Electromagnetic Acquisition & Conductivity PDF

introduction¶ Fig. 138 Scales of electromagnetic aquisition¶ EM methods have played an important role in mineral exploration and engineering problems since at least the early 1960s. A plethora of EM systems have been designed over the years, varying in size, source functions and receiver-transmitt...

introduction¶ Fig. 138 Scales of electromagnetic aquisition¶ EM methods have played an important role in mineral exploration and engineering problems since at least the early 1960s. A plethora of EM systems have been designed over the years, varying in size, source functions and receiver-transmitter configurations. The great variety of surveys is reflective of the scalability EM methods. As illustrated in Fig. 138, EM data can be acquired at the centimeter scale (mine tunnels, structures), to meters (ground survey) to kilometers (airborne). While the instrumentation may differ in shape and name, they are all based on the same basic principals of EM induction. The generic electromagnetic (EM) survey is summarized in Fig. 139. The energy source is either an electric field or changing magnetic field. The physical property of interests are magnetic permeability, electrical permitivity and conductivity. The data can also be either electric or magnetic field values. Fig. 139 A general electromagnetic survey¶ Conductivity¶ Electromagnetic methods are sensitive principally to electrical conductivity 𝜎 (Siemens/meter). We sometimes work with the inverse of conductivity which is electrical resistivity 𝜌 which has units Ω𝑚 (ohm- meters). Electrical conductivity characterizes the ease that current flows through the material when an electrical force is applied. Electric current (units of Amperes) quantifies the amount of charge that is moving by an observer in one second. The electrical conductivity of Earth’s materials varies over many orders of magnitude. It depends upon many factors, including: rock type, porosity, connectivity of pores, nature of the fluid, and metallic content of the solid matrix. A very rough indication of the range of conductivity for rocks and minerals is presented in Fig. 140. Fig. 140 Rough ranges of conductivities¶ While conductivity is the generally the main physical property of interest, EM induction methods also depend on the magnetic permeability and electrical permitivity of rocks. Their importance depends upon the frequency of the EM signal used for given a system. Electromagnetic survey methods are based on two fundamental principles: Faraday’s law of electromagnetic induction and the fact that electric currents generate magnetic fields, expressed in Ampère’s law. In its simplest form Faraday’s law states that the electromotive force (EMF) in a closed circuit is proportional to the rate of change of magnetic flux through the circuit, or in even simpler terms: a changing magnetic field will induce an EMF. The magnetic flux 𝜙𝐵 which crosses a closed loop is given by → ^ → 𝜙𝐵 = ∫ 𝐵 ⋅ 𝑛𝑑𝑎 𝑎𝑟𝑒𝑎 where 𝑛^ is the outward pointing normal vector for the loop and 𝐵→ is the magnetic flux density, which is proportional to the magnetic field in free space. This is illustrated in the diagram below Faraday’s law relates the magnetic flux through the surface bordered by the loop to the induced EMF in the loop 𝑑𝜙𝐵 𝑉=−. 𝑑𝑡 𝑉=−𝑑𝜙𝐵𝑑𝑡. Recall that the current 𝐼 flowing in the wire is related to the EMF through Ohm’s law 𝑉 = 𝐼𝑅, where 𝑅 is the electrical resistance of the circuit. We can start to develop an intuition about Faraday’s law using the example of a permanent magnet moving through a coil of wire. The electric field generated by the moving magnet creates an electric force on the charges in the wire, causing current to flow. 1. The voltmeter only registers a signal when the magnet is moving, regardless of its absolute position. 2. The sign of the induced voltage changes depending on the direction of motion and orientation of the magnet 3. The magnitude of the voltage depends on how quickly the magnet is moving 4. All else being equal, the voltage induced in the four coil loop is larger than in the two coil loop. Lenz’s Law:The direction of the induced current in Faraday’s law is such that its magnetic field opposes the change in flux. That is, nature does not like changing magnetic fields. This is the reason for the minus sign in Faraday’s law. The following video from the Technical Services Group at MIT’s physics department shows Lenz’s law in action. The magnetic fields of various current sources¶ The shape of the magnetic field due to an electric current in a wire depends on the shape of the wire. The magnetic field of a closed loop source will be approximately that of a perfect magnetic dipole when observed far enough from the loop. A good rule of thumb is that we can use the dipole approximation when the distance from the loop is more than five times its diameter. Put mathematically, the approximation holds when 𝑟>>𝑎 where 𝑟 is the distance from the observer to the center of the loop and 𝑎 is the radius of the loop. The magnetic moment from a loop is 𝑚→=𝐼𝐴𝑛^, where 𝐼 is the current in the loop, 𝐴 is its area, and 𝑛^ is the unit vector perpendicular to the plane of the