gpgn303 dc methods

7/30/2019 Gpgn303 Dc Methods

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Course Notes (Fall 2011)

GPGN 303: Section 3

Introduction to Electrical Methods

Yaoguo Li

Department of Geophysics

Colorado School of Mines

(For class use only, do not distribute!)

Outline

Introduction Electrical conductivity Electrical current in conductive media Charge accumulation

Middle gradient mapping Apparent resistivity

Vertical electrical sounding Survey configuration interpretation

2D and 3D imaging Array and survey geometry Inversion

Induced polarization


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Conventional geophysical methods: Gravity Magnetics DC resistivity/Induced polarization Electromagnetic induction (EM) Ground penetrating radar (GPR) Seismic

Energy

Source

Measured

Data

Images

(surface / subsurface)

Interaction

between fields andmaterial properties

Altered fields to be

measured


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1. Introduction: Basic concept of electrical method

Inject direct current into conductive ground. Measure the voltage produced on the surface or in boreholes. Always involves four electrodes.

Different components of the model

Energy source: batteries or generator Field: electric field / electrical current Material property: electrical conductivity (resistivity) Interaction: conductivity changes the flow of

electrical current (*)

Altered field: different electrical field distribution Data: voltage measured on the surface or in the

boreholes.


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Conceptual model

Given the above configuration: One would measure higher voltages over a resistive

body and lower voltages over a more conductive

body (to be discussed soon).

The voltage senses the change in resistivity orconductivity.

Historical Development The first S.P. survey conducted in 1820 by Fox in

England.

S.P. over a massive sulfide body Schlumberger brothers in 1920s

1D sounding and borehole logging 1940s and 50s: multiple position & multiple offset

used in mineral exploration

1950: Induced Polarization (IP) for disseminatedsulfides


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Ohms Law: R = V/I Resistance = Voltage/Current Voltage is directly related to resistivity: Voltage

increases when resistance increases.

Electrical Conductivity

Cross-section area: A

Length: L

V

A

L

Electrical Conductivity and Resistivity

Rock conductivity: Ohms Law

Express in current density (j) in terms of electric field (E) andmaterial property (resistivity !).

Conductivity is the more fundamental quantity


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Factors affecting rock conductivities

Porosity Permeability (pore connectivity) Fluid saturation Electrical conductivity of the fluid


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(Ward, 1990)


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Anisotropy!

in general, electrical conductivity is really a tensor!! The conductivity values are different in different directions

Simple Example:

The conductivities in

longitudinal and transversedirections are different

2. Theoretical background: Current flow

across a boundary between two media

Tangential component

Normal component of 1E

! = conductivity (S/m), S="-1

" = resistivity ("*m)

j = current density (A/m2)

E = Electric field (V/m)

# = charge density (C/m2)

Q = charge (C)


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On a planar boundary: (all quantities in thetwo media are labelled with a subscript of 1and 2, respectively)

Integration along a rectangular loop,

Current density is continuous across the boundary(i.e., normal components are continuous)

Electrical field: tangential component is continuous,but normal component is discontinuous!

Summary

Current density does not change across the interface. The electric field is discontinuous across the interface. The only field generator of static electric field is electrical

charges

There must be accumulation of the electrical charges at theinterface.

This leads to the only conclusion:There must be charges accumulating on the interface!


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The questions are then:

What is the sign of the charge and how much is there? Lets approximate the charges locally as an infinite sheet

with surface charge density, , which produces an

electrical field normal to the interface.

The normal field is given by

Such that the total normal components are given by

Set:

Surface density of charges on the interface


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Summary of charge accumulation

Two cases:1. From conductive to resistive region

Positive charges accumulate

V

2. From resistive to conductive region

Negative charges accumulate

^


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How does the current flow?

Combining the two boundary conditions toderive the angle of current flow with respect

to the normal vector

i.e., current bends towards normal when

entering resistive medium, and away from

normal when entering conductve medium!

