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Lecture notes on Geophysical methods

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Introduction to Geophysics – Lecture Notes Jan Valenta March 23, 2015Contents 1 Introduction 1 1.1 What is geophysics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Gravimetry 5 2.1 Newton’s Law of Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Gravity field of the Earth and data reduction . . . . . . . . . . . . . . . . . . . . . 6 2.3 Gravity meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Rock densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Gravity effect of selected bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.6 Gravity data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.7 Gravity data interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.8 Applications of the gravity method . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Magnetometry 25 3.1 Basic principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Magnetic field of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.1 The main field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.2 The external magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2.3 Spatial variations of the main field . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Magnetism of rocks and minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Field instruments for magnetic measurements . . . . . . . . . . . . . . . . . . . . . 34 3.4.1 Proton-precession magnetometer . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5 Magnetic surveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5.1 Magnetic effects of a sphere and a vertical sheet . . . . . . . . . . . . . . . 36 3.5.2 Computer modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.5.3 Magnetic gradiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.6 Magnetic measurements for an archaeological prospection . . . . . . . . . . . . . . 46 4 Geoelectrical methods 49 4.1 Elementary theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Resistivities of rocks and minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3 Resistivity surveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.1 Electrode configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3.2 Vertical electrical sounding . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.3 Resistivity profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5 Final word 65 31 Introduction 1.1 What is geophysics? Essentially, as the word suggests, geophysics is the application of method of physics to the study of the Earth. The rocks does not differ only by their macroscopic or microscopic properties studied field geologists or petrologists. They also differ by their chemical and physical properties. Hence as the rocks differ according to their origin, structure, texture, etc. they also differ by their density, magnetisation, resistivity, etc. The bad news is that the physical properties do not always clearly correlates with geological classifications and do not necessarily easily translates into the geological terms. What does this mean? Lets take the density as an example. We have a rock sample and we have measured the value of density to be 2.60 g/cm3. According to this value we could assume that the rock sample could be, e. g. a limestone, some shale, compact sand- stone, rhyolite, phonolite, andesite, granite, pos- sibly some kindof schist and many others. The widerangeofpossiblerocktypessuggeststhatthe physical properties does not directly refer to the geological classification. This is a principal prob- lem of geophysics, however, as we will see later, there are ways to overcome this. So, what we can conclude from this example? The geophysics is a kind of proxy in our attempts to study the geological structures. It does not “talk” to us in geological terms and we have to in- terpret obtained physical parameters in a ge olog- ical sense. Moreover, the icentrifugal forcenter- pretation is not unique as we have seen in our example. The successful interpretation is based on experiences of an interpreter and on the a pri- ori knowledge of the geological environment stud- ied. In the terms of our example – if we know that we are working in the crystalline complex we can mostly likely leave sedimentary rocks out of our interpretation and we are left with rhyo- lite, phonolite, andesite, granite or schist. And if Figure 1.1: Possible inferences of structure we study the geological sources a little bit more at depth (Musset and Khan 2000). we could also discriminate between the rock types left.2 Introduction When we have discussed the essential and unavoidable drawback of geophysics it is time to look on the bright side. Why do people bother with geophysics, what problems can it solve and how it can help me in my particular problem? The advantage of geophysics is that it is able to image hidden structures and features inaccessible to direct observation and inspection. That from measurements on the surface we can deduce what is in the depth. Moreover, we