loop. In this course we will consider frequency domain transmitters. These are transmitters driven by a harmonic current, that is, a current that varies sinusoidally in time. The magnetic field of a dipole is given by the magnetization multiplied by a geometric factor, which implies that the primary magnetic field due to the transmitter will be harmonic in time: 𝐻→𝑝=𝐻→0cos⁡(𝜔𝑡). Circuit model for EM induction¶ Consider the goal of using an inductive EM source to locate a conductive body buried in a relatively non-conductive (also called resistive) host material. The basic picture is shown in Fig. 143. Fig. 143 : Conceptual diagram for three loops¶ Eddy currents are generated in the buried body by changing magnetic flux passing through the body. We can learn a lot about the coupling between the transmitter, buried body and receiver by approximating the buried body by a wire coil with resistance 𝑅 and inductance 𝐿. The resistance approximates the electrical resistivity of the earth and the inductance is a geometrical quantity that depends on the shape of the loop. The following discussion of the circuit model will be mostly conceptual. For a more detailed and quantitative discussion please see the em.geosci resource–(not required for eosc 350. Transmitter and primary field¶ In this course we will consider small loop transmitters with current varying sinusoidally in time. These are known as harmonic or frequency domain transmitters. We will only consider transmitters small enough that the primary magnetic fields they generate are approximately dipolar, as illustrated in figure Fig. 141 above. Electromagnetic induction transmitters operate over range of frequencies— roughly 101 Hz - 104 Hz. Note that this is a much lower frequency band than is used in GPR surveys, which can range from 106 Hz - 109 Hz. Receiver¶ The receiver is most often also a wire coil The voltage recorded in the receiver coil will be proportional to the rate of change of magnetic flux through the loop. One could also measure the magnetic field directly using a magnetometer but this is not common practice. Coupling between transmitter and buried loop¶ Recall that current is only generated in a loop by the normal component of the changing magnetic flux passing through it. The magnetic flux is vector quantity. The closer the direction of the primary magnetic flux is to the normal of the buried loop, the better the coupling, as illustrated in figure Fig. 144 below Fig. 144 : Couppling effects.¶ Measured responses¶ The basic understanding of the different coupling between the source and receiver that is due to geometry allows us to sketch the expected responses that arise from a frequency domain horizontal loop survey taken over a conductor which is buried in a resistive host. This is a two-stage process. 1. Use the geometries of the source and receiver to sketch the characteristic curve. 2. Use the response diagram and the knowledge of whether you are dealing with a good conductor or poor conductor to determine the relative amplitude of the in-phase and out-of-phase parts. Part I: Consider the basic geometry shown in the figure below here is a time-varying magnetic field due to the transmitter passing through the buried loop and hence induced currents in the buried loop. Those currents generate secondary magnetic fields. The primary field is shown in grey in the left-hand image and the secondary field due to that transmitter is shown in red on the right. Note that the primary and secondary fields point in opposite directions as they pass through the receiver loop. We adopt the convention that if the secondary field is in the same direction as the primary field then the response will be plotted as a positive value. Alternatively, when the two fields are in opposition the response will be negative. The distance between the transmitter and receiver loops is held fixed and the-datum is plotted at the midpoint between the coils. When both loops are to the left, or to the right, of the buried loop then the response is positive. The response will be zero when either coil is over the buried loop. When the receiver, which is a horizontal coil, is over the loop, then no magnetic flux is passing through the coil. There will be zero voltage induced. When the transmitter is directly over the buried loop, there is no flux crossing the loop, hence no currents will be generated in it and the secondary magnetic field is zero. Part II: The basic sketch for the shape of the anomalous signal is determined from the geometry of the coils and the relative locations of transmitter, receiver and the conductive body. In practice we measure both an in-phase and an out-of-phase component. Each of these curves will have the same general shape as the one plotted above. We need only establish their relative amplitudes. From the general response curve we find that the in-phase (or real component) is larger than the out-of-phase (imaginary) component when 𝜔𝜎 (or 𝜔𝐿/𝑅) is large. Below we plot the responses for a survey taken over a buried loop Because the body is conductive and the frequency of the survey is high, the value of 𝜔𝐿/𝑅 is large and the in-phase response is larger than the quadrature response.