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http://www.geo.wvu.edu/~wilson/geo252/lect12/mag2.pdf Environmental and Exploration Geophysics I Magnetic Methods (I) tom.h.wilson [email protected] Department of Geology and Geography West Virginia University Morgantown, WV Anomaly associated with buried metallic materials Computed magnetic field produced by bedrock Results obtained from inverse modeling Bedrock configuration determined from gravity survey Where are the drums and how many are there? Locating Trench Boundaries Theoretical model Examination of trench for internal magnetic anomalies. actual field data Gilkeson et al., 1986 Trench boundaries - field data Trench Boundaries - model data Gilkeson et al., 1986 Locating abandoned wells Abandoned Wells From Martinek Abandoned Well - raised relief plot of measured magnetic field intensities From Martinek Falls Run Coal Mine Refuse Pile Magnetic Intensity Wire Frame Gochioco and Ruev, 2006 40 30 Site 3 2:34 20 55000 45000 55000 20 50000 40000 50000 45000 10 35000 40000 10 40 45000 0 0 0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 100 25000 25000 35000 20 20000 20000 Site 3 2:39 40 35000 30000 40000 30000 30000 15000 15000 25000 10000 0 0 20 20 40 60 80 100 120 140 5000 10000 20000 0 5000 15000 -5000 10 30 0 20 0 10 20 30 40 50 60 70 80 90 100 0 -10000 10000 5000 10 0 0 0 10 20 30 40 50 60 70 80 90 100 Magnetic monopoles Fm12 p1 p2 4 r122 1 p1 r12 Fm12 Magnetic Force Magnetic Permeability p1 and p2 pole strengths Coulomb’s Law p2 Fm12 p1 p2 4 r122 1 F 1 po Ho o pt 4 r 2 Force Magnetic Field Intensity often written as H pt is an isolated test pole F 1 pE " FE" pt 4 r 2 The text uses F instead of H to represent magnetic field intensity, especially when referring to that of the Earth (FE). The fundamental magnetic element is a dipole or combination of one positive and one negative magnetic monopole. The characteristics of the magnetic field are derived from the combined effects of non-existent monopoles. Dipole Field monopole vs. Toxic Waste dipole The earth’s main magnetic field Measuring the Earth’s magnetic field Proton Precession Magnetometers Steve Sheriff’s Environmental Geophysics Course Tom Boyd’s Introduction to Geophysical Exploration Course Source of Protons and DC current source Proton precession generates an alternating current in the surrounding coil M GF f F 2L 2 Proton precession frequency (f) is directly proportional to the main magnetic field intensity F. L is the angular momentum of the proton and G is the gyromagnetic ratio which is a constant for all protons (G = 0.267513/ sec). Hence - F 23.4874 f Magnetic Elements Magnetic north pole: point where field lines point vertically downward The compass needle points to the magnetic north pole. Geomagnetic north pole: pole associated with the dipole approximation of the earth’s magnetic field. 61000 F (nanoteslas or gammas) 60000 59000 58000 57000 56000 55000 54000 53000 1900 1920 1940 1960 Date 1980 2000 Inclination (degrees) 72 71 70 69 68 1900 1920 1940 1960 1980 2000 Date W declination (degrees west) -9 -8 -7 -6 -5 -4 -3 -2 1900 1920 1940 1960 1980 2000 Date Magnetic Elements for your location Today’s Space Weather Magnetic Field Variations Magnetic field variations generally of non-geologic origin Long term drift in magnetic declination and inclination Magnetic fields like gravitational fields are not constant. Their variations are much more erratic and unpredictable Diurnal variations http://www.earthsci.unimelb.edu.au/ES304 /MODULES/ MAG/NOTES/tempcorrect.html Today’s Space Weather Real Time Magnetic field data In general there are few corrections to apply to magnetic data. The largest non-geological variations in the earth’s magnetic field are those associated with diurnal variations, micropulsations and magnetic storms. The vertical gradient of the vertical component of the earth’s magnetic field at this latitude is approximately 0.025nT/m. This translates into 1nT per 40 meters. The magnetometer we have been using in the field reads to a sensitivity of 1nT and the anomalies we observed at the Falls Run site are of the order of 200 nT or more. Hence, elevation corrections are generally not needed. Variations of total field intensity as a function of latitude are also relatively small (0.00578nT/m). The effect at Falls Run would have been about 1/2 nT from one end of the site to the other. International geomagnetic reference formula The single most important correction to make is one that compensates for diurnal variations, micropulsations and magnetic storms. This is usually done by reoccupying a base station periodically throughout the duration of a survey to determine how total field intensity varies with time and to eliminate these variations in much the same way that tidal and instrument drift effects were eliminated from gravity observations. Anomalies - Total Field and Residual The regional field can be removed by surface fitting and line fitting procedures identical to those used in the analysis of gravity data. Magnetic susceptibility is a key parameter, however, it is so highly variable for any given lithology that estimates of k obtained through inverse modeling do not necessarily indicate that an anomaly is due to any one specific rock type. N S Opposites attract N S N S Magnetic fields are fundamentally associated with circulating electric currents; thus we can also formalize concepts like pole strength, dipole moment, etc. in terms of current flow relationships. Cross sectional area A + pl = n iA pl is the dipole moment l Units of pole strength - niA p ampere meter l I=kF I kFE I is the intensity of magnetization and FE is the ambient (for example - Earth’s) magnetic field intensity. k is the magnetic susceptibility. The intensity of magnetization is equivalent to the magnetic moment per unit volume or M Magnetic dipole I V moment per unit volume and also, I kFE . M pl I V V M pl Thus p and A kFE p kAFE where yielding The cgs unit for pole strength is the ups p kAFE Recall from our earlier discussions that magnetic field intensity p H or F 2 so that r p Fr 2 Thus providing additional relationships that may prove useful in problem solving exercises. For example, F kFE A r2 What does this tell us about units of these different quantities? We refer to the magnetic field intensity as H or, more ambiguously, as F dyne 1 an Oersted ups dyne Force H pole strength ups p ups H (or F ) 2 2 r cm ups thus 1 Oersted 1 2 cm p Fr 2 yields p Oersted-cm2 Note also that 1 Oersted = 105 nT & 1 nT = 1 Force varies inversely as the square of the distance between charges, masses or poles. It has the general form F m1m2 r2 Potential on the other hand refers to the energy available to do work and is the integral of the force times displacement. V Fdr m1m2 dr 2 r What is this integral? m1m2 V Fdr 2 dr r Remember the general power rule for integration n r dr 1 n 1 r C n 1 Since n is -2, n+1 = -1 so that the potential V (per unit pole) is simply m r As we have done repeatedly with the force, we divide it by unit mass, charge or pole to obtain m " F" 2 r an acceleration, electric or magnetic field intensity. Doing the same with the potential yields a potential per unit pole strength, or just m V r Most importantly, working with potentials offers us some simplification since the denominator is in r and not r2. It offers useful simplification when characterizing the dipole field. Basic Magnetic Unit and Vector Concepts Problem - At a point 20 cm from the center of a thin magnetized rod 40 cm long and equidistant from its ends, the magnetic field is 500 nT. What is the pole strength in Oersted-cm2? Sign conventions imply that the test pole is positive. HR=2Hx=500nT UNITS - nanoteslas, ups, Oersteds ….. 105 Given H R 2 H x what is H x ? HRX = 500nT Then, what is H+ or H-? Once we know this, we can then determine the pole strength. H = p/r2 so p = Hr2 Bring questions to class Tuesday after Thanksgiving break – November 28th We will meet in the 310