can measure on traverses or even make a grid and hence obtain a profile view, map or even a 3d image of a subsurface. Compare this with a geological mapping where we study the outcrops and, if we are lucky, have also a few trenches or boreholes. There we have just a surface situation and we can only guess how the surface structures continues to the depth. Imagine the situation illustrated in the Figure 1.1. From the surface geological mapping we would see a sediment filled valley with inclined strata on both sides. However, we have no clue how it looks like in the depth. Four possibilities are sketched in the figure. The surface geological mapping cannot give us any hint which of these is correct unless we would make a line of boreholes. This, of course, would be both – time consuming and extremely expensive. How the geophysics can help us here? Lets assume that we have collected geophysical data on a traverse across the structure. The methods used were gravimetry, magnetometry and a DC resistivity profiling. The gravimetry distinguish rocks according to their densities, hence if we see an increase in gravity we can assume rocks with increased densities – e.g. a mafic intrusion (Fig. 1.1c). Decreased densities of rocks would also decrease the gravity readings we can assume presence of rocks with low densities – e.g. a salt dome (Fig. 1.1d). The magnetometry indicates rocks with increased magnetisation – in case of mafic intrusion (Fig. 1.1c) we would see an increase in magnetometry data. The fault zones are usually connected with low resistivities. Hence if Fig. 1.1b or Fig. 1.1d would be the case we would see a low resistivity zone over the fault. In such a manner the geophysics can add to the surface geological prospection. In this particular case the geophysics provided us with the third (desperately needed) dimension. The only necessary condition is that the target structure must differ in some of the physical properties from its surroundings (Tab. 1.1).Introduction 3 Table 1.1: Physical properties of common rocks and ore minerals (Milsom 2011).4 Introduction2 Gravimetry The gravimetry detects tiny differences in the gravitational force. Since, according to the New- ton’s law, the gravitational force depends on masses of the bodies, it allows us to differentiate underground bodies and structures if their densities differ. 2.1 Newton’s Law of Gravitation Everyone is familiar with the Earth pull or attractive force. It causes thing s to fall and is also responsible for a pretty hard work if we need to carry stones to build a house. The man who discovered that every mass attracts another one was Sir Isaac Newton. In 1687 he formulated his discovery into the equation (2.1) called the Newton’s Law of Gravitation: m m 1 2 F = ; (2.1) 2 r where F denotes the gravitational force, is the universal gravitational constant (6:673 11 2 10 N(m=kg) ), m are weights of attracting bodies and r is the distance between them. This equation (2.1) enables us to calculate a gravitational force the Earth is pulling e.g. a rock on the Earth surface: M m E r F = ; (2.2) 2 R E where M is the weight of the Earth, m is the weight of the rock and R is the diameter of E r E the Earth. We can see that it is inconvenient to use and measure the gravitational force, since it depends on weights (masses) of both bodiesM andm . Dividing both sides of equation (2.2) by E r m we get: r F M E = : (2.3) 2 m R r E Since the force is computed asweightacceleration we can transform the equation (2.3) into: M E g = ; (2.4) 2 R E defining the acceleration caused by the Earth. The acceleration g is called the “acceleration 2 due to gravity” or “acceleration of gravity”. The value of g on the Earth surface is 9:80665 m=s 2 2 which is often simplified to 10 m=s . The unit of acceleration of gravity – 1cm/s – is also referred to as galileo or Gal, in honour of Galileo Galilei, who was the first who measured its value. The 2 modern gravimeters are capable of readings with the precision of 0.001mGal (0.01m=s ).6 Gravimetry Figure 2.1: Topographic corrections (Musset and Khan 2000) 2.2 Gravity field of the Earth and data reduction Because the Earth is not a perfect homogeneous sphere, the gravitational acceleration is not con- stant over the whole Earth’s surface. Its magnitude depends on five following factors: latitude, elevation, topography of the surrounding terrain, earth tides and density variations in the subsur- face. Within the geophysical prospection, we are interested in the last one, which is usually much smaller then the latitude and altitude changes. The removal of unwanted components is often referred to as reduction. Latitude correction. The reason for the latitude correction is two-fold. First of all, it is caused by the Earth’s centrifugal force being added to the gravitational force (vector sum). This decreases the gravitational force with an increase of a radius of rotation. Hence the smallest gravitational force is on the equator (maximal centrifugal force) and the largest is on the pole. Second, the gravitational force is