Electrical Resistivity of Soil

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This paper is a learning tool addressing soil resistivity consisting of an introduction to electrical resistivity, a brief history, the fundamentals of soil resistivity, data graphing, interpretation, and results. The paper then addresses the basics, building and operation of a soil resistivity meter, graphing and interpreting the data collected.


Electrical Resistivity of SoilSoil Resistivity Fundamentals and the Soil Resistivity MeterBy Rex A. Crouch

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Copyrighted by Rex A. Crouch, 2008 Page 2 of 20

Electrical Resistivity of Soil Soil Resistivity Fundamentals and the Soil Resistivity Meter By Rex A. Crouch

Abstract This paper is a learning tool addressing soil resistivity consisting of an introduction to electrical resistivity, a brief history, the fundamentals of soil resistivity, data graphing, interpretation, and results. The paper then addresses the basics, building and operation of a soil resistivity meter, graphing and interpreting the data collected.

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Introduction. Electrical resistivity of soil may be made with low frequency alternating current in which the current is applied at two locations, and the potential difference is measured between two points where the term potential difference, as used in physics, means voltage difference. Along this same method, a direct current may be applied in lieu of an alternating current thus causing an induced polarization in subsurface features wherein, the operator times how long the potential difference lasts after the current is removed for the purpose of identifying large subsurface conductors. These aforementioned means are considered active as the operator is inducing a current into the ground for the purpose of measuring a potential difference. Passive means would be the measurement of self-potential which is sometimes called spontaneous potential. This occurs as a sulfide breaks down into a sulfate. This is an indicator of an ore body that may be residing in a moist environment. Brief History. Electrical resistivity means of prospecting is documented in the 1830s through experiments conducted by Robert W. Fox, an English geologist, and natural philosopher. Fox concentrated his experiments on sulfide ore deposits near Cornwall, England. Foxs techniques were passive in approach. Not until the 1920s did the approach become active wherein Schlumberger, located in France, and Wenner, located in United States, began applying current into the ground, and measuring the potential difference. Wenner was the forerunner in this

technique. While a multitude of other approaches have been applied with Rooney and Gish presenting strong techniques, Hummel with impressive theoretical techniques, the Schlumberger and Wenner methods, which will be addressed in detail, prevailed as the most effective, and accurate techniques in active electrical resistivity measurement. All original techniques assumed a single uniform overburden with a second layer being of indefinite thickness. One initial shortfall was equipment. The equipment shortfall did not entail enough current for deep penetration nor were the meters accurate enough to distinguish between multiple layers; with an increase in current and accuracy, new formulas and methods of calculation were developed which created a more inclusive picture of the subsurface features [1] and [4]. This paper will focus on the Schlumberger and Wenner methods.

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Basic Formulas. There are four basic formulas employed when discussing electrical resistivity and these are current, current density, Ohms law, and resistivity [1]. Current is determined by charge in columbs over a given period of time in seconds where current is represented as I, columbs in q, and time as t.I q t



Ohms law is the relation of voltage, resistance, and current. This was first presented by the German physicist Georg S. Ohm. In this formula the term V represents voltage and R represents resistance.I V R

Current density is the amount of current flowing through a particular area in which the current density is represented by a j, and the area is represented by an A.

Resistivity is the relation of resistance, area, and current and is written as:R A I

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Generalizing the Concept. Figure 1 represents a generalized configuration of a soil resistivity measurement

figure 1 In this configuration we see that the current measurement is taken through the voltage source where the positive end is considered the source, and the negative end is considered the sink. For convenience, we label these C1 and C2. The voltage measurement is represented by P1 and P2, and in both cases it does not matter which is labeled 1 or 2. The distances r1, r2, r3, r4 represent the distances between posts. The curved lines running through the ground from C1 to C2 represent how the current may flow through a homogeneous soil. Using the below formula we can solve for the resistivity [1].

2 I

V 1 r1 1 r2

1 1 r3 1 r4

This is also known as the apparent resistivity.


