Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems

The general theory of nuclear magnetic resonance (NMR) imaging of large ele ctromagnetically active systems is considered. We emphasize particularly no ninvasive geophysical applications such as the imaging of subsurface water content. We derive a general formula for the NMR response voltage, valid fo r arbitrary transmitter and receiver loop geometry and arbitrary conductivi ty structure of the medium in which the nuclear spins reside. It is shown t hat in cases where the conductivity is large enough such that the electroma gnetic skin depth at the Larmor frequency is of the same order or smaller t han the measurement depth, there are diffusive retardation time effects tha t significantly alter the standard NMR response formula used in the literat ure. The formula now includes the full complex response, the imaginary part of which has previously been observed but not modeled. These differences a re quantified via numerical investigation of various effectively one-dimens ional model inverse problems with a horizontally stratified nuclear spin an d conductivity distribution. It is found that inclusion of the imaginary pa rt of the response significantly stabilizes the inversion. Large quantitati ve differences are found between conducting and insulating cases in physica lly relevant situations. It is shown also that the diffusive long time tail of the signal may be used to infer the distribution of time constants T-1, normally not mensurable in geophysical applications. Although in present a pplications the signal due to this tail is immeasurably small, this relatio nship may become useful in the future.