further affected by the fact that the Earth is not spherical but ellipsoidal. This further decreases the gravitational force on the equator. Both of these effects could be removed by the International Gravity Formula: 2 2 g = 978031:8(1 + 0:0053024 sin  0:0000059 sin 2) mGal (2.5)  It is clear that the centrifugal force changes only in the N–S direction, not in the W–E. As we have seen from the Newton’s Law of Gravity – equation (2.1) – the gravity decreases with the square of distance. Hence, if we lift the gravimeter from the surface (or any other datum), the gravity will change. To be able to compare data measured in different elevations we have to reduce them to a common datum. This correction for the topographic effects has several steps. Their description follows. Free-air correction. This is the first step of reducing topography effects. It simply corrects for the change in the elevation of the gravity meter, considering only air (hence a free-air) being between the meter and selected datum (leftmost part of the Figure 2.1). To get the change in gravity acceleration with height we can differentiate the equation (2.4): g M 2g FA E =2 = mGal=m: (2.6) 3 R R R Raising the gravity meter (e.g. extending its tripod) decreases the measured gravity values by 0:3086 mGal=m. Hence to measure with an accuracy of 0.01mGal we have to measure the elevation of the gravity meter with an accuracy of 3cm. The free-air correction varies slightly with latitude: 2 2 Clearly, the sin  and h parts are very small and could be neglected and we end up with the above mentioned ratio. Bouguer correction. The Bouguer correction removes from the data an effect of rocks laying between the measured point and reference datum (Fig. 2.1 in the centre). This effect wasGravimetry 7 Figure 2.2: Gravimeter profile across Sierra Madera, Pews County, Texas, illustrating the im- portance of terrain corrections (Hammer 1939). ignored during the free-air corrections. Hence we add a slab with an average density of surrounding rocks – the Bouger correction: g B = 2  = 0:04192 mGal=m; (2.7) R where  is the density of the Bouguer slab. The free-air and Bouguer correction is often combined into an elevation correction: g g g E FA B = = (0:3086 0:04192) mGal=m: (2.8) R R R Terrain correction. The Bouguer correction assumed the slab to be infinite in the horizontal direction. This is not true, due to a topography and Earth curvature. The correcton for the Earth curvature is used in a large scale surveys and we will leave it out now. The topography correction, however, might be important (Fig. 2.1, right). The hill above the Bouguer slab with its own gravity force pulls in the opposite direction than the Earth, therefore decreasing the measured acceleration (Fig. 2.2). In a similar way, the valley also decreases the value, because when computing the Bouguer correction we have already subtracted the Bouguer slab (with a flat surface) and did not account for the missing masses of the valley. Hence the terrain correction is always added. There are several methods of calculating terrain corrections. In any of these we need to know the relief to certain distance from the station in detail. The common method is to divide the surroundings of the gravity stations into zones, estimate average altitude in every zone and compute the gravity effect of the zones. Several versions of these zones were already published (e.g. Hammer 1939). The easiest way is to print the zoning chart (Fig. 2.3) into the transparent sheet and overlay it over the topographic map. Then the average altitude in each zone and compartment is estimated and the difference between estimated value and8 Gravimetry Figure 2.3: Zone chart for use in evaluating terrain corrections at grav- ity stations (Hammer 1939). station elevation is computed and a gravity effect of this compartment is found in the table (Figs. 2.4 and 2.5). Finally, sum of effects in all compartments and zones forms the terrain correction for the current station. It is clear that this method of computing terrain corrections is very tedious. Hence now usu- ally the computer programs compute the corrections based from the DEM (digital elevation model of the terrain). Note that the effect of the innermost zone – A – is not computed in the table. The reason is that in such small surroundings the terrain should be flat if possible. The gravity effects of irregularities in such close vicinity is very large, precise topography maps in scales large enough are not common and dense precise measurements of relief would be inadequately expensive. Tidal correction. The tidal correction accounts for the gravity effect of Sun, Moon and large planets. Modern gravity meters compute the tide effects automatically. For the older in- struments, one must compute the corrections by himself, e.g. according to the Longman (1959), or consider the tides as a part of the drift of the instrument and remove it via a drift correction. Drift correction. This correction is intended to remove the changes caused by the instrument itself. If the gravimeter would be at one place and take periodical readings, the readings would not be the same. These are partly due to the creep of the measuring system of the gravimeter, but partly also from the real variations – tidal distortion of the solid Earth, changes of the ground water level, etc. The drift is usually estimated from repeated readings on the base station. The measured data are then interpolated, e.g. by a third order polynomial, and a corrections for profile readings are found. 