TESTING OF THE METHOD FOR THE CONVERSION OF THE MT APPARENT RESISTIVITY CHANGES INTO THE RELATIVE CHANGES

IN THE ROCK ELECTRICAL RESISTIVITY USING THE 2D MODEL OF THE GEOELECTRIC STRUCTURE

Marina E. SholpoSPbF IZMIRAN, Russian Academy of Sciences, Muchnoy 2, St.Petersburg, 191023, Russia,

e-mail: msholpo@mail.ru

Abstract. A method for direct conversion of observed variations in magnetotelluric apparent resistivity ρa into relative variations in the resistivity of elements of a well-studied geoelectric structure is tested on a 2-D model structure of Petropavlovsk geodynamical polygon. It is shown that (1) the study of the frequency and spatial dependences of the sensitivity of ρa to changes in the resistivities of the structure elements allows us to choose the optimal observation regime and (2) the application of the proposed method makes it possible to define relative changes in the rock resistivity with sufficient accuracy.

The MT apparent resistivity is extensively investigated at present as a possible prognostic parameter in many geodynamic research areas. But it is clear that these researches can hardly be effective, if the source of the variations in the apparent resistivities ρa is unknown. If we have in mind that the cause of variations in ρa is the changes in the rock resistivity (that is the seismic- electrical effect of first kind) then the direct relative variations in the resestivity of elements of a geoelectric structure are a more effective prognostic indicator compared to observed variations in the magnetotelluric apparent resistivity. In this connection the method for the separation of the contributions of individual elements of the geoelectric structure to the variations in the apparent resistivity is proposed. It is the method for the estimation of the relative variations in the resistivities ρi of some elements of the geoelectric structure responsible for variations in ρa.. It reduces to the construction and solution of the following system of equations:

∏ xi aij = сj, j = [1, m]. i Here i is the number of the structure element ( it is comfortable to give to this number the value of the structure element resistivity in Ω m), xi = ρi2 /ρi1 is the relative change in the resistivity of the ith element of the structure, aij = εiav(Tj) is the [ρi1, ρi2]-averaged sensitivity of ρa to changes in the resistivity of the ith element of the structure at the electromagnetic field period Тj, cj=ρa2j /ρa1j , were ρa1j and ρa2j are the apparent resistivities at two different moments at the jth period, and m is the number of the periods used. (We remind the reader that the sensitivity of ρa to changes in the resistivity of the ith element of the structure is defined here as a value that determines the relation between relative variations in the resistivity of the ith element of the structure and the corresponding relative variations in the apparent resistivity: εi (ρi,Tj) = dlogρa/dlogρi = (dρa/ρa)/ (dρi/ρi) [Sholpo, 2003].) Taking the logarithm of these equations, we obtain the system of linear equations. The solution of the latter involves no fundamental difficulties if the values ρa1, 2 are determined with a sufficient accuracy in the entire range of required periods. The main problem in the realization of this method is the correct determination of the aij = εiav (Tj) using numerical modeling of a well-studied geoelectric structure. The results of testing of this method on a 1D model structure were published in [Sholpo, 2006]. This article is dedicated to its testing on a 2D structure. Testing of the proposed method was performed using 2D model of Petropavlovsk geodynamical polygon (Kamchatka). The geoelectric model of this polygon includes three deep and a few surface high conductive elements (Fig.1. The numbers within the model are electrical resistivities in Ω m). Figure 2 presents spatial dependences of maximal values of the function εi(√ T) calculated for i = 8, 10, 20, 30 at the number of points of profile AA. Taking into account the investigation purpose and using these dependences it is possible to determine the best place for MT monitoring.

Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)

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A x, km A

depth, km

Fig. 1. Geoelectric structure of the earth crust at Petropavlovsk geodynamical polygon (Kamchatka)

0 40 80

0.0

0.4

0.8

1.2

x km

ε i max

8

1020

30

Fig. 2. Spatial dependences of maximal values of the function εi(√T) on the profile AAi = 8, 10, 20, 30 – the numbers of the structure elements and its resistivities in Ω m

ε8 --------------------------------- √T = 3.5 - - - - - - - - - - √T = 5ε10 --------------------------------- √T = 14 - - - - - - - - - - √T =17ε20 --------------------------------- √T = 12 - - - - - - - - - - √T =17

ε30 --------------------------------- √T = 1

At the same time it is necessary to study the frequency responses εi in the different points of the profile, because the possibility of the separation and the accuracy of the estimation of contributions of the individual elements of the geoelectric structure are dependent on the correlation between the periods of its maximums. Thanks to that it is possible to determine the optimal frequency interval. Figure 3 presents the frequency responses of ρa sensitivity to variations in the resistivity of four structure elements for the profile points with x = 37, 45, 60km.

