THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR

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21 L Regarding the ratio the thickness h has been reduced in cases 1 to 3 h assuming a constant L. Practically h is constant, and therefore the varia- tion of the current density can be simulated by an enlargement of the distance L between A and B. The following equivalent cases are the result of an enlargement of L. Case 1 in Fig.12 where L is equal to h, corresponds consequently to case 1' in Fig.15. In case 2 in Fig.13, L is twice of h corresponding to case 2' in Fig.12. Case 3 in Fig.14 where L is four times as large as h, corresponds to case 3' in Fig.12. Comparing the cases 1 to 3 with the cases 1' to 3' they obviously corre- L spond in the quotient . However there is no congruence. With respect to h the real current density we have to transform 1-3 into 1'-3' by a geomet- rical factor. This factor is just the constant K in the now already well- known formula (13) U ρ a = K def I At this point the reader will think that concerning the geometric factor K he would have found similar sentences before and that the authors have only repeated what they already have written. The reader is right. The role of K has been discussed in chapter 1.3. but under another aspect. Or is it the same aspect? The reader may decide by himself and then perhaps may get a deeper insight into the physical content of the two formulas homogeneous earth layered earth ρ = U K I ρ a = def U K I “true”-resistivity “apparent” resistivity
with just the same factor K. 22 After this we now return to our two-layer case discussed by aid of Fig.12- 15 and shall proceed to plot the result in a diagram. i.e. we want to con- struct a "sounding graph" ρa( L 2 ) as already mentioned at the end of chapter 1.4. Fig.16 L As is a quotient within the description of the zooming process, the h adequate measure would be a logarithmic scale. Normalizing the apparent resistivity to the resistivity ρ1 of the top layer we get another quotient ρa . Consequently this leds to a bi-logarithmic diagram. From the histori- ρ1 cal development instead of the distance L between the current electrodes L L / 2 the distance from the centre point is in use, i.e. . Taking as ab- 2 h scissa and ρa as ordinate the three data of the normalized apparent re- ρ1 sistivities for the cases 1’-3’ in Fig.15 will result in the three points plotted as open circles in Fig.16. Combining them to a curve we get an ascending ρa branch asymptotically starting at = 1 according to case 1 in Fig.12. ρ 1 Looking at Fig.14 we find, that the current is al ready flowing nearly par- allelly to the surface at the centre point. Reducing the thickness h again
Page 1 and 2: THE SMOOTH SOUNDING GRAPH A Manual
Page 3 and 4: Preface 2 This manual shall be a pr
Page 5 and 6: 1. Basic rules 4 The first chapter
Page 7 and 8: This current density is marked as j
Page 9 and 10: 8 Fig.2 Fig.3 Fig.4 Fig.5
Page 11 and 12: 10 1.3. The four-electrode arrangem
Page 13 and 14: 12 Fig.6 Fig.7 Fig.8
Page 15 and 16: 14 If we compare equations (10) and
Page 17 and 18: Case 2 (Fig. 10) 16 Now we observe
Page 19 and 20: 1.5. The fundamental principle for
Page 21: Case 3 (Fig.14) 20 The electrode di
Page 25 and 26: 24 Fig17 layers with different resi
Page 27 and 28: 26 Simulating this zooming by enlar
Page 29 and 30: 28 1.6. Shifting of potential elect
Page 31 and 32: 30 Fig.21 Fig.22 Fig23
Page 33 and 34: 32 2.1. How to carry out a field me
Page 35 and 36: L/2 a/2 1,5 6,28 2 11,8 2,5 18,9 34
Page 37 and 38: 36 Fig.27 Fig.28 Before we start th
Page 39 and 40: 38 fence, ditch) especially, if the
Page 41 and 42: 40 by experience. The measurement i
Page 43 and 44: 42 2.2. Possible errors influencing
Page 45 and 46: 2.2.4. Crossing a ditch (Fig.26/29)
Page 47 and 48: 46 accuracy is not so important the
Page 49 and 50: 2.2.8. Insulation and leakage curre
Page 51 and 52: 50 Fig.31. They are ascending with
Page 53 and 54: 52 If j' is negative, i.e. the dist

THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR

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