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Magnetic Resonance Sounding (MRS)

A Joint Project of USGS, U.S. Environmental Protection Agency Region 5,
and Bureau de Recherches Géologiques et Minières (BRGM), France

Geophysical Applications of Magnetic Resonance Sounding (MRS)

Surface proton magnetic resonance sounding (MRS), or nuclear magnetic resonance (NMR), measurements can be used to indirectly estimate the water content of saturated and unsaturated zones in the earth's subsurface. MRS is used to estimate aquifer properties, including quantity of water contained in the aquifer, porosity, and hydraulic permeability.

A typical MRS survey is conducted in three stages, as shown in the diagram below. First, the ambient electromagnetic (EM) noise is measured.  Then, a pulse of electrical current is transmitted through a cable on the surface of the ground, applying an external EM field to the subsurface. Finally, the external EM field is terminated, and the magnetic resonance signal is measured.

Diagram of Three Stages of Typical MRS Survey
Ambient Electromagnetic Field	Electromagnetic Pulse	Magnetic Resonance Signal

Three parameters of the measured MRS signal are:

• Amplitude (E₀), which depends on the number of protons and hence on the quantity of water.
• Decay time (T*₂), which generally correlates with the mean size of the pores in water-saturated rocks. This is important for aquifer characterization.
• Phase (j₀), which is measured in the field and is used for a qualitative estimation of the electrical conductivity of rocks.

For examples of Surface MRS applications, see the following:

• Example of MRS work in Arizona
• Example of MRS work in Connecticut
• Example of MRS work in Massachusetts

Magnetic Resonance Sounding Theory 

MRS is based on the principals of nuclear magnetic resonance in bulk matter and is a method that uses the macroscopic magnetism of a large number of atomic nuclei to obtain information about their physical and chemical environment (Lieblich and others, 1994). The method is based on the magnetic moment of a single atomic nucleus (nuclear paramagnetism), which is caused by a nonzero spin angular momentum. When placed in a static magnetic field, a macroscopic sample containing many such nuclei develops a macroscopic magnetism aligned with the static magnetic field. This macroscopic magnetization is the vector sum over all individual nuclear magnetic moments but is conveniently described by the magnetic moment per unit volume, which is the product of the nuclear magnetic susceptibility and the static field vector.

Incident electromagnetic (EM) energy at the Larmor frequency can be absorbed by the nucleus. Upon absorption of a unit of incident energy, the magnetic moment vector is deflected from its equilibrium position in the static magnetic field, reflecting the changed energy state of the nucleus. 

If the incident EM field is then rapidly extinguished, the nuclear precession about the static field can be measured. Decay of the net magnetization vector, after deflection from its equilibrium position, is exponential and can be described by two characteristic times: T₁ (the spin-lattice or longitudinal relaxation time) and T₂ (the spin-spin or transverse relaxation time). T₁ is the time required for the macroscopic magnetization vector to regain thermal equilibrium with the static field. T₂ is the time required for the component of the macroscopic magnetization vector perpendicular to the static field to decay to zero; this decay is caused by the dispersal of individual magnetic moment vectors away from the expected direction of the macroscopic magnetic moment vector in a homogeneous field. Because of the dispersal of individual magnetic moments, the magnitude of an induced electromotive force in a coil oriented (for example) perpendicular to the static field direction will decay at a rate that is faster than the characteristic time T₁, for undispersed moments.

Because g has a specific value for each nuclei, the Larmor frequency is a physical property of the nuclei.
g is 2p x 4.254597x10^-2 = 0.2675 radians per second per nano-Tesla (rad/s/nT) for protons in water molecules.

The empricial method used in determining the permeability of a formation is then based on the following relationship:
k = C_k(fT₁*²)
where
 k is permeability;
 C_k is a permeability constant based on pumping tests in France;
 f is porosity; and
 T₁* is the longitudinal decay time constant.

For more information on this method, see the following references:

Abragam, A., 1961, The Principles of Nuclear Magnetism: Oxford University Press, 648 p.

Legchenko, A., Baltassat, J-M., Beauce, A., and Bernard, J., 2002, Nuclear magnetic resonance as a geophysical tool for hydrogeologists: Journal of Applied Geophysics, v.50, no.1-2, p. 21-46.

Legchenko, A., and Valla, P., 2002, A review of the basic principles for proton magnetic resonance sounding measurements: Journal of Applied Geophysics, v.50, no.1-2, p. 3-19.

Lieblich, D.A., Legchenko, A., Haeni, F.P., and Portselan, A.A, 1994, Surface nuclear magnetic resonance experiments to detect subsurface water at Haddam Meadows, Connecticut, in Bell, R.S., and Lepper, C.M., eds., Symposium on the Application of Geophysics to Engineering and Environmental Problems, Boston, Massachusetts, March 27-31, 1994, Proceedings: Englewood, Colorado, Environmental and Engineering Geophysical Society, p. 717-736.

Pake, G.E., 1993, Nuclear magnetic resonance in bulk matter: Physics Today, v.46, p. 46-51.