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1E-4 1E-3 1E-2 1E-1 1E+0

0.0

0.5

1.0

1E-4 1E-3 1E-2 1E-1 1E+0

0.0

0.5

1.01E-4 1E-3 1E-2 1E-1 1E+0

0.0

0.5

1.0

x

x

Hz

Hz

Hz

108

20

10

20 8

10

20

8

ε i

x = 37 km

f

= 47 km

f

= 60 km

f

30

30

30

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

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impossible to observe the changes in the resistivity of all three deep structure elements with the sufficient accuracy using only one observation point.

Table 1. Results of the testing of the method at three points of the profile AA( x = 37, 45, 60 km )

for two variants of the changes in the resistivity of three structure elements

Table 2. Defining of the changes in the resistivity of 20th structure elementsby the observations at the point x = 14.5 km

i 10 8 20

(ρi2/ρi1)и .905 1.286 .818

εi max .45 .0038 .40(ρi 2/ρi 1)э

δ%0.906

0.1

1.685

31

0.799

2.3δ%

(noise 3%)6.6 281 12.4

( ρi 2 /ρi 1)э

δ%0.882

2.5

0.859

4.9δ%

(noise 3%)4.9 10.1

1 Variant 1 Variant 22 i 10 8 20 10 8 20

3 ρi1 Ω m 9 7 15 10.5 7 22

4 ρi2 Ω m 11 9 25 9.5 9 18

5 (ρi2/ρi1)и 1.222 1.286 1.667 .905 1.286 .818

6 x = 37 km, ε10 max = 0.75, ε8 max = 0.20, ε20 max = 0.25

7 (ρi 2/ρi 1)э

δ%1.2875.3

1.1897.6

1.48411.0

.8733.5

1.3243.0

.8989.8

8 δ%(noise 3%) 20 13.4 38 13.3 7.7 759 x = 47 km, ε10,max = 0.77, ε8,max = 0.91, ε20,max = 0.1710 (ρi 2/ρi1)э

δ%1.2340.9

1.2602.1

1.6730.3

.8990.5

1.2980.9

.8250.9

11 δ%(noise 3%) 2.8 1.8 17 1.4 1.2 7.1

12 δ%(noise 5%) 7.6 1.6 37.8 7.1 1.7 23

13 x = 60 km, ε10,max = 0.74, ε8,max = 0.51, ε20,max = 0.14,14 (ρi2/ρi1)э

δ%1.2190.2

1.2294.4

1.7535.2

.9040.1

1.3112.0

.8120.7

15 δ%(noise 3%) 2.9 4.4 10.5 3.1 3.0 2016 δ%(noise 5%) 6.0 5.0 23.5 6.0 2.8 32

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To investigate the influence of the surface layer on the results of the estimations of the values of the relative variations in the resistivities ρi there was studied a model where to three deep elements the fourth one with the number i = 30 was added (see Fig.1). The results of the calculations of the values ρi2/ρi1 at the point x = 47 km for the changes in the resistivity of four structure elements are given in Table 3. As is seen the introduction into the model of the surface element capable of time- change of its resistivity does not increase the errors of the determining of the relative variations in the resistivity of the deep structure elements, which is evidently the consequence of the isolated position of the frequency response maximum of ε30 (Fig.3).

Table 3. Results of the testing of the method at the point x = 47 km in case of the changes

in the resistivities of four structure elements.

I 10 8 20 30ρi1 Ω m 10.5 7 22 20ρi2 Ω m 9.5 9 18 40(ρi2/ρi1)и .905 1.286 .818 2

εi max .77 .91 .17 .51(ρi 2/ρi 1)э

δ%.903.2

1.3031.3

.812.7

2.052.5

δ%(noise 3%)

4.4 1.8 21.9 2.7

Conclusions(1) To choose the regime of observations of variations in the rocks conductivity suitable for the investigation aim it is needed to study the frequency and spatial dependences of the sensitivities εi(T, x) using numerical modeling of a well-studied geoelectric structure.(2) The application of the proposed method in optimal points of observation allows us to estimate values ρi2 /ρi1 with accuracy sufficient for monitoring of relative changes in the electrical conductivity of rocks.

ReferencesSholpo, M.E. (2003), Magnetotelluric monitoring of variations in the electrical resistivity of a conducting

layer: numerical modeling. Physics of the Solid Earth, Vol. 39, No. 2, 112-117.Sholpo, M.E. (2006), Monitoring of relative changes in the electrical conductivity of rock from

observations of the magnetotelluric apparent resistivity (numerical modeling). Physics of the Solid Earth, Vol. 42, No. 4, 323-329.

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