I) Resistivity. Literatur: Telford, Geldart und Sheriff (1990): Applied Geophysics, Second Edition, Cambridge University Press, NY.

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1 I) Resistivity Literatur: Telford, Geldart und Sheriff (1990): Applied Geophysics, Second Edition, Cambridge University Press, NY. Bender, F. (Hg.) (1985): Angewandte Geowissenschaften, Bd. II, Enke Verlag, Stuttgart.

2 Specific resistivity of rocks: most minerals form isolators (z.b. NaCl Ωm). given some amount of water the apparent resistivity changes dramatically. Sediments resistivity values: Ωm; granite and metamorphic rocks: Ωm The resistivity of rocks with no clay content can be expressed by Archie s law: ρ = AFρ w ; ρ specific resistivity; A amount of pore fluid; F formation factor (depends on the total volume of porosity) resistivity of pore fluid ρ w large bandwidth of resistivity values for different rocks (partially overlapping) without further geological knowledge no unique interpretation possible

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4 1) Basic physical relations In 1860 James Clerc Maxwell founded the complete theory of electromagnetic properties: D B H = roth = j + ; E = rote = ; B = divb = 0; t t D = divd = q; H magnetic field strength; B magnetic induction; E electric field strength; D electric displacement; j electric current density; q space charge density, = x + + y z Nablaoperator.

5 There are four additional important equations: D = εe; B = µh; ε electric permittivity; µ magnetic permeability current density equation: j = j( p) + σe σ tensor of conduction. in a charge free space, we can write: j = 0 = 2 U Laplace-equation U electric potential (Voltage)

6 common classification in geophysics: D B electro magnetic Waves: H = j + ; E = t t (VLF,Radiowaves) High frequency methods B Quasi-stationary: H = j; E = t (Slingram, MT, induced polarization) Low frequency methods stationary fields: H = j (resistivity methods,telluric) DC methods

7 DC - Methods We have to deal and solve following equations: j = σe = σ U ; j = 0 = 2 U ; with U electric potential (Voltage)

8 Ohm s Law: U Voltage, I current, R resistivity U = RI Rewriting the equation leads to: U = ρ l q -- I ρ -- l q specific resistivity ratio length to cross section of conductor Rewriting current density law: j = 1 --E ; ρ i.e. the tensor of specific resistivity is reciprocal to the tensor of conductivity

9 Assumption (often made): isotropic subsurface structure j 1 1 = --E = -- U ; ρ scalar ρ ρ Question: Which quantities we are able to measure? current and voltage differences!

10 Buried source in homogeneous full space: lines of current (j) equipotential lines (U=const) Q Exercise: How doe the current lines look like if we assume a homogenous half space? Hint: free surface conditions can be modelled by a mirror charge placed in the same distance in open space

11 Solving Laplace equation: 2 U d 2 U 2 = dr 2 + dv = 0 r dr ; (problem is radial symmetric); multiplying with r 2 and integrating the equation: dv A = ---- dr. r 2 repeated integration gives the solution: V = A -- + B r. What about A & B? V 0 when r B = 0 We can only measure current (not the density) directly. Therefore we must integrate over the surface of the complete equipotential shell in a distance of r: I = 4πr 2 j.

12 The equation for the current is then: I 4πr 2 j σ4πr 2 du = = = 4πσA dr Now we can estimate the constant A as: A = Iρ π Substitution gives desired equation for specific resistivity: 4πrU ρ = I In case of half space and electrode at the surface we have to divide the latter equation by a factor of 2: 2πrU ρ = ; I

13 In the more realistic case of two electrodes at the surface, we can apply the principle of superposition: U 1 + U 2 = Iρ π r r 2 ; the negative sign represents a source and a sink In real world problems often the voltage difference is measured. Then the equation can be rewritten to: Iρ U = π r3 this is the fundamental equation for DC - resistivity measurements r 1 r 2 r 4

14 I C1 P1 U P2 C2 r1 r2 r3 r4 Using specific electrode configuration the latter equation can be much more simplified (Schlumberger, Wenner, Dipol-Dipol etc.): ρ s = k U I with k geometry factor (depending on the configuration used)

15 2) Known Problems: a) Anisotropy: Microanisotropiefactor is defined as: ρ t ρ l θ transversal resistivity; longitudinal resistivity ρ t = ---- = ρ l σ l ---- > 1 σ t ; Mean value of resistivity is defined as: ρ = ρ t ρ l. Effect of micro anisotropy wrong layer thickness!

