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
1.3.1. Wenner configuration (L=3a) 13 The proposal of Wenner was an equidistant electrode spacing AMNB with AM = MN = NB (see Fig.8). Substituting L=3a in equation (8) we get 2 2 π ⎡⎛ 3a ⎞ ⎛ a ⎞ ⎤ K = ⎢⎜ ⎟ − ⎜ ⎟ ⎥ = 2π a (9) a ⎢⎣ ⎝ 2 ⎠ ⎝ 2 ⎠ ⎥⎦ This formula is very handy. But for field work on a non-homogeneous earth, where the electrodes M and N have to be shifted (see chapter 4.6), there are many disadvantages which were observed by C. Schlumberger who first applied the method in practice. 1.3.2. Schlumberger configuration (a
14 If we compare equations (10) and (11) i.e. K = 2 ⎟ π ⎛ L ⎞ ⎜ a ⎝ ⎠ and replacing in the general formula (8) 2 ρ = U and = j ρ a U K I valid for the homogeneous underground the constant resistivity ρ, we get U 1 ⎛ L ⎞ U MN = ⎜ ⎟ a j a ⎝ 2 ⎠ I π 2 2 2 ⎟ ⎛ L ⎞ I = jπ ⎜ (12) ⎝ ⎠ From this equation we can see very clearly the regulating function of the geometric factor K: Enlarging the spacing L of the current electrodes on the surface of a homogeneous earth the same current intensity I will pro- duce a decreasing current density j between the potential electrodes M and N. This decrease is compensated by π(L/2) 2 that means in Schlum- berger configuration (a=const.) by K. The reader should study carefully these just described physical connections between ρ , U , a I, L, K and especially j , to get a real feeling for the process of running a direct current through a homogeneous earth. 1.4. The layered underground The aim is to analyse quantitatively a layered underground by aid of the four-electrode arrangement according to Schlumberger. Case 1 (Fig.9) We observe a two-layer-case and assume that an electrode spacing is very small compared with the depth of the first layer boundary. We are measuring according to the formula U ρ = K . Because the dis- I tance of the second layer is far enough, the course of current lines is hardly influenced. In this case we get approximately ρ ≈ ρ1.
- 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: 12 Fig.6 Fig.7 Fig.8
- Page 17 and 18: Case 2 (Fig. 10) 16 Now we observe
- Page 19 and 20: 1.5. The fundamental principle for
- Page 21 and 22: Case 3 (Fig.14) 20 The electrode di
- Page 23 and 24: with just the same factor K. 22 Aft
- 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
14<br />
If we compare equations (10) and (11) i.e.<br />
K<br />
=<br />
2 ⎟ π ⎛ L ⎞<br />
⎜<br />
a ⎝ ⎠<br />
and replacing in the general <strong>for</strong>mula (8)<br />
2<br />
ρ<br />
=<br />
U<br />
and = j ρ<br />
a<br />
U<br />
K<br />
I<br />
valid <strong>for</strong> the homogeneous underground the constant resistivity ρ, we get<br />
U 1 ⎛ L ⎞ U MN<br />
= ⎜ ⎟<br />
a j a ⎝ 2 ⎠ I<br />
π<br />
2<br />
2<br />
2 ⎟ ⎛ L ⎞<br />
I = jπ<br />
⎜<br />
(12)<br />
⎝ ⎠<br />
From this equation we can see very clearly the regulating function of the<br />
geometric factor K: Enlarging the spacing L of the current electrodes on<br />
the surface of a homogeneous earth the same current intensity I will pro-<br />
duce a decreasing current density j between the potential electrodes M<br />
and N. This decrease is compensated by π(L/2) 2 that means in Schlum-<br />
berger configuration (a=const.) by K.<br />
The reader should study carefully these just described physical connections<br />
between ρ , U ,<br />
a<br />
I,<br />
L,<br />
K and especially j , to get a real feeling<br />
<strong>for</strong> the process of running a direct current through a homogeneous earth.<br />
1.4. The layered underground<br />
The aim is to analyse quantitatively a layered underground by aid of the<br />
four-electrode arrangement according to Schlumberger.<br />
Case 1 (Fig.9)<br />
We observe a two-layer-case and assume that an electrode spacing is<br />
very small compared with the depth of the first layer boundary.<br />
We are measuring according to the <strong>for</strong>mula<br />
U<br />
ρ = K . Because the dis-<br />
I<br />
tance of the second layer is far enough, the course of current lines is<br />
hardly influenced. In this case we get approximately ρ ≈ ρ1.
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