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## Varying Current Methods, Physics tutorial

Varying Current Methods:Alternating electrical currents circulating in wires and loops can cause currents to flow in ground without actual physical contact, using either inductive or capacitative coupling. Non-contacting methods are obviously necessary in airborne work but can also be very helpful on ground, as making direct electrical contact is tiresome business and may not even be possible where surface is concrete, asphalt, ice or permafrost.

Depth penetration:Currents which are caused to flow in ground by alternating electrical or magnetic fields attain their energy from fields and so decrease their penetration. Attenuation follows exponential law managed by attenuation constant (α) provided by:

α = ω[μ

_{a}ε_{a}{√(1+ σ^{2}/ω^{2}ε^{2}_{a})-1)}/2]^{1/2}μ

_{a}and ε_{a}are absolute values of, respectively, magnetic permeability and electrical permittivity and ω (=2πf ) is angular frequency. Reciprocal of attenuation constant is called as skin depth and is equal to distance over which signal falls to 1/e of original value. As e, base of natural logarithms, is approximately equivalent to 2.718, signal strength decreases by almost two-thirds over single skin depth.Rather intimidating attenuation equation simplifies significantly under certain restrictive conditions. Under most survey conditions, ground conductivity, σ is much greater than ωε

_{a}and α is then about equal to √(μ_{a}σω). If, as is generally the case, the variations in magnetic permeability are small, skin depth (=1/α), in metres, is approximately equal to 500 divided by square roots of frequency and conductivity.Depth of investigation in situations where skin depth is limiting factor is usually quoted as equivalent to skin depth divided by √2, i.e. to about 350√ (ρ/f ). Though, separation between source and receiver also influences penetration and is dominant factor if smaller than skin depth.

Induction:Varying magnetic field related with electromagnetic wave will induce voltage (electromotive force or emf) at right-angles to direction of variation, and currents will flow in any nearby conductors that form parts of closed circuits. Equations governing this phenomenon are relatively simple but geological conductors are very complex and for theoretical analyzes induced currents, called as eddy currents, are estimated by greatly simplified models.

Magnitudes of induced currents are determined by rates of change of currents in inducing circuits and by the geometrical parameter called as mutual inductance. Mutual inductances are large, and conductors are said to be well coupled if there are long adjacent conduction paths, if magnetic field changes are at right angles to directions of easy current flow and if magnetic materials are present to improve field strengths. When current changes in the circuit, opposing emf is induced in that circuit. Consequently, a tightly wound coil strongly resists current changes and is said to have high impedance and large self-inductance.

Phase:In most continuous wave systems, energizing current has form of sine wave, but may not, as a true sine wave must, be zero at zero time. Such waves are called as sinusoidal. Difference between time zero and zero point on wave is generally estimated as angle related to 360

^{0}or 2π radians of complete cycle, and is called as phase angle. Induced currents and their related secondary magnetic fields vary in phase from primary field and can, in accordance with the primary property of sinusoidal waves, be resolved in components which are in-phase and 90^{o}out of phase with primary. These components are at times called as real and imaginary respectively, terms deriving originally from mathematics of complex numbers. Out-of-phase component is also (more precisely and less confusingly) explained as being in phase quadrature with primary signal.As electromagnetic waves travel at speed of light and not immediately, their phase changes with distance from transmitter. Small distances between transmitters and receivers in most geophysical surveys make sure that these shifts are insignificant and can be ignored.

Transients:Conventional or continuous wave (CW) electromagnetic methods depend on signals produced by sinusoidal currents circulating in coils or grounded wires. Extra information can be attained by carrying out surveys at two or more different frequencies. Skin-depth relationships point out that penetration will rise if frequencies are decreased. Though, resolution of small targets will reduce. As alternative to sinusoidal signals, currents circulating in the transmitter coil or wire can be terminated suddenly. Such transient electromagnetic (TEM) methods are efficiently multi-frequency, as square wave has elements of all odd harmonics of fundamental up to theoretically infinite frequency. They have several benefits over CW methods, most of which derive from fact that measurements are of effects of currents generated by, and circulating after, termination of primary current. There is therefore no option of part of primary field leaking into secondary field measurements, either electronically or due to errors in coil positioning.

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