electrical resistivity of soil

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Electrical Resistivity of Soil- Soil Resistivity Fundamentals and the Soil Resistivity Meter

By Rex A. Crouch

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Copyrighted © by Rex A. Crouch, 2008

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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. Fox’s 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, Ohm’s 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.

t

qI

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.

A

Ij

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.

R

VI

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

I

AR

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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].

4

1

3

1

2

1

1

1

12

rrrr

I

V

This is also known as the apparent resistivity.

4

1

3

1

2

1

1

1

12

rrrr

I

VA

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, 21 .

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, 21 .

figure 3

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

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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].

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.

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, 25 measurements were taken:

Measurement Ohms

1 4

2 3.8

3 3.6

4 3.4

5 3.2

6 3.2

7 3.2

8 3

9 3

10 2.8

11 5.8

12 6.4

13 6.6

14 6.6

15 6.6

16 5.8

17 4.2

18 3.8

19 3.2

20 3.2

21 3.2

22 3.2

23 3.2

24 3.2

25 3.2

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

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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.

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.

Material

Ohm Meters

Clay and marl 1 to 100

Loam 5 to 50

Top soil 50 to 100

Clayey soils 100 to 500

Sandy soils 500 to 5000

Typical mine water 1 to 10

Typical surface water 5 to 50

Shale 10 to 80

Limestones 80 to 1000

Sandstones 50 to 8000

Coal 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.

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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

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 9. I mounted the entire system is an all-terrain 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 % [email protected] % 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); B=p; end m=max(distance); % Finding the max distance in the array z=max(p); % Finding the max resistance in the array % Establishing Axis bounds on the graph to % the max distance and resistivity + 10% overage axis ([0 m 0 z+(z*.1)]) loglog(B) % plotting the data as loglog % Graph Titles and Labels title('Soil Resistivity Reading') ylabel('Resistivity Scale (Ohm/Meters)') xlabel('Electrode Separation (Meters)') text(10^.2,10^2.3,'Area Name') text(10^.2,10^2.14,'GPS DATA') B % Display the array for saving % End of script Script 1

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My first test-run of the my soil resistivity meter was conducted adjacent to the road that parallels the Quincy Mine, next to the Quincy fire station (above Hancock, MI along state road 41). I have previous inspected this area from underground through one of the civil war era drifts in the Quincy Mine, and the area, although copper rich, had not been fully stoped. In conducting a passive survey from the surface using the Geonics EM 16, I also confirmed a very strong conductive ore body. Subsequently, I knew the dip angle of the stratigraphic layers was about 45 degrees and that there was in fact a significant conductive ore body at my test-run survey site. Using the Wenner method, I began with a 1.5 meter separation in the posts and increased in increments of 1.5 meters until I had reached 15 meter, roughly 50 foot, separations in each of the posts. At this point I knew I had passed the ore body in question but the raw data on a piece of paper made little sense so returned to my computer to enter the data, and produced a log log graph. The below image is of me taking measurements at the first test-run site.

image 1. The below graph is from my very first test-run of the resistivity meter at the mentioned location.

graph 1. Graph 1 is produced by my MATLAB script, the blue line represents the raw data where the resistivity continued to climb and then dropped sharply leveling out to a constant low and then begin to climb again. The green line was a function I applied to data to show a curve while maintaining the form of the data. This is what I was expecting to see. The graph indicated that we went through several different contact layers to include an area that could be considered highly conductive. With data from the USGS, the known layers are an overburden, footwall, Pewabic lode, and a hanging wall [5] were all well known here, thus my first application was confirmed. My next application of the soil resistivity meter was along the Green Stone ridge on Cliff Drive on the south side of the North America Mine. Because I was running near perpendicular to the strike I was

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expecting to see dike like features. Also, the terrain was very rugged. For these two reasons I chose to use the Schlumberger method. My traverse line was N40W running 150 meters. The first anomaly was the current reading. The current rapidly fluctuated between 1.1 mA to 2.3 mA. I reviewed multiple articles on current but found nothing that immediately explained why it fluctuated. I also contacted several leaders in -soil resistivity meter- manufacturing and asked how their professional systems reconciled this problem. I received no responses, and worked on my own conclusions. Considering the terrain and the fact that a stream was at the top of the ridge but disappeared into a hole—left me to believe that this fluctuation may represent a pulsating flow of an underground stream. Considering that, I assumed a mean current of 1.7 mA for all calculations. The data depicted what I would interpret as possibly six contacts with strong variation in the conductivity of the various layers.