2.3 Gravity meters Basically, there are two main gravity types – the absolute and relative gravity meters. In geophys- ical prospection solely the former are used. They measure relative gravity – the gravity changes, not the value of gravity itself. If we want to measure the absolute value of gravity we must use some point with already known gravity value and start our measurements there. Then, by adding the measured differences, we know the absolute values of gravity on all our points. However, this is needed only in large scale mapping, where we want to add our data to already existing grid.Gravimetry 9 Figure 2.4: Original Hammer’s table for the terrain corrections (Hammer 1939).10 Gravimetry Figure 2.5: Original Hammer’s table for the terrain corrections – continue (Hammer 1939).Gravimetry 11 Figure 2.6: Schematic sketch of the astatic gravity meter. The zero-length spring supports the mass M and keeps it in balance in a selected gravity fieldg. Measurements are done by rotating the dial, which raises or lowers the measur- ing spring and provides additional force Mg to return the mass to the stan- dard position (Milsom 2011). Thegravitymetersusedforthegeophysicalprospectionaretheastatic gravity meters (Fig.2.6), where the mass is hold by the measuring spring. Elongation of this spring is proportional to the gravity force pulling the mass. The older models of gravity meters used a dial to raise or lower the measuring spring to place the mass to a standard position. In modern gravimeters this is done automatically. From the sketch it is clear that the springs used in the meters must be extremely thin and sensitive. There are two main types of the springs – steel springs in the LaCoste-Romberg gravity meters and quartz springs in the others. Currently, there are two manufacturers of the prospection gravity meters – the Scintrex with quartz springs and Burris, resembling the old LaCoste-Romberg and using the steel springs. To minimise effects of thermal changes, the spring is in thermally insulated chamber (vacuum chamber), the new models are also equiooed with an additional heater to keep the internal tem- perature as stable as possible. Hence, removing batteries from the gravity meter leads to change in the inner temperature resulting in unstable and unreliable readings due to changes of mechanical properties of the measuring spring. When the gravimeter is without the power supply for a long time (several hours) it could take as long as 48hours before realiable readings could be done again. 2.4 Rock densities The densities of rocks (Tab. 1.1), naturally, depends on the mineral composition of particular rock. However, not only mineral composition, but also other factors influences densities. The next main factor, mainly when dealing with sedimentary rocks, is the porosity and kind of media filling the pores. Increasing porosity decreases the density, since air (or any other media filling the pores (water, gas, oil, etc.) has lower density than any of minerals. The other factors are weathering of rocks, fractures and joints, etc. Combining all these factors clearly explains the high variance of measured values reported in a literature. Densities needed for a data and interpretation interpretation (e.g. for the Bouguer anomalies) could be either measured in laboratory (keeping in mind the laboratory values could differ from the reality mainly due to change of the media filling the pores in the nature and in laboratory) or could be estimated from the gravity measurements. One of widely used methods for density estimation is the Nettleton’s method (Nettleton 1939). This method is based on the fact that the Bouguer anomaly depends on the density of rocks as well as on the topography. If the topography along the profile is changing but the density is constant then, according to the equation (2.7), the Bouguer anomaly should be constant as well. If it is not constant then the density estimate is wrong and the topography changes are not compensated well. Therefore, if we compute a set of Bouguer anomaly curves with different densities and compare them with the topography the Bouguer curve which correlates the least with a topography is the curve with a correct density estimate.12 Gravimetry Figure 2.7: Illustration of the Net- tleton’s method for density estimate. The Bouguer curve which correlates least with the topography is calcu- lated with a correct density estimate. The top graph shows the topography along the profile. In the middle graph Bouguer curves for different densi- ties are plotted, the curve for the se- lected density estimate is plotted in red. The bottom graph depicts cor- relation (Spearman’s correlation co- efficient) of topography and Bouguer curves for different densitites. This method could be applied if a) the profile crosses some distinct topographical feature, b) the density of the subsurface is not expected to change substantially. 