the all points. This could be
expected because ε20max is small and at the point x=37 km the frequency response maximums of ε10(Tj) and
ε20(Tj) are located at close frequencies (Fig.3). Because of this the relative changes in resistivity of 10th
element are determined at this point with the greater errors as at others. The point x = 47 km is most
favorable for the investigations of 10th and 8th elements but at this point the errors δ20 are also too great. To
observe the variations in the resistivity of the 20th element it is reasonable to choose the observation point at
the beginning of the profile, for example at x=14.5. Here it is possible to neglect the influence of the 8th
element and to solve the system of linear equations for two unknowns (Table 2). Thus, in present case it is
480
30
30
30
f
Hz