graph 2 To confirm the data, I ran a second traverse line still N40W, 18 meters S50W away from the first traverse line and found that the two major features in the middle of the graph were still

present and plunging in the direction of the dipping stratigraphic layers. My second test run was over a known area of geologic stratigraphy, and the results, other than the fluctuating current, were somewhat as expected when applying a best fit curve which removed many jumps in data, but without the best fit curve the data was otherwise complicated as depicted above. The running of a second traverse to confirm data from the first traverse has inspired the thought of creating a contouring script for visualizing an entire area. Choosing the site was the first consideration. I wanted a flat area to work with this time; an area without boulders, falling rocks, trees, bushes, needles, and growling noises that came from the cave like cavities in between the rocks. I also wanted to develop some knowledge about the area before working on it. The MTU football field is probably the largest and flattest area around Houghton, Michigan. Going to the Copper County Archives, I researched mapping of the area and found a bedrock mapping of the area as well as a soil resistivity mapping of the area in preparation for construction of the Student Development Center (SDC). The soil resistivity mapping was based on various gray scale shading, and had lost is shading, and was of no use but the bedrock mapping was still usable. As no development was going to take place on the football field, this area was not mapped but the contour lines stopping at the edge of the football field could be used to help confirm my data. As many items in the archives cannot be photographed or photocopied I redrew the map by hand

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retaining it to scale to the best of my ability. Below is my redrawing of the area in question.

figure 10 I conducted the survey over the football field behind the STC on 9 Jun 2007. The first observation that was made was the topography. The northeast side of the football field had been built-up about 4 meters to make the field level. There were probably some sections of fill-in as well. Because of this, I do not expect the data from the northeast side of the field to be truly representative of nature. I ran six traverse lines 30 meters apart to include the entire field. There were four measurements taken using the Wenner method on each traverse line beginning with a 10 meter separation and increasing in increments of 10 meters.

Below is a picture which represents how my system was setup:

image 2. My cart, behind me in the photo, contained most of the equipment used in the survey:

image 3. The data was collected, and ran through the script I presented earlier. This provided the log log plots for each traverse, and Ohms per meter data for each traverse line. I used this data to create a matrix of resistivity data that covers the entire field. This included the area that had been built-up in the northeast side of the field. I then wrote another short script to take the matrix, and create a contour map of resistivity measurements.

MTU FOOTBALL

FIELD

Bedrock Survey compiled by W. John and J Ringler Date: unknown (assumed to be before construction of MTU SDC. On file at the Copper Country Achieves, MTU, Drawer 48,c. Redrawn by R.A. Crouch

25 May 2007

N

100

120

140

160

140

120

80

80

80

140

140

160

180

120

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Below is the script used for creating my subsurface contour map:

% Written by Rex A. Crouch % [email protected] % For: Special Topics in Geophysics - GE 4933 - 01 % Soil Resistivity Graphing % This script accompanies a soil resistivity meter I built % For creating a contour of resistivity based on previous input % This script Does the following saves the data from the resistivity matrix % as "A" and then conducts a contour map of the resistivity %================================ A= [1.1053 0.2512 0.3391 0.0816 0.2449 0.0942 0.7285 2.1352 0.6908 1.884 0.9546 1.6077 1.9028 0.5652 0.2638 1.7898 3.8245 1.055 2.4366 0.1256 1.4821 0.1005 2.0598 1.1555] %Ohms per meter 1X10^7 C=contourf(A,10); colorbar caxis([-20 20]) % Graph Titles and Labels title('Soil Resistivity Reading') % End of script Script 2

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The contour plot was then taken and placed over the football field. The northeast section of the football field that was built-up does not really correlate to the bedrock diagram on the northeast edge. Mindful that this is two different types of data-the bedrock data and the resistivity data. Despite this difference in data types, correlations can still be drawn.