2.5 Gravity effect of selected bodies The simple geometrical bodies are often used for the modelling before the survey is carried out. The aim is to get a rough estimate of the anomaly effect of the target structure. If we, for example, find that the amplitude of a modelled anomaly is lower than sensitivity of our instrument then there is no need to do any measurements at all...Estimating the amplitude and width of the anomaly also enables us to plan a density of profiles and station spacing. For an interpretation at least three stations within the anomaly are necessary. There is a small number of simple basic bodies, however, combining them together can build up even a complex model. Gravity effect of a sphere A sphere is the most basic body and usually is used as a part of other models or could approximate symmetrical bodies. The gravity effect of a sphere at point P (Fig. 2.8) is: 4 3 a z M 3 g =g cos  = = ; (2.9) r 3 2 2 2 r 2 (x +z ) where is a density of the sphere,a is a radius of the sphere andz is the depth of the center of the sphere.Gravimetry 13 Figure 2.8: Gravity effect of a sphere (Telford et al. 1990) g max The depth z of the sphere could be estimated from the measured anomaly. When g = 2 1 thenz = 1:3x . In other words, the depth of the sphere center could be estimated from the 2 half-width of the anomaly at half of its value (see Fig. 2.8). Gravity effect of a vertical cylinder The gravity effect on the axis aces of a vertical cylinder is: n o 1   1 2 2 2 2 2 2 g = 2  L + (z +R ) (z +L) +R ; (2.10) where L is the vertical size (length) of the cylinder z is the depth of its top and R is its diameter. IfR1, we have an infinite horizontal slab, which we used also for the Bouguer correction (2.7): g = 2 L: (2.11) Gravity effect of a horizontal rod Assuming a horizontal rod perpendicular to the x axis at a depth z, the gravity effect is: 8 9 = m 1 1 g =  ; (2.12) 2 1 1 h i h i x 2 2 z 1 + 2 2 2 2 2 : ; x +z x +z z 1 + 1 + 2 2 (y+L) (yL)14 Gravimetry Figure 2.9: Gravity effect of a horizontal rod. a) Three dimensional view. b) Projection of the plane containing the rod and the y axis. c) Projection on the xz plane. d) Gravity profile along the x axis. (Telford et al. 1990) where m is the mass of the rod. If the rod is expanded into the cylinder with a dimension 2 a then m = a . When the length L of the rod is infinite (usually a good approximation when the L 10z then the (2.12) simplifies into the: 2 m g = : (2.13) 2 x z 1 + 2 z The depth z of the rod could be estimated from the half-width of the anomaly: z =x1. 2 A lot of other geometric bodies could be found in the literature, enabling us to build a complex models. Examples of changes in gravity effect of dofferent bpdies with depth could be found in Figs. 2.10 and 2.11. Two examples of models using the spheres and cylinders are plotted in the Figs. 2.12 and 2.13. More complex modelling could be done using the computer modelling and irregular bodies. Check, e.g. the Gordon Cooper’s web page at the University of Witwatersrand (Cooper 2012).Gravimetry 15 Figure 2.10: Anomalies of a sphere and a horizontal cylinder at different depths. (Musset and Khan 2000) Figure 2.11: Anomalies of narrow sheets at different depths and dips. (Musset and Khan 2000)16 Gravimetry 2.6 Gravity data processing Once the gravity data are measured the more demanding task is to be carried out – the data processing and interpretation. Some procedures of data processing has been already mentioned in the section 2.2. Figure 2.12: Approximation of an anti- Figure 2.13: Approximation of a salt di- cline (Mareš and Tvrdý 1984). a) A geolog- apir (Mareš and Tvrdý 1984). a) A geo- ical section of an anticline. b) A schematic logical section of a diapir. b) An approx- representation with density distribution. c) imation of the diapir by two spheres. c) An approximation of the anticline by three An approximation of the diapir by a verti- infinite horizontal cylinders. cal cylinder. The first step in the data processing is deleting of wrong gravity readings. During the the field measurements there is usually several gravity readings taken at every station. Now, the outliers are removed and the rest of gravity readings from every station are averaged. Next, the readings from the base station are taken to determine the drift of the instrument. First, these data need to be corrected for the different heights of the tripod, the free-air correction – equation (2.6). Second, the drift should be estimated – usually the data are interpolated using the second or third-order polynomial (Fig. 2.14). Third, the readings at individual stations are corrected from the drift. The drift is estimated from the fitted polynomial according to the time of the gravity reading.