Remote magnetic resonance sounding for exploration of pore space microstructure and aquifer macrostructure

Proton nuclear magnetic resonance is a type of nuclear magnetic resonance (NMR), which is widely used to detect hydrogen containing liquids, like water or hydrocarbons. The use of the Earth’s magnetic field allows remote detection of fluids sub surface without generating an independent magnetic field that is expensive and complex enough to apply. An important feature of NMR in the Earth’s field is that the signals produced by snow and ice are generally unobservable under experimental conditions created for liquid water prospecting. The characteristics of the RF response are associated with the molecular environment of the nuclei. This allows detecting NMR signals of water in pores of various size.


Introduction
Magnetic resonance sounding (MRS) is a direct method to detect aquifers, in contrast to conventional indirect geophysical methods, such as electrical exploration, seismic prospecting, etc. It has been proved that MRS in geomagnetic field can be applied to detect aquifers at depths up to 100 m and even deeper depending on the electromagnetic shielding provided by formations and the intensity of natural and anthropogenic electromagnetic noises [1][2][3]. The physical principle of this method implies detecting a resonance signal emitted as a result of the water proton spin magnetization. Macroscopic zones of aquifers are investigated through measurement of water proton nuclear magnetic relaxation (NMR) in geomagnetic field within rock pores and fractures. To excite the spins and receive the magnetic resonance signal, the antenna loop is laid out on the ground, in a circle of 100 m in diameter or in a figure-of-eight shape to minimize the effects of extraneous noises. A radiofrequency (RF) current 00 ( ) cos I t I t   is applied to the antenna thus producing alternating RF magnetic field in the space nearby. The frequency of oscillation is equal to the Larmor frequency of protons in the geomagnetic field. Due to resonance effect, nuclear magnetization vector is tilted away from its equilibrium direction alond the geomagnetic field and rotates around both the direction of the RF magnetic field and the geomagnetic field. After switching off of the excitation RF pulse, the magnetization precesses freely around the geomagnetic field direction. This precession induces alternating voltage in the same antenna thus producing the so called free nuclear induction signal. Magnetic resonance frequency in the geomagnetic field is several kilohertz, deadtime of measurement system is several milliseconds (Figure1.). The signal detected is produced by hydrodynamically mobile water molecules only. The water in very small pores of water-resisting rocks, e.g. clays, as well as crystallized, chemically bound, or frozen water, is characterized by shorter relaxation time, therefore, the signal is not detected after the system deadtime. The NMR amplitude is proportional to free-fluid index (i.e. movable fluid).

Bloch-Siegert effect in magnetic resonance sounding
If the water temperature is Т = 293 К, and geomagnetic field strength is , is applied. Interaction of nuclei (protons of water molecules) with external magnetic field, which is a sum of static geomagnetic field and RF field, , may be expressed in terms of spin Hamiltonian The Bloch-Siegert shift (Eq. 4) provides an additional rotation of nuclear magnetization around z axis within the rotating ( ,, x y z ) frame during pulse duration t p : where  is the angle between static Earth's 0 B  MRS method calibration with regard to Bloch-Siegert effect was conducted via experiments on ice covered Novosibirsk Reservoir (Figure 2). Ice thickness and water depth were measured directly via drilling holes in the ice, and were 1±0.05m and 11±0.5m, respectively. Antenna of 50 m radius was used both for RF field generation and for the signal detection. The geomagnetic field  was 74, proton resonance frequency was 2514 Hz (

MRS relaxation and screening mechanisms
The investigation of double dielectric screening of the MRS signal allows estimating the total dissolved diamagnetic solids content in groundwater without drilling. For example, in the half-space z > 0 with the uniform conductivity σ the magnetic field of the loop in the cylindrical frame has the form [1-3]: where R 0 is the antenna radius, 2 1/2 () u m i  , J 0 and J 1 are Bessel functions. Distribution of water concentration with depth may be determined by inversion of the integral equation with experimentally measured and modeled NMR signal dependent on excitation intensity [3]. Figure 5 shows a comparison between MRS results in geomagnetic field and drilling and logging data of borehole 37, Novosibirsk. The relaxation of the magnetization M that is proportional to the NMR signal is described using the Bloch-Torrey equations [5]: , , where D is the self-diffusion coefficient, T 1bulk and T 2bulk are the longitudinal and transverse relaxation times of bulk water.
The boundary conditions characterize the longitudinal (ρ 1 ) and the transverse (ρ 2 ) relaxivity on pore surface.
In resonance within rotating frame between RF-field pulses ∂U/∂t = D ∆U -i γ G z U (15), where G is the magnetic field gradient, U = M' x + i M' y .
If we assume the uniformity of fluid in pore space and fast diffusion, the solution for the relaxation times is as follows [6]: where S/V is the surface-to-volume ratio of pores, a is a core grain radius.
By the example of borehole 37 in Novosibirsk the spin-relaxation times were studied using twopulse sequences (Figure 6 Figure 6 illustrates the measurement of the homogenous spin-spin relaxation time T 2 equal to 220 ms via spin-echo method (the first pulse rotates the magnetization by 90 о , the second oneby 180 о ). In this case the free-induction decay time T 2 * is 60 ms. Figure 7 exemplifies the measurement of the spin-lattice relaxation time T 1 equal to 700 ms via inversion-recovery method (the first pulse rotates the magnetization by 180 о , the second one -by90 о ).