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where
W x
2
W y
2
1
|
x
| ≤
1
|
y
| ≤
B x ( x )
=
B y ( y )
=
W x
2
W y
2 ,
0
|
x
| ≥
0
|
y
| ≥
N is a total number of observation sites located inside the window and x o ,
y o is its
middle point (Fig. 11.20). The filter provides a fair smoothing of the geoelectric
noise on condition that lengths W x and W y are more than twice the autocorrelation
radius of local anomalies of apparent resistivities. To filter
A -curves, we repre-
sent MT-data as a set of apparent-resistivity maps for various periods. Each map is
smoothed using a sliding window (11.11). The apparent resistivities from smoothed
maps are synthesized, thereby yielding filtered
fl A -curves that reflect the regional
structures.
By way of example, we will show the filtration of the apparent-resistivity curves,
xy and
yx , obtained in southwest Jakutiya. High geoelectric noise caused by
permafrost lenses is observed in this province. Dimensions of lenses vary from
0.5-1 km to 10-20 km. The dimension W
W y of the sliding window
have been determined from an analysis of the normalized autocorrelation functions
of apparent resistivities calculated along several profiles crossing the region under
investigation. The autocorrelation function R(t) along the profile AB is demonstrated
in Fig. 11.21. It consists of a wide maximum related to local anomalies and a sub-
horizontal oscillating branch associated with regional structures. A radius of auto-
correlation of local anomalies has been taken to be equal to a distance t =42km,at
which R ( t ) = 0. Estimates for other profiles are about the same. Doubling the radius
of autocorrelation, we have constructed a filter with square window 84
=
W x
=
×
84 km.
Figure 11.22 presents the filtration of the
xy -resistivity map for T= 225 s. The
initial map exhibits a mosaic of apparent resistivities that veils the effects of regional
structures. Upon filtering we have got a smoothed map with fairly visible large-scale
structures - Botuobian elevation (maximum of
xy ) and Iggiattian depression (min-
imum of
xy ). The filtered apparent-resistivity curves are exemplified in Fig. 11.23.
Fig. 11.20 Rectangular
window for the
two-dimensional filtration
 
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