## Basic Principles

The fundamental principle of EM induction is illustrated in Figure 6.1. In environmental, agricultural, and engineering applications, EM methods are used primarily for locating either metallic conductors or conductive fluids, and determining soil moisture and mineralogy variations. The underlying concept of induction is widely known, and it is used for a variety of common tasks that include metal detectors at airport security entrances, the measurement of electrical current flowing in wires, and hunting for buried treasure with metal detectors.

The EM theory that underlies EM techniques has been developed since the later part of the nineteenth century, with the work Lenz, Biot, Ampere, Faraday, and Maxwell. There are numerous excellent physics and engineering texts on the subject at all levels of mathematical complexity, including works by Stratton (1941), Balanis (1989), Morse and Feshbach (1953), and many others. Excellent summaries are present in the geophysical literature (e.g., Keller and Frischknecht, 1966, and Ward and Hohmann, 1987). The following discussion is intended to cover some of the fundamentals that are essential to a basic understanding of the concepts underlying EM methods.

Ampere was the first investigator to recognize that a current passing through a wire has an associated magnetic field. A simple experiment, shown in Figure 6.1a, is often used to demonstrate the principle of Ampere's law. Iron filings laying in a plane perpendicular to a current-carrying wire (e.g., a wire sticking up through a table containing iron filings) will form circular patterns around the wire when current flows through the wire. The path of the line integral for the case of a straight current-carrying wire becomes a circle with its center on the wire. The integral sum of the magnetic field along this path is 2nr, which is the circumference of a circle of radius r, and the relationship between the EM field caused by current flow can be stated as follows:

2 n r where B is the magnetic induction (magnetic field strength), I is the current flowing in the wire, and r is the distance from the wire.

The magnitude of the magnetic field increases proportionally to the electric current, and there are no magnetic fields in any direction other than the circular path around the wire. Furthermore, the direction of the magnetic field is in a path determined by the "right-hand-rule," which states that

Iron filings

No current \ flow

Current flow

(a) Effect of electric current on iron filings

Current flow

Resulting magnetic field in space

Resulting magnetic field in space

(b) Magnetic field from current along a straight wire

(b) Magnetic field from current along a straight wire

Source: current flow through wire .

Source: current flow through wire .

Resulting magnetic field in space ""'""

(c) Magnetic field from current through a coil

Resulting magnetic field in space ""'""

(c) Magnetic field from current through a coil

FIGURE 6.1 Ampere's law: (a) current flowing through metal filings resting on a table will cause magnetic filings to arrange in a circumferential pattern around the current-carrying wire; (b) current flowing through a wire causes a magnetic field that is circumferential to the wire carrying the current; and (c) current flowing through a coil of wire causes a perpendicular magnetic field that is in the shape of a toroid around the coil. Note the current flow and magnetic field directions in all cases of the primary and secondary fields follow the right-hand rule.

if we think of placing our right hand around the current-carrying wire, with our thumb in the direction of current flow, then the direction of the magnetic field is in the same direction as our fingers point. We often call the directional lines that represent the magnetic field, lines of force. Maxwell's contribution was to modify Ampere's law to include time-varying EM fields (a changing electric field) along with conduction currents.

Ampere looked at induction from the point of view of the magnetic field caused by the flow of electric current and only perceived the phenomenon in terms of his concept of action-at-a-distance. Conversely, Michael Faraday turned the problem around and considered it from the perspective of the magnetic field. He developed the concept of lines of magnetic induction. Faraday's concept is the basis for our way of visualizing the magnetic field in terms of lines-of-force and flux-density. Faraday's law states that a moving magnetic field can change current flow in a conductor in a manner that is the converse of Ampere's law. The simplest experiment to demonstrate Faraday's law is to move a magnet through a loop of wire, as shown in Figure 6.2a. If a current-flow meter (Amp meter) is attached to the loop, then the current flow that is measured is proportional to how fast the magnet is moved through the loop. The current in the loop is called the induced current, and the moving magnet that is inducing the current is called an induced electromotive force. An analogous experiment utilizes two loops, as shown in Figure 6.2b, with current flowing through the loop on the

