用灵敏度和转换函数法评估电阻率和介电常数同时测量的不准确度
Inaccuracy Assessment for Simultaneous Measurements of Resistivity and Permittivity applying Sensitivity and Transfer Function Approaches
摘要：
本文提出了一种利用四极探头同时无创测量地下介质电阻率和介电常数的理论模型。基于灵敏度函数工具，对电阻率和介电常数测量中的误差传播进行了物理-物理模型分析。研究结果还比较了经典的频域分析方法的结果，这是有用的，用于确定零和极点频率的行为中的线性时不变（LTI）电路的四极。本文强调，电阻率和介电常数的平均值可用于估计各种地形和混凝土的复阻抗，特别是当它们的特点是低水平的水饱和度（含量）和分析范围内的带宽仅从低（LF）到中（MF）频率。为了满足设计规范，确保满意的性能的探头（不准确度不超过10%），由灵敏度函数的方法提供的预测是不那么严格的比那些预见的转换函数方法（在一个较大的频带f和电阻率或介电常数的更宽的可测量范围）。
英文摘要：
This paper proposes a theoretical modelling of the simultaneous and non invasive measurement of electrical resistivity and dielectric permittivity, using a quadrupole probe on a subjacent medium. A mathematical-physical model is applied on propagation of errors in the measurement of resistivity and permittivity based on the sensitivity functions tool. The findings are also compared to the results of the classical method of analysis in the frequency domain, which is useful for determining the behaviour of zero and pole frequencies in the linear time invariant (LTI) circuit of the quadrupole. The paper underlines that average values of electrical resistivity and dielectric permittivity may be used to estimate the complex impedance over various terrains and concretes, especially when they are characterized by low levels of water saturation (content) and analyzed within a bandwidth ranging only from low (LF) to middle (MF) frequencies. In order to meet the design specifications which ensure satisfactory performances of the probe (inaccuracy no more than 10%), the forecasts provided by the sensitivity functions approach are less stringent than those foreseen by the transfer functions method (in terms of both a larger band of frequency f and a wider measurable range of resistivity or permittivity).
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