V I 1 r1 1 r2

1 1 r3 1 r4

The apparent resistivity is a sampling of one location. Multiple samplings will help to discern variation in

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resistivity, and subsequently variations in the subsurface features. In terms of homogeneous space, the electric current is applied to the medium creating an electrical field. Within this field there are various potential differences between all of the possible points that may be

chosen. The character of the electrical field depends on the properties of the space that the current is passing through. A strong electrical field will occur in moist silt whereas a weak field will occur in dry gravel. In either case, a homogeneous space is the easiest to work with or model [4].

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Current in Multiple Layers. As current is applied to the ground, it will always attempt to follow the path of least resistance or the path of lowest resistivity In figure 2 below, rho 1 has a lower resistivity than rho 2, and the majority of the current passes through the rho 1, 1 2.

You can easily imagine taking your voltage probes as represented in figure 1, and placing them in figure 2, you would have a high voltage measurement as most of your current is passing through the area you are measuring. Conversely, if you were to place your voltage probes as represented in figure 1 into figure 3, you would have a low voltage measurement because the majority of the current is passing through a lower layer with lower resistivity. This is the foundation for a horizontal interface in electrical resistivity. The next step is to apply this information to the two most common approaches of resistivity measurements

figure 2 In figure 3 below, rho 1 has a higher resistivity then rho 2 and the majority of the current passes through the rho 2, 1 2.

figure 3

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Basics of Conducting Soil Resistivity Surveys. As previously mentioned, the Schlumberger and Wenner methods are the two most commonly used, and accepted methods of conducting soil resistivity surveys. Both the Schlumberger and Wenner use the same configuration as seen in figure 1. In this respect, each are similar yet use distinct approaches with their individual pros and cons. Wenner. The Wenner method is the most simple to apply. The spacing of the probes are maintained the same throughout the survey. You may begin with a separation of 1 meter between each of the probes, then increase it to 5 meters between each of the probes, then 10 meters. The distance is not so much important, it is the fact that the spacing between each of the probes is exactly the same. As resistivity graphing is done in a log log plot, it may be best to make the spacing 1.0, 1.47, 2.15, 3.16. 4.64, 6.81, and 10.0 meters and increase this distance in decades. The drawback to using the Wenner method is that you must move P1, P2, and C2 after every measurement and remember to turn the power off prior to moving the posts. Figure 4 below depicts a standard Wenner configuration maintaining the same spacing between post.

figure 4 Schlumberger. The Schlumberger method takes more thought upfront because the spacing between the post must maintain the relationship of 2L > 5M. In this configuration the C1 and C2 posts remain stationary during the survey and the P1 and P2 posts traverse between C1 and C2 but maintain the same separation from each other. This is to say that during the first traverse P1 and P2 will remain 1 meter apart. Then the distance between C1 and C2 is increased and then you may increase the distance between P1 and P2 to 1.47 meters, and conduct the traverse again. The Schlumberger method is faster in that you have to move all of the post fewer times. Figure 5 below depicts how the Schlumberger configuration may appear.

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figure 5 An additional consideration is that the Schlumberger configuration does not require that you remain on a straight traverse line but have the freedom to move your P1 and P2 to the left and right of the traverse as demonstrated in the below map view as derived by Roman [4].

figure 6 Applying some entirely fictional data to log log graph for the purposes of understanding, we can develop something to interpret. In the following table, measurements were taken:Measurement 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Ohms 4 3.8 3.6 3.4 3.2 3.2 3.2 3 3 2.8 5.8 6.4 6.6 6.6 6.6 5.8 4.2 3.8 3.2 3.2 3.2 3.2 3.2 3.2 3.2


map view 1. Graphing and Interpreting. Graphing the information is done on a log log plot, and if done in the aforementioned increments will be easy to plot on the paper. Figure 6 below depicts such a graph.

