Chapter 21, Problem 72RPP

BIO Magnetic induction tomography (MIT) Magnetic induction tomography is an imaging method used in mineral, natural gas, oil, and groundwater exploration, as an archaeological tool; and for medical imaging MIT has also been used to measure topsoil depth in agricultural soils. Topsoil depth is information that many farmers need for instance, corn yield is much higher in soil that has a deep topsoil layer above the underlying, impermeable claypan. Using a trailer attached to a tractor, a farmer can map an $\text{80}{\text{.000-m}}^{\text{2}}$

(about 20-acre) field for topsoil depth in about 1 hour.

Figure 21.28 shows how MIT works A time-varying electric current in a source coil (Figure 21.28a ) induces a changing magnetic field that passes into the region to be imaged—in this case, the soil (Figure 21.28b). This changing magnetic field induces a weak induced electric current in topsoil and a stronger induced current in the more conductive claypan soil at the same depth. (Figure 21.28c; the current direction here is drawn as though the source current and source fields are increasing) This changing induced electric current in turn produces its own induced magnetic field (Figure 21.28d ). The induced magnetic field passes out of the region being mapped to a detector coil (Figure 21.28e) near the source coil. The nature of the signal at the detector (its magnitude and phase) provides information about the region being mapped A strong signal returned to the detector coil indicates a claypan layer near the surface; a weak signal returns if the clay layer is deeper below the surface.

72 Describe all the changes that would occur if the source current were in the direction shown in Figure 21.28 but decreasing instead of increasing. a The induced current would be in the opposite direction.

b. The induced magnetic field would be in the opposite direction.

c. The detected current would be in the opposite direction.

d. a and b e a, b, and c