THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR
THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR
THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR
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21<br />
L<br />
Regarding the ratio the thickness h has been reduced in cases 1 to 3<br />
h<br />
assuming a constant L. Practically h is constant, and there<strong>for</strong>e the varia-<br />
tion of the current density can be simulated by an enlargement of the dis-<br />
tance L between A and B.<br />
The following equivalent cases are the result of an enlargement of L.<br />
Case 1 in Fig.12 where L is equal to h, corresponds consequently to case<br />
1' in Fig.15.<br />
In case 2 in Fig.13, L is twice of h corresponding to case 2' in Fig.12.<br />
Case 3 in Fig.14 where L is four times as large as h, corresponds to case<br />
3' in Fig.12.<br />
Comparing the cases 1 to 3 with the cases 1' to 3' they obviously corre-<br />
L<br />
spond in the quotient . However there is no congruence. With respect to<br />
h<br />
the real current density we have to trans<strong>for</strong>m 1-3 into 1'-3' by a geomet-<br />
rical factor. This factor is just the constant K in the now already well-<br />
known <strong>for</strong>mula (13)<br />
U<br />
ρ a = K<br />
def I<br />
At this point the reader will think that concerning the geometric factor K<br />
he would have found similar sentences be<strong>for</strong>e and that the authors have<br />
only repeated what they already have written. The reader is right. The<br />
role of K has been discussed in chapter 1.3. but under another aspect. Or<br />
is it the same aspect? The reader may decide by himself and then perhaps<br />
may get a deeper insight into the physical content of the<br />
two <strong>for</strong>mulas<br />
homogeneous earth layered earth<br />
ρ<br />
=<br />
U<br />
K<br />
I<br />
ρ<br />
a<br />
=<br />
def<br />
U<br />
K<br />
I<br />
“true”-resistivity “apparent” resistivity