Case II:

Negative charge

pulls E in towards

interface

Case I:

Positive charge

pushes E away from

interface

V ^


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Case Charge Electrical current

Conductive to Bends towards

Resistive the normal

Resistive to Bends away

Conductive from the normal

Key Points:

charges accumulate and current flow

(Burger, 1992)


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Current flowing in and around conductivity anomalies

Current channels into

a conductor

Current flows arounda resistor

Arrowed lines are

current flow; dashedlines are supposed

to be equipotentiallines.

Background electrical field:1. Point current on surface of a uniform half-space.

Equivalent charges

at the source point:


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2. Buried point current source in a half-space

spreads out on the surface!

at the source location!

is the mirror point of

w.r.t. the sound surface

Mise-a-la-masse method

An illustration of the role of charge accumulation in

DC resistivity method


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1. Mise-a-la-masse method

Direct application of charge accumulationCharge an in-place conductive body, creating

charges on the surface of the body as current

flows outwards.

Measure the potential at the surface.Similar to gravity, except in this case you are

measuring potential.

Schematics of a mise-a-la-masse survey


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Conceptual summary of DC resistivity method

We inject electrical current into the ground (source andfield)

Electrical charges accumulate on the interfaces betweenregions with different electrical conductivity (physical

property and interaction with the input primary field).

Accumulated charges produce additional electric fieldthat is superimposed on the primary field (altered field).

We measure the resultant field (data), which carryinformation about the conductivity variation.

(Hattula and Rekola, 2000, Geophysics)

Mise--la-masse surveys:

delineated the extent of sulfides method for correlating drill holeore intersections

guide drilling during a deepexploration program.


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2. Middle Gradient Survey

Middle Gradient Survey

Inject current into the ground using a pair of widely separatedA &B electrode, so as to create nearly horizontal priamry field

in the middle.

As current passes through regions of varying conductivity,charges accumulate at the interfaces between regions with

different conductivities.

Measure the potential differences produced by theseaccumulated charges together with the primary potential.

Rely on the fact that the horizontal component of the primaryelectric field is nearly constant with the central 1/3 bewteen

the AB electrodes


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Set-up of Middle Gradient

Measures the horizontal variation in voltage. Use fixed electrode (A and B) positions at large separation. Move MN around inside AB (central 1/3) Originally: measurements only along the line passing AB Commonly: measurements over a grid MN electrodes are parallel to AB electrodes (important!)

A B

Primary Field in the direction paralle to AB

-1000 m 1000 m

Linear scale log scale


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Primary Field in X-direction: in the central area

Linear scale log scale

Middle gradient: over a conductive Body

Primary field

Total field


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Middle gradient: over a resistive Body

Primary field

Total field

Charge accumulation & anomalous potential Two parts of potential difference Primary Anomalous

The anomalous potential can be eitherconstructive ordestructive to the primary field, depending on location.

Over a conductive body: we measure a central lowwith two positive side lobes

Over a resistive body: we measure a central high withtwo negative side lobes


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Variation of Potential Difference

The current is closer to the surface near theelectrodes. Therefore, the potential is also larger near

the electrodes, but this is due simply to the geometry

of the survey (not ideal for interpretation)

V

X

Uniform half-space

Apparent Resistivity:

Lets define a quantity, apparent resistivity. It should:

Be constant over a uniform half-space (preferred) have the units of resistivity

X

Uniform half-space


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The apparent resistivity is the measured voltage scaled by thecurrent and by a geometrical factor (K).

The geometrical factor depends on the type of survey, basedon the electrode and voltmeter positions.

Generally:

Apparent Resistivity: Definition

A few comments about the apparent resistivity

It is a convenient quantity to work with for thefollowing two reasons:

It has the units of resistivity (!m) It is equal to the true value if we have a uniform halfspace

However, apparent resistivity is NOT the primarydata. Measured voltages are the primary data, which

are used by most modern inversion algorithms

In true 3D acquisition where the MN and ABelectrodes are not aligned in the same direction, we

may NOT be able to define an apparent resistivity,

because the geometric factor is undefined (infinite).


