Spin dynamics of Carr-Purcell-Meiboom-Gill-like sequences in grossly inhomogeneous B0 and B1 fields and application to NMR well logging

The spin dynamics for Carr-Purcell-Meiboom-Gill-like sequences is analyzed in grossly inhomogeneous B-0 and B-1 fields. This problem is important for many applications, especially when the bandwidth of the signal is excitation limited. Examples include stray-held NMR or inside-out NMR probes used in well logging. The amplitudes of the first few echoes exhibit a characteristic transient behavior but quickly approach a smooth asymptotic behavior. For simple Hamiltonians without scalar or dipolar couplings, the evolution of a refocusing subcycle for a given isochromat is described by a rotation. Simple expressions for the signal of the Nth echo are derived in terms of these effective rotations that have a simple geometrical interpretation. It is shown that the asymptotic behavior is controlled by the direction of the axis of these effective rotations and the signal is dominated by magnetization "spin-locked" to the rotation axis. The phase of the signal is independent of the details of the held inhomogeneities. Relaxation in inhomogeneous fields leads to a signal decay that is in general nonexponential with an initial decay rate that is a weighted sum of T-1(-1) and T-2(-1). At long times, the echo amplitudes decay to a finite value. Phase cycling eliminates this offset. The effect of diffusion is also studied. This analysis has been applied to an inside-out NMR well logging apparatus. Good quantitative agreement is found between measurements and calculations that are based on the measured B-0 and B-1 field maps. (C) 2000 Academic Press.