(a) Moving bar magnet inducing an electric current in a loop
(b) Current flow in right loop causes a magnetic field which induces current flow in the left loop

Source: current flow through wire cflooiwl through wire

Resulting inducing PRIMARY ,

MAGNETIC FIELD in space

Receiver: induced current flow through wire coil

Receiver: induced current flow through wire coil

SECONDARY MAGNETIC FIELD ? from "receiver" coil

SECONDARY MAGNETIC FIELD ? from "receiver" coil

(c) Current source causes magnetic field inducing a current flow in receiver coil

FIGURE 6.2 Principles of induction: (a) a magnet moving through a loop causes current flow in the coil;

(b) current generated in one wire loop causes a magnetic field that induces current flow in a second coil; and

(c) the combination of Ampere's and Faraday's laws as used in geophysical electromagnetic equipment. (Parts (a) and (b) modified from Halliday, D., and Resnick, R., 1960, Physics (parts I and II), John Wiley & Sons, New York. With permission.)

right-hand side of the figure caused by a battery. The right loop emits a magnetic field according to Ampere's observations, with the vector direction of the magnetic lines of flux governed by the right-hand-rule. The induced magnetic field propagates through the air and induces current to flow in the passive loop that is shown on the left-hand side of the figure. Figure 6.2c shows how these laws can be combined in a "source" and "receiver" arrangement, with the receiver "detecting" the EM field, as follows: (1) current flowing in the source coil creates a "primary" magnetic field, (2) flux lines from the primary field flow through the second coil on the right creating a flow of current in the second coil (called an induced current), and (3) the flow of current in the second coil, in turn, creates a "secondary" magnetic field. It logically follows that this secondary magnetic field can, in turn, create another secondary magnetic field that will induce another current flow in the source coil. This is called mutual coupling. It should also be noted that if the secondary coil is oriented perpendicular to the primary coil, then no current will be induced in the secondary coil. The vector nature of the EM field is often used to determine the maximum and minimum direction of the EM field by rotating the receiver coil.

So far in this discussion, we have only been concerned with static, or steady, fields (i.e., constant, or direct, current; magnetic moving at a constant velocity, or no acceleration, through the loop). If we consider that the field is time varying (e.g., and alternating, or AC current), then Faraday's law expressed as a time-varying magnetic field can be combined with Ampere's law to form the wave equation. We will not show the differential equations for these expressions, but they show that any time-varying EM energy (AC current, or sinusoidal magnetic field) will move (propagate) through time and space. The wave equation governs the propagation of all EM waves, including radio waves. There is also a mechanical analog of the EM wave equation for acoustic and seismic wave propagation.

Ampere's and Faraday's laws are the two fundamental laws for all of EM theory, and the governing principles for the EM induction geophysical method. The practical challenge for the geophysical interpreter is to visualize how this applies in the subsurface. We need to combine the principles of Faraday's and Ampere's laws, visualizing the EM field interacting with an object in the subsurface, as illustrated in Figure 6.3. The source, or EM transmitter, energized by a time-varying current, emits an EM field that propagates into the subsurface. If the EM field encounters a change in electrical conductivity, then a change in the EM field is induced in the object. The object-induced

FIGURE 6.3 Basic principle of geophysical induction. A primary electromagnetic field emitted from a transmitter propagates through space until it encounters a conductor. Eddy currents induced in the conductor radiate a secondary field that is measured at the receiver location.

Magnetic field from electromagnetic transmit

Magnetic field from electromagnetic transmit

FIGURE 6.3 Basic principle of geophysical induction. A primary electromagnetic field emitted from a transmitter propagates through space until it encounters a conductor. Eddy currents induced in the conductor radiate a secondary field that is measured at the receiver location.

secondary EM field propagates into the surrounding media. Some of the secondary EM energy (flux) is detected by an EM receiver on the surface. The receiver records both the primary field from the source and the secondary field from the object in the subsurface. These two signals must be separated in the electronics of an EM system.