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

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5 where R is the resistance [Ohm] of the wire, U is the voltage [Volt] measured between the wire-ends when a current of an intensity I [Am- pere] flows through the wire. Fig.1 This means: the longer the wire, the greater the resistance, but the resistance decreases, when the cross-section is enlarged. The influence of the material of the wire (iron, copper) is expressed by a material constant ρ, i.e. the resistivity of the wire measured in [Ohm.m] or [Ωm]. This dimension can easily be proved from equation (1) in order to have equal dimensions on both sides. Now we have to change our mind from the wire to the half-space. Some difficulties arise, because the infinite half-space possesses neither a length nor a cross-section. We also do not know in which direction the current flows. Obviously this problem depends on the points of grounding the electrodes. Between which points the voltage U has to be recorded? We now shall reduce these difficulties step by step. Starting from formula (1) valid for the wire (Fig. 1) we try to remove the length a and the cross- section q from this formula, transforming it into U a = I ρ q (2) At the left side appears a voltage normalized to the unit length and ex- pressing the intensity E of the electric field. E has the dimension [Volt/m]. At the right side the quotient current/cross-section expresses nothing else then the density of the current within the wire.
This current density is marked as j measured in [Amp/m 2 ] E = 6 is a form of Ohm's law, valid at any point in the underground and not con- taining any boundaries. This so-called "infinitesimal" form is the fundamental formula to be used in the field of resistivity measurements. j ρ (3)
Page 1 and 2: THE SMOOTH SOUNDING GRAPH A Manual
Page 3 and 4: Preface 2 This manual shall be a pr
Page 5: 1. Basic rules 4 The first chapter
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 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

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

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