 Welcome to this lecture 27. So, in this lecture, so we are continuing with the surface investigation of groundwater and specifically we are continuing with electrical resistivity method. So, then we will move on to seismic refraction method and followed by gravity method and lastly magnetic method. So, coming to this electrical resistivity method which we started in the previous lecture, the electrical resistivity, so this is the electrical resistivity it is denoted by the letter rho and this rho is given by R into A divided by L. So, here this R is the resistance, so this is the resistance which is measured in ohm. So, this is the notation for ohm and A is the area the cross sectional area, so this is measured in square meters and L is the distance, so the distance between opposite faces, so that is also measured in meters. So, this electrical resistivity, so it has a units of ohm meter and so this electrical resistivity it varies for different materials and so the factors influencing electrical resistivity material, density, porosity, water content, quality, temperature, pore, shape and size etc. So, the variation of generally this igneous and metamorphic rocks have, so this rho in the range of 10 to the power 2 to 10 to the power 8 it is ohm meter. On the other hand the sedimentary and unconsolidated rocks rho which is varying between 10 to the power 0 and 10 to the power 4 that is 1 that is ohm meters and so the in porous formations, so the water content influences significantly influences the electrical resistivity. So, the American society of civil engineers has given the representative variation ranges of electrical resistivity in one of its document published in 1972, so this is representative electrical resistivity variation ranges for various formations. So, in this case it is say the material and the electrical resistivity range, so this in ohm meter and here, so this starts with the scale starts with 10 to the power minus 1 and moves on to 10 to the power 1, 10 to the power 3, 10 to the power 5, then 10 to the power 7. So, in this case we have this clay whose electrical resistivity varies in the range of because it is a more or less symmetrical variation, so in the range of 10 to the power 0 to 10 to the power 1, so followed by this is a soft shell which is also quite fine grained like this one and in this case also the variation is somewhat similar like clay, only thing is in here it may show a larger variation on the lower side, then followed by hard shell in this case the it varies between 10 to the power 1 and 10 to the power 2 and which shows a skewness to the right, then the fourth one is the till or the tilled earth which shows skewness to the left, of course in case of hard clay, so it will show this is to say 10 to the power 2 and till which will show a variation which is skew to the left followed by sand and sand shows again a skew to the power that is skew which is skew to the left with the mode around 10 to the power 2 ohm meter, then followed by the sandstone, so this is the fifth one is sand, sixth one is sandstone, sandstone is even shows it is even higher electrical resistivity which is almost showing a symmetrical variation with the mode of the electrical resistivity lying between 10 to the power 2 and 10 to the power 3 followed by this porous limestone, so this porous limestone also it has the mode value of the electrical resistivity only thing is it is skew to the left, then lastly it is the dense limestone and this dense limestone shows a large variation in this case, so this variation it starts with say 10 to the power 3 and it continues even beyond 10 to the power 6, so this is how the variation of this electrical resistivity it is and as you can see this clay will have a very clay and soft shale will have a very high very small value of very low value of electrical resistivity. Now let us go to the electrical resistivity, in this case the electrical circuit for determining electrical field electrical resistivity in a homogeneous formation, so there are basically all the two current electrodes which are located far away in the same line as the potential electrodes, so in this case so this is the, so these are the potential electrodes, so this P implies a potential electrode and C implies a current electrode, it is a symmetrical formation in this case, so between the potential electrode, so there is a voltmeter and between the current electrodes, so there is a battery source and an emitter and here in this, so this is the, so this is C is the current electrode, in this case the current lines ellipses and the equipotential lines, let me show with a different colour and the equipotential lines are confocal hyperbola which are orthogonal to the current lines like this, so these are the equipotential lines, so these are in the form of confocal hyperbola and then these are the current lines, so these are the equipotential lines and these are the current lines, so these are equipotential, I am sorry this confocal ellipses, so this is the arrangement and in this case the, so what is measured is the apparent resistivity and this, so the electrodes now before going to that one, so the electrodes are metal stakes which are driven into the ground and sometimes this saturated solution, so potential electrodes porous cups with saturated copper solution and here, so this one there are actually two types of arrangement, so the two say two common arrangements for electrical resistivity for electrode spacing, one the Wiener arrangement the second one is the Schlumberger arrangement, so in the Wiener arrangement basically the potential electrodes are, now let us discuss about this Wiener arrangement in which the distance between the potential electrodes is one third the distance between the current electrodes, so there is a voltmeter between the potential electrode and the distance is A and the same distance on either side of the each of the potential electrodes along the same line, there are two current electrodes the left current electrode and the right current electrode, so there will be a battery source followed by a emitter to measure the current and this is the Wiener arrangement for electrode spacing, so the now let us discuss the Schlumberger arrangement, so the Schlumberger arrangement for electrode spacing for this electrical resistivity determination, so here the distance between the potential electrodes is somewhat less that is say B, if B is the distance between the potential electrodes there will be a voltmeter which connects the potential electrodes and then, so the current electrodes are far off of course it is again a symmetrical arrangement, so these are the current electrodes and there will be a battery source followed by this emitter to measure the current and in this case the distance between the current electrodes is taken as capital L and it gives better results, so it is said that, so gives better results when L is greater than 5 B greater than or equal to 5 B, so this is the second common arrangement for the electrodes and now let us discuss about the interpretation of the results, so the solution can be interpreted in two parts rather solution can be