Efficient numerical Bloch solutions for multipulse surface NMR

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