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Middle Gradient Array Over a Vertical Contact

A (-1000 m) A (+1000 m)

MN=20 m

Apparent resistivity mapfrom a middle gradient

Survey at the BallengerRanch, NM

Two surveys merged

AB1: (-20,60 ) (280,60) AB2: (-40,0) (260,0) MN= 10 m


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Utility of middle gradient surveys

Areal mapping to characterize the lateral variation ofsubsurface conductivity

Has little information about the vertical variation Often used:

to map elongated linear features such as a vein, an intrusivedyke, or a paleochannel

As a reconnaissance tool to locate targets for furtherinvestigation

Vertical electrical sounding (VES)


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VES (Vertical Electrical Sounding)

Used to detect the vertical variation of resistivity as afunction of depth.

Designed to work in 1D environment (layer cakedearth): Assumption!

Length AB increases sequentially For each AB separation, measure the potential using a

small MN separation

Schlumberger sounding

Designed to work over 1D earth MN located in the center between A & B Measure electric field


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Schlumberger Sounding

When ,

Geometrical factor:

Consider a half-space with 2 layers of differing resistivity.Resistivity of top layer is and the bottom layer is .

At small AB, the current does not flow deep enough tosignificantly detect the deeper layer. Most current flows in thetop of the first layer.

The potential reflects the resistivity of the top layer. At large AB, most of the current flows in the deeper layer. The potential reflects the resistivity of the bottom layer.


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Summary of 2-layer half-space

Depth of investigation: on the same order as AB/2 For small AB (Lh): The apparent resistivity changes monotonically

between layers (it only increases or decreases).

h

h


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Plot the apparent resistivity data as a function of AB/2 on a log-log plot.

Depth of current penetration

AB determines the current distribution The current distribution determines the depth of

investigation.

Depth of investigation is proportional to ABseparation (not linearly, though!)

In order to have 50% of current flowing beneath agiven depth, the length AB must be twice that depth.

Nominally: the depth of investigation is half ABspacing


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Current density at depth h directionbelow th emiddle point between AB

Fraction of current above depth h

Depth of 50% current partition: h=AB/2

Current distribution in a uniform half-space

(Burger, 1992)

However, the current flowdepends strongly on electricalconductivity.

Less current goes to the depthwhen there is a more conductive

surface layer:smallerdepth of

investigation

More current goes to the depthwhen there is a more resistive

surface layer:greaterdepth of

investigation


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Practical implementation of

Schlumberger Sounding Select a set of AB separations that increases

logarithmically, so there are several values per decade

Keep the MN separation much smaller, so weeffectively measuring the horizontal electric field atthe mid-point between A and B..

To keep the measured #VMN well above noise, weincrease the MN separation for every half decade ofAB separations.

Two AB separations are repeated using two adjacentMN separations (see next slide for example).

Sample separations for

Schlumberger sounding


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Depth of investigation as a function of MN spacing

(in VES over 1D earth only)

For a given AB separation, an increase in MNseparation leads to decreased depth of investigation.

The reason: As M and N electrodes move apart, they each become

closer to the current electrode A or B

Correspondingly, the relative contribution to the measuredvoltage by deeper charges decrease, so the data are more

sensitive to shallower conductivity.

An end-member scenario: As MN separationapproaches AB separation, the depth of investigation

becomes zero.

Measurements with same AB

but different MN

Exapnding MN causes the curve to shift to the right!

-- decreasing depth of investigation


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3-Layer Cases

1. A:2. Q:3. K:

4. H:


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Wenner array beside a

dipping contact(parallel to contact)

1D Interpretation

Curve matching by manual approach (ancient): comparing measured curve with pre-calculated curves

to find a macthing one, thus the resistivities andthickness

Works for two- and three-layered cases Least-squares solution to find the resistivities and

thicknesses of a small number of layers.

Generalized nonlinear inversion to find a minimumstructure function of resistivity as a function of depth.


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Theoretically:

Uniqueness Theorem: Lange 1932 1D: perfect data for all AB offset and fixed MN Practically: Many similar solution exists because we have only

finite number of data with measurement errors.