16 . ρ t H ρ s = ρ θh ρ l Anisotropy is one of the main sources of errors in DC-resistivity measurements! Without a prior knowledge no distinction possible!

17 b) Non-uniqueness Problem Same data can be modelled equally well with different model parameters.

18 c) Thin layers thin layers in greater depth are often missed. In order to judge whether this happens we can define a relative thickness measure: H layer thickness; h depth of layer. H --- = m h To recognize a layer the following relation must be fulfilled: m > 1 d) Topography/surface conditions/3d effects resistivity measurements are strongly influenced by surface conditions (weathering; water content etc.) topography has a similar effect; valleys - current is focussed; ridges - current is dispersed. Important for slopes > 10 strong variations of apparent resistivity for short electrode spacings indicate surface/ topography problems

19 3D bodies can show up with wrong parameters when modelled by 2D or even 1D models:

20 3) Common electrode configurations and sensitivity

21 Choosing the best configuration for your problem: sensitivity in vertical and horizontal direction desired penetration depth horizontal data coverage signal strength

22 i) Wenner sensitive for changes in vertical - insensitive for changes in horizontal direction high signal strength depth resolution is in between other configurations; ii) Schlumberger (-Wenner) increased horizontal resolution (ref. Wenner) increased vertical resolution (10% ref. Wenner) decreased signal strength increased data coverage iii) Dipol-Dipol widely used configuration (minor EM coupling) high horizontal sensitivity; low vertical sensitivity low depth resolution; low signal strength; best method to map lateral structures

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25 Up to date array measurements: DC - AC?.

26 4) Measurement and Interpretation 1D experiment ~ measurements/profile 2D experiment ~ measurements/profile costs! a) 1D Sounding computing the apparent specific resistivity vs. the half profile length on a double logarithmic scale; in order to estimate the number of layers and layer parameters you can choose between different possibilities: i) computing sounding curves with predefined simple models using simple software (2-4 layers) ii) computing the optimal model graph by comparing with master graphs iii) estimating the optimum model graph with starting models from i) & ii)

27 Aufgabe 2: Bestimmen Sie die scheinbaren spezifischen Widerstände aus folgender Widerstandssondierung; Tragen Sie dies auf doppellogarithmischen Papier auf ( ρ s l gegen -- ). 2 Was kann über die Anzahl der Schichten und deren relatives Widerstandsverhältnis ausgesagt werden? Bestimmen Sie die Schichtmächtigkeit und den scheinbaren spezifischen Widerstand der ersten Schicht.

28 b) 2D Sounding closer to reality; all varia- Variations possible in vertical and horizontal direction tion perpendicular to the profile are neglected good compromise between model error and experiment costs. DC-array measurements (>25 electrodes); results plotted as pseudo-section.

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31 NOTE: Pseudo-sections are not the result of the measurement but rather a first step in interpretation and data quality check. In order to get the true resistivity of the subsurface, we have to invert (!?) the data using computer software. ALSO NOTE: non-uniqueness of DC-measurements. Aufgabe: Erstellen Sie eine Pseudosektion aus folgenden Messdaten. Was lässt sich über den Untergrund aussagen?

32 II) Induced Polarization (IP) first mentioned by Conrad Schlumberger in further developed 1940s theoretical work in 1990s Used for ore exploration, ground water exploration and geothermal field mapping. Principle. Switch off current Voltage over-voltage switch on current Time

33 1) Basics physical reasons only partially known. two mechanisms are known better: a) Electrode Polarization (Grain Polarization) Nernst Potential caused by local concentration differences of solution: U N = C 1 RT nf ln C2 ; R universal gas constant; T temperature in Kelvin; n valence; F Faraday s constant; solution concentrations. C 12,

34 Zeta-potential; adsorption of anions at veins and fissures of quartz or pegmatite - important for clay bodies

35 b) Electrolytic Polarization.

36 2) Measurement of IP-Effect most commonly Dipol-Dipol configuration used measurement electrodes must be un-polarized electrodes

37 a) Time domain measurements U p Definition of Chargeability: = M U Definition of apparent Chargeability: 1 M a = U p () t dt = U 0 t 2 t A U 0

38 b) Frequency domain Percentage frequency effect: PFE = ( ρ s ( f 1 ) ρ s ( f 2 )) ρ( f 1 ) ρ s ( f 1 ) > ρ s ( f 2 ) mit ;. PFE Metal Factor: MF = i ; with i = 2 5; ρ s

39 3) Interpretation commonly the data or parameters (PFE,MF etc.) are plotted in pseudo sections. This is NOT the result of true subsurface structure! Inversion

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