figure 11 Looking further southwest we see lower resistivity values approaching yellow in color which more closely correspond to the tight contour lines of the bedrock topography. If you were to remove this built-up overburden in the northeast of the football field you could envision the contour lines finding a common ground. Also, in the very south corner of the contour map

we see the imaging going to yellow again being the area of the field adjacent to a stream. The fill areas of the football field were probably the darkest green. Summary. I found that the Wenner method was the easiest to employ with a self built 4 lead system because it gave the most control, and ease in calculations, but I can see that the Schlumberger method would be the most effective with a multi-lead self calculating system. I am still not entirely sure how to treat/interpret an area that may have rapidly flowing underground water sources, and can see this as being a study in of itself. Setting this topic aside, and addressing resistivity surveys in general, I have to note that they are an effective way of visualizing the subsurface, and identifying various layers with minimal cost associated with the equipment however, the employment of the four lead system, particularly while working alone, is a time intensive task. Despite this drawback I will continue to use the system because it is effective. I highly recommend any student interested in geophysics to build their own equipment whenever possible as it brings you closers to understanding the system you are studying. The theory of geophysics is fine, but the actual applied geophysics is a hands-on adventure.

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Works Cited. [1] Burger, Sheehan, and Jones, eds. 1992. Introduction to Applied Geophysics: Exploring the Shallow Subsurface. New York: W.W. Norton & Company Inc [2] Johnson and Monroeville, eds. 2005. Geophysical Technologies for Detecting Underground Coal Mine Voids: Applications of the Electrical Resistivity Method for Detection of Underground Mine Workings. U.S. Department of Transportation [3] Nostrand and Cook, eds. 1966. Interpretation of Resistivity Data: Geological Survey Professional Paper 499. U.S. Department of the Interior. 224. [4] Roman, eds. 1960. Apparent Resistivity of a Single Uniform Overburden: Geological Survey Professional Paper 365. U.S. Department of the Interior.

[5] Pewabic Amygdaloid Lodes, USGS Professional Paper 144 p 178-181

Figure 1. Basic configuration of soil resistivity system derived from [1], illustrated by R.A. Crouch April 2007 Figure 2. Example of layering when layer 1 has lower resistivity then layer 2 [1], illustrated by R.A. Crouch April 2007 Figure 3. Example of layering when layer 2 has lower resistivity then layer 1 [1], illustrated by R.A. Crouch April 2007 Figure 4. Example of Wenner Configuration derived from [1], illustrated by R.A. Crouch April 2007 Figure 5. Example of Schlumberger Configuration derived from [1]. illustrated by R.A. Crouch April 2007 Figure 6. Example of loglog graphing, illustrated by R.A. Crouch May 2007 Figure 7. Example of loglog graphing as used with fictional data, illustrated by R.A. Crouch May 2007 Figure 8. Example of resisitivty measurements over an area that includes high conductive clays, low conductive limestones, infinite resistance caverns derived from [3], illustrated by R.A. Crouch May 2007 Figure 9. Block diagram of a soil resistivity system, illustrated by R.A. Crouch May 2007

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Figure 10. Representation of the subsurface bedrock of the area adjacent to the MTU football field derived from the Copper Country Archives, map drawer 48c, compiled by W Johnson and J Ringler (undated), illustrated by R.A. Crouch May 2007 Figure 11. Representation of the subsurface bedrock of the area adjacent to the MTU football field derived from the Copper Country Archives, map drawer 48c, compiled by W Johnson and J Ringler (undated), illustrated by R.A. Crouch May 2007 with overlay of resistivity contour map. Table 1. Fictional data to develop a working example of plotting on log log graphs, in support of Figure 7. R.A. Crouch May 2007. Table 2. Table depicting resistance of some materials. Derived from [2]. Graph 1. Graph from data collected during initial test run of soil resistivity meter orthogonal to the strike along the road adjacent to the fire station next to Quincy Mine (Houghton Co, MI), R.A. Crouch May 2007. Graph 2. Graph from data collected during second test run of soil resistivity meter near base of Green Stone Ridge running parallel to the strike along Cliff Drive (Keweenaw Co, MI), R.A. Crouch May 2007. Image 1. R.A. Crouch collecting data during initial test run of system during the first quarter of May 2007. Image 2. R.A. Crouch collecting data during initial run on football field behind SDC during the second quarter of June 2007 Image 3. Resistivity system as used on football field behind SDC during the second quarter of June 2007 Script 1. R.A. Crouch, MATLAB script. Converting distance, amperage, and voltage into a log log plot. May 2007. Script 2. R.A. Crouch, MATLAB script. Matrix of resistivity into a contour plot. June 2007.

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