分层多指数磁共振弛豫信号反演方法研究

磁共振测深技术传统反演方法包括平滑反演和分块反演,通过分别获取初始振幅和平均弛豫时间构建地层含水量及有效孔隙度.然而,这些方法局限于单指数拟合方式,损失了大部分有效采集信息,受限于多孔地质环境解释,并在某些情况下无法刻画含水层清晰分界面.针对上述问题,本文建立了基于MRS全数据的多指数反演方法,依据全部采集时间下的有效信息,通过弛豫时间e指数分解,推导出新的磁共振正演核函数,结合泛函极小值方程,直接反演建立含水量,弛豫时间及地层深度三个重要参数关系,适用于复杂地质环境解释.为得到快速稳定的反演结果和更清晰的含水层分界面,本文借鉴分块反演思想,进一步构建了新的反演目标函数,利用基于不等式约束的空间信赖域算法进行优化,最终实现了一种基于分层反演与多指数结合的磁共振弛豫信号反演方法.模型数据以及实测算例表明该方法的效果和优势,并具备较高的计算效率,本研究为地面磁共振反演提供了一种新的思路与方法.

Layered multi-exponential inversion method on surface magnetic resonance sounding dataset

Smooth inversion and block inversion are two main methods for surface magnetic resonance sounding (MRS) at present, which can construct water content and average effective pore size of aquifer through initial amplitudes and mean relaxation times, respectively. However, these inversion methods are limited in porous geological environment and in some case the interface of aquifers can not be portrayed clearly due to the loss of valid information during mono-exponential fitting. Aiming at these problems, we studied multi-exponential inversion method, which is found to solve inversion problem on the basis of MRS signal inherent multi-exponential behavior, by taking the entire MRS signal datasets into account in this paper. The multi-exponential MRS inversion of porous geological environment was realized through decomposing the relaxation time, deducing a new magnetic resonance forward kernel function and then calculating the functional minimum equation, which directly estimates the partial water content distribution and thus provides both the water content and relaxation time depth distribution. In order to get the fast and stable result, layered inversion model is referenced and the optimized inversion is proposed based on inequality constrain of the trust region algorithm. The inversion examples for synthetic data and field data from Baicheng city Sifangtuozi show that this method is better than smooth inversion and block inversion. We can get more accurate water content distribution and depict porous geological structure with high efficiency of inversion calculation. This paper confirms that the inversion has properties of accuracy, applicability and extensibility, which provide a new thought and method for surface magnetic resonance sounding.