obtained in two parts, so in the first part that is the interpretation in terms of various layers of actual resistivities and their depths and in the second part it is the interpretation of actual resistivities in terms of subsurface geological and ground water formations, ground water conditions or formations and here one thing I need to mention here say in case of the vener arrangement this there is what is called the apparent resistivity apparent electrical resistivity in vener arrangement, so is given by, so this is rho A, so this rho A is 2 pi into A into V by I, so V is the voltmeter reading or the potential difference and I is the current, so this is the potential difference and I is the current, so the same apparent resistivity in Schlumberger, so this rho A in Schlumberger arrangement, Schlumberger arrangement, so this rho A is given by pi into L by 2 square minus B by 2 square divided by B into V by I where has shown L is the distance between the current electrodes, B is the distance between the potential electrodes, so this is the expression for the apparent resistivity in case of Schlumberger arrangement. And now let us go for say the interpretation of a 2 layer electrical resistivity measurement from Schlumberger arrangement, so this is taken from the source Zodie et al, Zodie et al in the year 1974. In this the apparent resist electrical resistivity rho A is indicated along a vertical logarithmic scale, so this is the apparent resistivity, so this is in ohm meter and it varies all the way from say 10, this is say 20, then let us say this is 100, then let us say this is say 200 and on the horizontal scale which is also on logarithmic scale which is the electrode spacing this is L by 2 in meters and it as per this Zodie's results it varies all the way from 2 and here it is 5, 10, 20, 10 to 100 and 100 to 1000, so here this is 100 and then this is 1000 and here in between we have say 20, then 50, similarly here we have say 200, then say 500, this case the, so there are basically two curves that is the one is a theoretical curve and the observed curve, so this the theoretical curve, so it has this points and the observed curve, so this case, so this is the theoretical curve and this is the observed curve and here so this is the asymptote, so this indicates a rho 1 and there is a higher level asymptote which is say this rho 2, so this rho 2 is say 100 ohm meter and this rho 1 is 10 ohm meter and if you take the, so here we have this h 1 is 14 meter and basically, so this h 1 is the depth of, so this is the depth of the sandy aquifer and this, so basically this is and this is the asymptote and here in this case, so we need to match the theoretical curve and the observed curve, so that finally we get a, this one it shows a lower asymptote of say 10 ohm meter and a higher asymptote of say 100 ohm meter and so essentially this represents, so it represents a clay layer of 14 meter that is thickness over which is overlying a sandy aquifer, so based on the electrical resistivity values, so we can interpret that, so this two layer formation having a clay layer at the top which is over a sandy aquifer. There is also another method of interpretation of the results, so in this case this is using the Wiener arrangement, so here also, so this is semi logarithmic plot and in this case the horizontal scale is in terms of distance, so this is the horizontal distance which is in linear scale say 100 to 500 meters, so this is also taken from, so this is the horizontal profile by surface resistivity, so using Wiener arrangement, again the source is the same that is Zody et al 1974 and the vertical scale represents the Wiener apparent resistivity, so this is rho a in ohm meter and this is also in linear scale, so 50, 100, 150, 200, 250 and 300, in this case say suppose based on the electrical resistivity values we can identify this strata, so suppose it is a gravelly clay, in this case the resistivity will vary just in the range of 100 to 150 ohm meter and if it is gravel then the resistivity will be varying in the range of 200 to 250 and even slightly higher also and again when it is clay the resistivity again will drop back between the range of 100 and 150, then again when there is a gravel the resistivity goes up again in the above 200, in this case so again so based on the resistivity measurements we can interpret the formation, so in this case we can say that say up to this it is gravelly clay and here so this is indicating gravel and this is indicating clay, again this is indicating gravel and here it is indicating clay and again followed by gravel, so like this when the apparent resistivities are plotted at this horizontal distance between the electrodes in this vener arrangement and so based on the variation of this apparent resistivity we can interpret the ground water form at the subsurface geological formations as well as their ground water permeability and so this electrical resistivity method has also been employed for delineating geological formations or geothermal areas and for estimating aquifer permeability, so when the so this electrical resistivity when there is a pollutant when there is an electrical electrically conducting pollutant say for example there is a soluble salt, so the electrical resistivity method can be used in correlating the ground water pollutant spread, so now we will move on to the seismic refraction method, so in this seismic refraction method a small shock created at ground surface either by impact of a heavy instrument or by an explosive charge and the travel time required for shock waves to travel known distances is recorded, so this is the seismic refraction method and here so the there is also this seismic waves are similar to light rays showing reflection, refraction and simultaneous velocity change and in this case, so the seismic reflection, so the seismic refraction methods provide info on geological formations which are 1000s of meters greater than 1000s of meters below ground level, on the other hand seismic refraction methods provide information on formations geological formations say up to 100 meters and the characteristic seismic velocities, so the seismic velocities for different material, so this is taken from the source the of American society, the document of American society of civil engineers in 1972 and in this case, so this is the velocity meter per second, so this is 50, 100, 200, 500, 1000, 2000 and 5000 and in this, so here the loose sand will have a seismic velocity in the range of 100 to 200 meters, so this is loose sand and so the silt will have velocity slightly higher, so this is silt, so this is a top soil, so this is the top soil and this is the loose sand and this is followed by silt and so this is silt as well as gravel, so gravel will have a higher, so this is gravel followed by till, so this is till and then compacted till then sandstone and so on and this the highest this one by seismic refraction velocity is for igneous and volcanic rocks, so in between you have the sedimentary rocks which have the almost the same this one, so this is sedimentary rocks, so we will stop here and we will continue in the next lecture, thank you.