CAJ | 학술논문

磁共振地下水探测信号的弛豫时间 T 2和振幅与地下岩石孔隙大小和地下水的含水量直接相关。目前，磁共振地下水探测方法中，信号的衰减特性由平均弛豫时间 T *2来描述。然而，对于复杂的多孔介质组成的岩石结构，仅由 T *2无法准确描述地下孔隙情况。详细研究了基于不等式约束的多指数分解法，进行了信号 T 2谱的提取，并重新计算多指数形式下的信号初始振幅。结果表明：对比信号在不同采集时间下的 T 2谱提取结果，延长信号的采集时间有助于 T 2谱的准确提取；通过磁共振仿真信号计算并分析不同信噪比下的 T 2谱提取结果，信噪比大于30 dB 时相对误差平均值小于5％；进行算法改进，得到信噪比大于10 dB 时相对误差平均值小于5％的结果，且幅值和 T 2的相对误差平均值降低了约1/3。由此可知：采用多指数分解法能够获得磁共振信号的 T 2谱，正则化技术和加权修正能够提高 T 2谱的准确度和抗干扰能力；与单指数方式相比，采用多指数拟合能够更准确地恢复信号初始振幅。
자공진지하수탐측신호적이예시간 T 2화진폭여지하암석공극대소화지하수적함수량직접상관。목전，자공진지하수탐측방법중，신호적쇠감특성유평균이예시간 T *2래묘술。연이，대우복잡적다공개질조성적암석결구，부유 T *2무법준학묘술지하공극정황。상세연구료기우불등식약속적다지수분해법，진행료신호 T 2보적제취，병중신계산다지수형식하적신호초시진폭。결과표명：대비신호재불동채집시간하적 T 2보제취결과，연장신호적채집시간유조우 T 2보적준학제취；통과자공진방진신호계산병분석불동신조비하적 T 2보제취결과，신조비대우30 dB 시상대오차평균치소우5％；진행산법개진，득도신조비대우10 dB 시상대오차평균치소우5％적결과，차폭치화 T 2적상대오차평균치강저료약1/3。유차가지：채용다지수분해법능구획득자공진신호적 T 2보，정칙화기술화가권수정능구제고 T 2보적준학도화항간우능력；여단지수방식상비，채용다지수의합능구경준학지회복신호초시진폭。
The amplitude and relaxation time T 2 of magnetic resonance sounding (MRS)signal are directly related with water content and pore size of aquifers.Average T 2 ,denoted by T *2 ,is often used to describe the decay characteristic of MRS signal.However,in the case of porous media rock,pore size should be described by T 2 spectrum of MRS signal.To obtain the spectrum and estimate the initial amplitude more accurately,we studied multi-exponential decomposition method based on inequality constraint in this paper.Numerical results show that extending signal length helps the accuracy of T 2 spectrum estimation.With traditional method,average relative error is less than 5% when SNR is greater than 30 dB.With our modified algorithm,a SNR about 10 dB could lead to the same error. meanwhile,the error of the estimated amplitude is reduced by at least 1/3.It can be concluded that multi-exponential decomposition method could obtain T 2 spectrum of MRS signal, and adding regularization and weighted correction to the method could improve the accuracy of T 2 spectrum inversion.Comparing to mono-exponential fitting,multi-exponential inversion can estimate the initial amplitude more accurately.