Table 1. Applying this data to the same graph we can develop this image:

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Department of Transportation, [2] but by no means is comprehensive as all materials changes in Ohm meters based on a variety of factors using silt, Ohms meters as an example, it changes based on water content as well as sand percentage as well as other minerals present, but the below mine water mentioned will change based on the pH level of the water. figure 7 Without applying any formulas we can conduct some simple deductions from this. The first part of the graph decreases in resistivity over the first ten measurements and then abruptly stops. The next data point jumped to 5.8 Ohms, and climbed slightly leveling for a brief moment and then dropped dramatically to 3.2 Ohms where it levels out. We can easily envision a gentle decline in resistivity layer and then something of much higher resistivity intrudes and levels off for several measurement locations before dropping back, even more sharply back to resistance similar to left hand side of the graph. We can guess that there was undoubtedly an intrusion of some kind. While modern soil resistivity meters will take the guess work out of this, this can also be interpreted as four contact layers which is not much different than what was described above. Of course this data is fictional but real materials have real resistivity measured in Ohms meters There are multiple tables to assist you in determining what material you may be working with. The following information was derived from the U.S. Page 11 of 20Material Clay and marl Loam Top soil Clayey soils Sandy soils Typical mine water Typical surface water Shale Limestones Sandstones Coal Ohm Meters 1 to 100 5 to 50 50 to 100 100 to 500 500 to 5000 1 to 10 5 to 50 10 to 80 80 to 1000 50 to 8000 500 to 5000

Table 2. The below figure was developed on concepts presented in the Interpretation of Resistivity Data [3]. In an apparent resistivity survey, the image depicts a contrast between low resistivity clay, and higher resistivity limestone, as well as presenting the scenario of a cavern or cave in which resistance would approach infinity during measurements an as there is nothing to conduct the current in an apparent resistivity profile.

multi-meters are employed to monitor amperage, and voltage. For conducting induced polarization the inverter is removed from the system and the 12 volt source is use to apply the current. Below is a block diagram of my system:

figure 8. Summarizing the Theory. Thus far this paper has examined the history and concepts of soil resistivity, detection of multiple layers, and introduced the fundamental formulas employed. The basic survey with the Wenner and Schlumberger methods were discussed, and graphing, and interpretation were also presented. The next step is to build and use a soil resistivity meter to see all of the theory come together. Building a Soil Resistivity Meter. Soil resistivity meters are actually very simple to build. I designed my resistivity meter for portability as well as functionality. Most professional systems only use AC. I wanted to have the same performance as a commercial unit which required the use of AC but I also wanted to use straight DC for the purpose of creating induced polarization in conductive ore bodies. My system uses a 12 volt deep cycle marine battery which runs into a DC/AC off-the-shelf inverter providing a clean AC. Clean is meant to mean that there is little to no noise on the 60 Hz waveform unlike the 60 Hz that comes from a wall outlet in which there are spikes, and even low points (brown outs). Two highly sensitive

figure 9. I mounted the entire system is an allterrain cart for easy movement. As professional systems report findings in Ohms meter, a homemade system would report in Amperage and Voltage with the distance between probes being measured by myself, or the user. To compensate for this break in technology from the commercial to the homemade system, I wrote a MATLAB application for use specifically in the Wenner configuration. The application allowed me to handwrite the data, then enter the data into an Excel spreadsheet which I named resistivity, and saved in my default MATLAB folder. When the MATLAB application is ran, regardless of how long or short the data is or the spacing between the posts, the application will import the data set, and graph the data in a log log plot. Below is my MATLAB script:

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% Written by Rex A. Crouch % racrouch@mtu.edu % For: Special Topics in Geophysics - GE 4933 - 01 % Soil Resistivity Graphing % This script accompanies a soil resistivity meter I built % For simple one layer models using AC equidistant probe spacing % This script Does the following: %* Opens an Excel file named "resistivity" %* The scripts conducts a P calculation at each increment in the file %* Saves the data to a blank array "B" which is the same size as the data %* Plots the data saved in "B" as a loglog plot %* Produces an array named "B" that may be used to imagesc diagrams %================================ clear % Clearing all variables clf % Clearing any figure or graphs A=xlsread('resistivity.xls'); % Load the Resisitivy Excel file distance=(A(:,1)); % Establishing the distance variable voltage=(A(:,2)); % Establishing the voltage variable current=(A(:,3)); % Establishing the current variable B=zeros(size(distance)); % Creating a column the same size as the imported vector %'for loop' increments through the data index by index for i=1:size(B); p=2*3.14*distance.*(voltage./current);...


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