关键词: 磁共振测深, T₂谱, 多指数分解, 不等式约束, 加权修正

Abstract:

The amplitude and relaxation time T₂ of magnetic resonance sounding (MRS) signal are directly related with water content and pore size of aquifers. Average T₂, 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 T₂ 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 T₂ 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 T₂ spectrum of MRS signal, and adding regularization and weighted correction to the method could improve the accuracy of T₂ spectrum inversion. Comparing to mono-exponential fitting, multi-exponential inversion can estimate the initial amplitude more accurately.

Key words: magnetic resonance sounding, T₂ spectrum, multi-exponential decomposition, inequality constraint, weighted correction