Cross-hole resistivity inversion method constrained by prior information of incomplete boundary
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摘要: 跨孔电阻率CT方法是一种孔中精细化探测的方法。近年来,该方法在中小型地质异常（如溶洞、孤石等）探查方面取得了良好的应用效果。但是,作为一种直流电阻率法,其识别地质异常边界或界面的识别能力较差。通过钻孔、地震或者地质雷达方法,可以比跨孔电阻率CT方法更清楚的确定差异明显的岩性界面。从约束反演理论的角度出发,提出了不完整边界先验信息约束方法。首先依据地质雷达获得地质异常体的部分边界信息,定义从已知部分边界辐射的“虚拟内部区域”和“虚拟边界”虚拟边界的完整描述。通过设置具有“相同光滑度”的外部约束、“各向异性光滑度”的边界约束和“渐变光滑度”的内部约束,从而实现形态约束的构建。进一步的,将此先验信息约束融入跨孔电阻率CT反演方程中,形成了携带已知不完整边界信息的跨孔电阻率CT反演方法。然后,利用数值反演算例和孤石探测物理模型试验,检验了新方法的有效性和可行性。试验结果表明,新方法对异常体边界识别的效果得到明显改善。Abstract: The cross-hole electrical resistivity tomography method is a refined detecting method, and it has been well applied in the exploration of small and medium-sized geological anomalies such as caves and boulders. However, it’s poor in identifying the interfaces of geological anomalies. By geological drilling, seismic or ground penetrating radar methods,it is able to recognize the distinct lithological interface more clearly than the cross-hole electrical resistivity tomography. From the perspective of constrained inversion theory, a new cross-hole resistivity inversion method constrained by prior information of incomplete boundary is proposed. Firstly, the complete description of the "virtual internal region" radiated from the known partial boundary is defined, which is usually the interface of the geological anomaly detected by the ground penetrating radar. The construction of morphological constraints are then achieved by setting the external constraints with "same smoothness",boundary constraints of "anisotropic smoothness" and internal constraints of "gradient smoothness". Further, by adding these prior information constraints into the cross-hole resistivity inversion equation,the new inversion method carrying with known incomplete boundary information is formed. A numerical inversion test and a physical model test on detection of boulders are used to verify the effectiveness and feasibility of the new method. The tests results show that the new method has a significant improvement on the boundary recognition of the anomalous body.
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