Efficient numerical Bloch solutions for multipulse surface NMR

Abstract

Simplified solutions of the Bloch equation can lead to inaccurate estimates of hydrogeological parameters from surface nuclear magnetic resonance measurements. Even for single pulse measurements, using simplified forward models is common practice because of the computational intensity of obtaining the full-Bloch solution. These challenges are exacerbated for multipulse sequences. We show parallelizing the full-Bloch solver on a Graphics Processing Unit reduces the solve time by three orders of magnitude. Further optimizations by numerical, analytical and hybrid solutions yield an additional 3× speed up. We simulate the full-Bloch physics for free-induction decay, spin-echo and pseudo-saturation recovery excitation schemes for an unprecedented range of physical scenarios. We explore the time-dependence and relaxation time sensitivity in these solution spaces. Characterizing the solution spaces with polynomials of the relaxation times, the solutions can be rapidly reproduced; a technique known as fast-mapping. By fitting these higher dimensional solution ensembles with polynomials, the original fast-mapping technique is extended to include T₁ at arbitrary times. Accuracy of the 7th order polynomial is such that a minimum 96 per cent of the models are within a ±3 per cent relative error. This permits the rapid reproduction of full-Bloch solutions with a matrix multiplication and opens up surface NMR to time-series based inversion of single and multipulse data.