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## Electro-Magnetic Methods, Physics tutorial

Introduction:Electromagnetic (EM) induction that is a source of noise in resistivity and IP surveys is basis of a number of geophysical methods. These were initially largely utilized in search for conductive sulphide mineralization but are now being increasingly utilized for area mapping and depth sounding. Because a small conductive mass within a poorly conductive environment has a greater effect on induction than on 'DC' resistivity, discussions of EM methods tend to focus on conductivity (σ), the reciprocal of resistivity, rather than on resistivity itself. Conductivity is measured in mhos per metre or, more correctly, in siemens per metre (Sm

^{-1}).There are two limiting case. In the one, eddy currents are induced in small conductor embedded in insulator, producing discrete anomaly which can be utilized to get information on conductor location and conductivity. In other, horizontal currents are induced in horizontally layered medium and their effects at surface can be interpreted in terms of apparent conductivity. Many real situations comprise combinations of layered and discrete conductors, making greater demands on interpreters, and at times on field personnel. Wave effects are significant only at frequencies above about 10 kHz, and methods can otherwise be most effortlessly understood in terms of varying current flow in conductors and varying magnetic fields in space. Where change in inducing primary magnetic field is generated by flow of sinusoidal alternating current in wire or coil, method is explained as continuous wave (CWEM).

Two-coil CW Systems:Current-carrying wire is enclosed by circular, concentric lines of magnetic field. Bent into small loop, the wire produces magnetic dipole field which can be differed by alternating the current. This varying magnetic field causes currents to flow in nearby conductors.

System descriptions In CW (and TEM) surveys, sources are (generally) and receivers are (virtually always) wire loops or coils. Small coil sources generate dipole magnetic fields which vary in strength and direction. Anomaly amplitudes depend on coil magnetic moments that are proportional to number of turns in coil, coil areas and current circulating. Anomaly shapes depend on system geometry and on nature of conductor.

Coils are explained as horizontal or vertical according to plane in which windings lie. Horizontal coils have vertical axes and are alternatively explained as vertical dipoles. Systems are also classified by whether receiver and transmitter coils are co-planar, co-axial or orthogonal (i.e. at right angles to each other), and by whether coupling between them is maximum, a minimum or variable. Co-planar and co-axial coils are maximum-coupled as primary flux from transmitter acts along axis of the receiver coil.

Primary field is not detected and small changes in separation have little effect. Though, large errors are generated by slight misalignments. In field it is simpler to maintain required coil separation than relative orientation, and this is one reason for favoring maximum coupling.

Dip-angle systems, in which receiver coil is rotated to find out dip of resultant field, were once very popular but are now usually limited to shoot-back instruments utilized in rugged terrain. Shoot-back receiver and transmitter coils are identical and are related to electronic units which can both transmit and receive.

Slingram:Most ground EM systems utilize horizontal co-planar coils ('horizontal loops'), generally with shielded cable carrying phase-reference signal from transmitter to receiver. Sight of two operators, loaded with bulky apparatus and related by umbilical cord, struggling across rough ground and through thick scrub, has given light entertainment on several surveys. Very sensibly, some instruments permit reference cable to be also utilized for voice communication.

Happily, memory units have not (yet) been added to record conversations. Slingram is frequently applied to horizontal-loop systems but without any general agreement as to whether it is fact that there are two mobile coils, or that they are horizontal and co-planar, or that they are related by reference cable, which makes term applicable.

Response functions:In Slingram survey, electromagnetic response of a body is proportional to mutual inductances with transmitter and receiver coils and inversely proportional to its self-inductance, L that restricts eddy current flow. Anomalies are usually stated as percentages of theoretical primary field and are thus also inversely proportional to mutual inductance between transmitter and receiver that determines strength of primary field. Four parameters can be combined in single coupling factor, Mts Msr/MtrL.

Anomalies also depend on response parameter that involves frequency, self-inductance (always closely associated to linear dimensions of body) and resistance. A response curve show simultaneously how responses differ over targets of different resistivity using fixed-frequency systems and over a single target as frequency is varied. The quadrature field is very small at high frequencies, where distinction between good and just moderate conductors tends to disappear. Most single-frequency systems operate below 1000 Hz, and even multifrequency systems which are now norm usually work completely below 5000 Hz.

Slingram practicalities:Coil separation in Slingram survey must be adjusted to desired depth of penetration. Greater the separation, the greater the effective penetration as primary field coupling factor Mtr is more severely affected by increase than are either Mts orMsr. Maximum depth of investigation of Slingram system is frequently quoted as being roughly equal to twice coil separation, if this is less than skin depth but this ignores effects of target size and conductivity and may be excessively optimistic.

As signals in Slingram surveys are referenced to primary field strengths, 100% level must be verified at start of each day by reading at standard survey spacing on ground that is level and thought to be non-anomalous. This check has to be performed even with instruments which have fixed settings for allowable separations, as drift is a continual problem.

Check should also be made for any leakage of primary signal into quadrature channel (phase mixing). Instrument manuals explain how to test for this condition and how to make any essential adjustments. Receivers and transmitters should, of course, be tuned to same frequency for sensible readings to be obtained, but care is required. A receiver can be seriously damaged if transmitter tuned to its frequency is operated close by.

