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
11 to get as a contribution from electrode A to the voltage between M and N U ( A) MN = Iρ ⎛ ⎜ 2π ⎜ ⎝ As the arrangement is symmetrical we get the same contribution from electrode B. This results into U MN = U ( A) MN + U ( B) MN = L 2 1 − 2 U For the earth-resistivity ρ we then obtain or a 2 A MN − L 2 = 1 + a 2 ⎞ ⎟ ⎠ Iρ × π ( L 2 ) 2 a − ( a 2 ) 2 (7) 2 2 π ⎡⎛ L ⎞ ⎛ a ⎞ ⎤ U MN ρ = ⎢⎜ ⎟ − ⎜ ⎟ ⎥ (8) a ⎢⎣ ⎝ 2 ⎠ ⎝ 2 ⎠ ⎥⎦ I U ρ = K , I K = 2 2 π ⎡⎛ L ⎞ ⎛ a ⎞ ⎤ ⎢⎜ ⎟ − ⎜ ⎟ ⎥ a ⎢⎣ ⎝ 2 ⎠ ⎝ 2 ⎠ ⎥⎦ i.e. the well-known formula used in calculating the resistivity ρ from the current I between A and B and the voltage U between M and N. K is called "factor of configuration" or "geometric factor". Its dimension is [m]. We now have to study the function of this factor K. As a homogeneous underground is concerned ρ be a constant. Working with a constant cur- rent I - this is technically no problem because I depends after equation (8) only on the quality of grounding the current electrodes A and B (con- tact resistance) and not on their distance - the voltage U decreases by enlarging L. This decrease is compensated by an increasing K. The regu- lating function of K now shall be discussed regarding both electrode con- figurations used nowadays in practical field work.
12 Fig.6 Fig.7 Fig.8
- 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: 10 1.3. The four-electrode arrangem
- 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 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
12<br />
Fig.6<br />
Fig.7<br />
Fig.8
Change language