风化基岩含水层含水率与弛豫参数的磁共振测深聚焦反演方法

Magnetic resonance sounding focusing inversion method for volumetric water content and mean relaxation time of weathered bedrock aquifers

  • 摘要: 陕北浅埋煤层开采中,风化基岩含水层富水性的准确评估对于水害防治工作至关重要。针对磁共振测深(Magnetic Resonance Sounding,MRS)传统平滑约束反演中含水层顶底界分辨率不足、单位体积含水率(w)与平均弛豫时间( T_2^* )不准确,以及由此引发的导水系数估算偏差较大问题,提出基于最小梯度支撑(Minimum Gradient Support,MGS)正则化的全包络信号聚焦反演方法。在迭代重加权最小二乘(IRLS)框架中引入MGS正则化,分别对w与 T_2^* 构造聚焦约束,形成含先验权重可选的混合目标函数。引入动态权重更新机制,在每次迭代中利用模型参数的梯度信息构造聚焦权重矩阵,控制w与 T_2^* 的分层能力。线性子问题采用预条件共轭梯度法高效求解,并以投影算子施加物理可行域约束。聚焦因子β控制分层程度,β较小增强界面聚焦,β较大退化为平滑约束。通过对比MGS反演与平滑约束反演结果,优选聚焦因子β。数值模拟表明,MGS反演显著增强了对w与 T_2^* 的分层刻画,对于风化基岩层含水层模型,w值的相对偏差约6%(平滑约束约20%),含水层上下界可准确分辨。红柳林矿区实测资料对比表明,依据含水率梯度确定的含水层顶底界,MGS的定位误差约14.1%,显著低于平滑约束的43.6%以及Samovar商用软件反演的34.4%;基于Seevers模型,由MGS反演结果计算的导水系数与抽水试验结果相比的偏差约31.35%,相较平滑约束与Samovar软件分别改善约15%与47%。基于MGS的聚焦反演可显著提升含水层边界分辨能力与w、 T_2^* 参数反演精度,间接提升基于Seevers模型计算的导水系数准确性。聚焦因子β是控制反演分层能力与平滑性的关键,如何更智能、稳健地选择β是下一步的研究重点。目前MRS在煤矿领域的应用较少,研究给出了红柳林煤矿风化基岩含水层的MRS实测数据与反演结果。实测信号清晰反映了地下水体产生的NMR信号的衰减特征,基于MGS反演的结果与同位置抽水试验结果吻合性较好,说明MRS在煤矿水害探查领域的应用潜力值得进一步开发。

     

    Abstract: Accurate evaluation of the water-bearing capacity of weathered bedrock aquifers is essential for water hazard prevention in shallow coal seam mining in northern Shaanxi. To address the limitations of conventional smoothness-constrained inversion in Magnetic Resonance Sounding (MRS), including insufficient resolution of aquifer boundaries, inaccurate estimation of volumetric water content (w) and mean relaxation time ( T_2^* ), and the consequent large deviations in hydraulic conductivity estimation, a full-envelope signal focusing inversion method based on Minimum Gradient Support (MGS) regularization is proposed. Within the framework of Iteratively Reweighted Least Squares (IRLS), MGS regularization is introduced to impose focusing constraints on w and T_2^* , forming a hybrid objective function with optional prior weighting. A dynamic weight updating mechanism is employed, in which a focusing weight matrix is constructed from the gradient information of model parameters at each iteration to control the layering capability of w and T_2^* . Linear subproblems are efficiently solved using the preconditioned conjugate gradient method, and a projection operator is applied to impose physically feasible bounds. The focusing factor β governs the degree of stratification. A smaller β enhances interface focusing, while a larger β reduces to smoothness constraints. The optimal β is determined by comparing the results of MGS inversion with those of smoothness-constrained inversion. Numerical simulations demonstrate that MGS inversion significantly improves the stratigraphic characterization of w and T_2^* . For the weathered bedrock aquifer model, the relative error of w is approximately 6% compared with about 20% for smoothness constraints, and the upper and lower aquifer boundaries can be clearly resolved. Field data from the Hongliulin coal mine indicate that, when aquifer boundaries are determined by water content gradients, the positioning error of MGS is about 14.1%, much lower than 43.6% for smoothness constraints and 34.4% for the commercial Samovar software. Based on the Seevers model, the hydraulic conductivity calculated from MGS inversion results deviates by about 31.35% from pumping test values, representing improvements of approximately 15% and 47% compared with smoothness-constrained inversion and Samovar, respectively. MGS-based focusing inversion markedly enhances the resolution of aquifer boundaries and improves the inversion accuracy of w and T_2^* , thereby indirectly increasing the reliability of hydraulic conductivity estimation using the Seevers model. The focusing factor β is a key parameter controlling the balance between stratification capability and smoothness, and more intelligent and robust strategies for selecting β will be the focus of future research. At present, the application of MRS in coal mines remains relatively limited. This study presents measured MRS data and inversion results for the weathered bedrock aquifer of the Hongliulin coal mine. The measured signals clearly capture the decay characteristics of NMR responses generated by groundwater, and the inversion results show good consistency with pumping test data from the same location, suggesting that the application potential of MRS in coal mine water hazard investigation warrants further development.

     

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