The horizontal-loop system anomaly over thin, steeply dipping conductor is shown below. No anomaly is detected by horizontal receiving coil immediately above body as secondary field there is horizontal. Likewise, there will be no anomaly when transmitter coil is vertically above body as no important eddy currents will be induced. Greatest (negative) secondary field values will be observed when conductor lies mid-way between two coils. Coupling depends on target orientation and lines must be laid out across expected strike. Oblique intersections generate poorly defined anomalies which may be hard to interpret. In all EM work, care should be taken to record any environmental variations which might affect results. These comprise obvious actual conductors and also feature like roads, alongside which artificial conductors are frequently buried. Power and telephone lines cause special problems as they broadcast noise which, though different in frequency, is frequently strong enough to pass through rejection (notch) filters. It is significant to check that these filters are suitable to area of use (60 Hz in most of the Americas and 50 Hz nearly everywhere else). Ground conditions must also be noted, as variations in overburden conductivity can drastically influence anomaly shapes and signal penetration. In hot, dry countries, salts in overburden can create surface conductivities so high that CW methods are ineffective and have been superseded by TEM.

Effects of coil separation:Changes in coupling between transmitter and receiver can generate spurious in-phase anomalies. Field at a distance r from coil can be explained in terms of radial and tangential components F(r) and F(t). The amplitude factor A depends on coil dimensions and current strength. For co-planar coils, F(r) is zero as Φ is zero and measured field, F, is equal to F(t). Inverse cube law for dipole sources then signifies that, for fractional change x

F = F

_{0}/(1 + x)3Here, F

_{o}is field strength at intended spacing. If x is small, this can be written as:F = F

_{0}(1-3x)Therefore, for small errors, percentage error in in-phase component is three times the percentage error in distance. As real anomalies of only a few percent can be significant, separations should be kept very constant.

Surveys on slopes:On sloping ground, distances between survey pegs may be estimated either horizontally (secant chaining) or along slope. If along slope distances are utilized in reasonably gentle terrain, coil separations must be constant but it is hard to keep coils co-planar without clear line of sight and simpler to hold them receiver axis is then equivalent to co-planar field multiplied by (1 - 3 sin² θ), where θ is slope angle. Correction factor 1/(1 - 3 sin² θ) is always greater than 1 (coils really are maximum-coupled when co-planar) and becomes infinite when slope is 35

^{0}and primary field is horizontal.If secant-chaining is utilized, distances along slope between coils are proportional to secant (=1/cosine) of slope angle. For co-planar (tilted) coils ratio of normal to slope field is therefore cos³ θ and correction factor is sec³ θ. If coils were to be held horizontal, combined correction factor would be sec³ θ/(1 - 3sin² θ).

Applying corrections:For any coupling error, whether caused by distance or tilt, in-phase field which would be seen with no conductors present can be stated as percentage of maximum-coupled field Fo. Field computed to be 92% of Fo due to non-maximum coupling can be converted to 100% either by adding 8% or by multiplying actual reading by 100/92. If reading attained actually were 92%, these two operations would generate identical results of 100%. If, though, there were a superimposed secondary field (e.g. if actual reading were 80%), adding 8% would correct only primary field (converting 80% to 88% and indicating the presence of a 12% anomaly). Multiplication would apply correction to secondary field also and would signify a 13% anomaly.

Ground conductivity measurement:Slingram-style systems are now utilized for rapid conductivity mapping. At low frequencies and low conductivities, eddy currents are small, phase shifts are close to 90

^{0}and bulk apparent resistivity of ground is roughly proportional to ratio between primary (in-phase) and secondary (quadrature phase) magnetic fields. Relatively high frequencies are utilized to make sure measurable signal in most ground conditions. If induction number, equivalent to transmitter-receiver spacing divided by skin depth, is considerably less than unity, depth of investigation is determined essentially by coil spacing.Induced current flow in homogeneous earth is completely horizontal at low induction numbers, despite of coil orientation, and in horizontally layered earth currents in one layer hardly affect those in any other. Response for vertical co-planar coils, and therefore apparent conductivity estimate, is dominated by surface layer. Independence of current flows at different levels signifies that curves that strictly speaking are for homogeneous medium, can be utilized to compute theoretical apparent resistivity of a layered medium.

Other CWEM Techniques:Fixed-source methods:Fields produced by straight, current-carrying wires can be computed by repeated applications of Biot-Savart law. Relationship for four wires forming rectangular loop is given. If measurement point is outside the loop, vectors which don't cut any side of loop have negative signs. Slingram anomaly was symmetrical as receiver and transmitter coil were moved over the body in turn. If source, whether coil or straight wire, were to be fixed, there would be zero when horizontal receiver coil was immediately above steeply dipping body and anomaly would be antisymmetric. Fixed-source systems frequently compute dip angles or (that is effectively same thing) ratios of vertical to horizontal fields. Turam methods utilize fixed extended sources and two receiving coils separated by distance of order of 10 m. Anomalies are estimated by computing reduced ratios equal to actual ratios of signal amplitudes through two coils divided by normal ratios which would have been observed over non-conductive terrain. Phase differences are estimated between currents in two receiver coils and any nonzero value is anomalous.

There is no reference cable between receivers and transmitter, but absolute phases and ratios relative to single base can be computed if each successive reading is taken with trailing coil placed in position just vacated by leading coil. CWEM Turam is now little utilized, but large fixed sources are common in TEM work.

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