Least-squares solution (parametric inversion): find theresistivities and thicknesses so as to minimize the data

misfit between observed and calculated apparentresistivities.

Parametric inversion for 1D parameters

We assume known number of layers, andparameterize the model by the resistivity and

thickness of each layer.

For example, a two-layered earth has threeparameters:

We can calculate the predicted apparent resistivityknowing the values of these variables and surveys

geometry:


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We solve a non-linear least squares problem to findthe values of that would have

produced the measured apparent resistivity data.

This is done by minimizing the following datamisfit function;

Because the forward modeling is non-linear, this issolved iteratively by starting from an initial guess

for

Equivalence:

one form of ambiguity Pertains to the cases when

A a thin resistive layer is sandwiched between moreconductive layers: K type:

Or: a thin conductive layer is sandwiched between resistivelayers: H type:

As long as the transverse resistance (K type) or thelongitudinal conductance (H type) remains the same,resistivity profiles with different middle layer thicknesswill produce the same apparent resistivity curve within

error tolerance.Transverse resistance

Longitudinal conductance


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Leyden Schlumberger Sounding

Four-layer interpretation

Leyden Schlumberger Sounding

Five-layer interpretation

This thin layer is clearly not required.


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2D and 3D Imaging (ERT)

2D imaging of subsurface

Multiple measurements at different surface locations withfixed array geometry: detects lateral variation of electricalconductivity

Multiple measurements at the same locations with expandingarray geometry: detects vertical variation of electricalconductivity

To detect the variation of conductivity horizontally andvertically in the surface, we require measurements at multiplelocations using expanding arrays (multiple electrode off-set)

Equivalently: multiple source locations and multiplemeasurements for each source location


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Traditional surveys conducted along lines(co-linear arrays)

Common survey geometriespole - polepole - dipole (PDR)pole - dipole (PDL)dipole dipoleWenner

2D acquisition: Co-linear survey geometry

I V

I

V I

V

I V

I

V

Apparent resistivity:

Organize data by TX-RX (current and potential)electrode locations

Plotting each datum (apparent resistivity directly belowthe mid-point of the array) at a pseudo-depth (array

separation)

Pseudo-sections: plotting raw data


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Example: Dipole-dipole pseudo-section

Pole-pole

Pole-dipole (R)

Pole-dipole (L)


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Pole-pole

Pole-dipole (R)

Pole-dipole (L)


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Comments on psudo-sections

Pseduo-section were developed as an easy way to organize andplot the data It has little to no correspondence to real geo-electrical sections

Recall: each datum is affected by the entire charge accumulationassociated with electrical conductivity variation in the subsurface

(volumetric effect)

Thus: CANNOTmake one-to-one correspondence between a givendatum and a point in the subsurface

Earlier interpretation using on pseudo-section was based onmatching anomaly patterns in the pseudo-section with known

conductivity anomalies in the subsurface

Can be effect when the subsurface is simple (such as a singleconductivity anomaly)

Difficult when multiple anomalies or geological noise is present

Example pseudo-sections: Illustration of Geological Noise

Resistivity model

Pseudo-section

Dipole-dipole; n=1,8; a=10mSimple scenario: clear anomaly pattern and interpretableMultiple bodies: overlapping anomalies dominated by effect of shallowconductivity variations

Ohm-m Resistivity model Ohm-m

Pseudo-section


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Comments on numerical modeling: 2D

There is no analytic solution for complicated 2D or 3D problem We utilize numerical solution of differential equation governing the

electrical potential in conductive media (refer to course on static field)

Finite difference or finite element methods Discretize a much larger region of earth than that of interest

Region of interest Entire discretized region

Interpretation of 2D DC resistivity data: Inversion

Similar to the 1D case, we resort to inversion to quantitatively interpret the measureddata by finding asimple conductivity distribution that could have produce the data

This is accomplished by requiring conductivity (referred to as model) to satisfy twocriteria:

It must reproduce the observed potential difference data to within the error tolerance(quantified by data misfit function, as in 1D)

It must be simple and geologically interpretable (quantified by a model objective function) Parameterize the conductivity by a piece-wise constant 2D function, such that the

number of cells is much greater than the number of data

Inversion finds the conductivity values in all cells

Mis the number

of unknown

conductivity

values


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Data misfit

Model objective function

N: number of data !i is the standard of error in ith datum

m=ln("): model used in inversion (log conductivity) m0is a reference model(we want the inverted model to be

close to it)

Inversion solution

Obtain the solution by Tikhonov regularization:

where is the regularization parameter determines the balance between the two parts

We look for an optimal balance between the two components so that we fit the signal in the data, but not the noise one simple condition: data misfit equal to it expectation

Solution obtained iteratively by starting with an initial guess


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A mystery example: DC resistivity inversion

dipole dipole

Pole dipole right

Pole dipole left

Pole pole

Apparent resistivity pseudo-sections Inverted resistivity sections

Inversions with different :

"-m

best model: m0 = 400 "m

m0 = 40 "m

m0 = 4000 "m


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Quantifying the Depth of Investigation

Invert data with two different reference models The regions that dont change very much are considered to be resolved

(investigated)

The regions that change a lot with reference model are not seen by data

Regions of investigation

Regions to which data

are insensitive

3D acquisition and imaging

Most readily (approach-I): co-linear arrays along multiple lines Line spacing should be shorter than the maximum depth of

investigation of the 2D arrays

More effectively (approach-II): True 3D acquisition with cross-line measurements Distributed data acquisition: measure potential data over a

portion of the 2D grid for each current-electrode location

Cross-line acquisition analogous to cross-holeacquisition


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Induced Polarization (IP) Methods

Phenomenological observation of induced polarization effect


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IP effect is characterized by a phase lag between the observed potential

and input current in the frequency domain

Definition of chargeability

Primary property characterizing the IP effect in a rock unit is thechargeability #: ratio of secondary potential over total potential

The secondary potential is a function of delay time, so is the chargeability

A similar quantity, apparent chargeability can be defined for fieldmeasurements using co-linear arrays

Intrinsic chargeability (measured on rock samples)

Commonly used as IP data,

but not always defined just as apparent resistivity


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Relationship between apparent chargeability and

intrinsic chargeabilities

Assume the subsurface is divided intoMsubregions (or cellsas in the DC inversion)

To the first order, apparent chargeabilities are the weightedsum of the intrinsic chargeabilities

The weighting factors in the equations are called IPsensitivities (see next slide)

This relationship also forms the basis for the most practical IPinversion used in interpretation.

Siegels (1959)

dilation equation


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Linear forward modeling of IP data: sensitivities

Plots of sensitivities with a chargeable block. Contributionfrom block$for#=0.1, is #a.I V I V

I VI V

At n=1, #a= 0.0608 At n=5, #a= -0.0897

At n=2, #a= 0.0358 At n=6, #a= -0.0103

Inversion of IP data

A two-stage process First, we invert the accompanying DC resistivity data to

recover the conductivity distribution

Second, we use that conductivity to invert IP data use the recovered conductivity to calcuate the sensitivities in Siegels

dilation equation

Invert the IP data (apparent chargeabilities) using a similar approach asin the DC resistivity inversion: finding a simple intrinsic chargeability

model that predicts the observed apparent chargeabilities.

We also impose the condition that the chargeability must be positive


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A mystery model - IP inversion results

dipole dipole

Pole dipole right

Pole dipole left

Pole pole

Apparent chargeability pseudo-sections Inverted chargeability sections

Apparent

conductivity data

mS/m

Apparent

chargeability data

mrad


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DC resistivity Example: McDermott deposit

Observed

data

Predicted

data

mS/m

mS/m

Recovered

model

mS/m

Overburden is delineated.

IP - McDermott deposit

Observed

data

mrad

Predicted

data

Recovered

model

mrad

Ore bodys depth and position are located.

gpgn303 dc methods

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