基于自旋回波探测的地面磁共振T2谱正反演策略

作为新兴地球物理方法之一,地面磁共振技术具有直接探测优势.但由于其发展时间较短,相关建模及反演方法介绍较少,传统的自由感应衰减探测方法不仅精度有限,且适应性较差.近年来,应用自旋回波信号直接探测横向弛豫时间是地面磁共振领域的研究热点.本文推导了其灵敏度核函数及正演公式,引入线性空间反演方案,即通过奇异值分解将含噪自旋回波信号由时间域变换至空间域.为避免矩阵病态问题,采用奇异值滤波法抑制分解病态程度,并联合同时迭代重建技术进一步提升空间域矩阵求解精度.结合非线性拟合对空间域矩阵参数进行提取,实现含水层对应含水量、横向弛豫时间的有效估计.通过模拟野外实验并进行数据解释,证实了该方案能够有效降低浅层含水量至1.5%,横向弛豫时间估测误差至0.02 s.本文的研究成果,将为地面横向弛豫时间探测及相关理论发展及方法在水文地质调查方面的推广应用提供有力支撑.

A modeling and inversion method of spin echoes to measure magnetic resonance sounding transverse relaxation time in surface applications

Surface magnetic resonance sounding(MRS)has generally been considered to be an efficient tool for hydrological investigations.As is well known,the effective relaxation time T₂^* which characterizes the decay rate of MRS free-decay-induction(FID)signal and is used to measure pore-scale properties,is particularly limited for several special cases(e.g.areas with magnetic rock subsurfaces).Recent years,the transverse relaxation time T₂obtained from spin-echo signal was adopted to implement the surface MRS,and showed great potentials for estimating the porosity and permeability.However,owning to the short period of development,the related modeling and inversion strategies are rarely introduced and summarized.Actually,the general practice for surface MRS T₂measurement fits the spin-echo by the exponential function and the fitting line was directly used as the FID signal for inversion.This scheme not only limits the precision of interpretation,but also loses part of valid information about original field data.Aiming at these problems,in this paper,we introduce the calculation of forward model and thus a two-stage framework with singular value decomposition(SVD)linear inversion involved is derived to quantify the T₂distributed with depth.Considering the fact that the inversion result of SVD is always strongly affected by the noise level,an improved method which combines the simultaneous iterative reconstruction technology(SIRT)with SVD is proposed.To be specific,we compare the measurement schemes with kernel functions between T₂and the original theory in MRS,and then provide the forward and inversion formulations.In order to substantiate the effectiveness of this method,we conduct the synthetic experiments for Carr-Purcell-Meiboom-Gill sequence and explain the dataset with the mentioned strategies.As expected,the combined approach possesses a better performance in shallow layer with an error of 1.5%and 0.02 s for water content and T₂for the contaminated data,respectively.With these advantages,it is expected to realize the adoption of the SVD with SIRT in field applications and further investigate the aquifer characterizations in the future.