铬污染土壤复电阻率数学模型参数反演

为使复电阻率探测方法在铬渣污染场地探测领域取得应用，需要建立土壤的复电阻率模型，包括模型选择及参数反演. 矩阵实验室(Matrix Laboratory，Matlab)的优化工具箱提供了基于置信域方法的最小二乘曲线拟合求解算法，为优化方法在工程中的实际应用提供了更方便、更快捷的途径. 在大量土壤样品复电阻率实测数据基础上，采用置信域方法并结合各模型的参数约束，反演了Cole-Cole模型的参数. 结果表明:基于置信域方法的最小二乘曲线拟合求解算法可以准确求取复电阻率模型参数，但前提是必须提供较精确的初始值；与使用复电阻率幅值和相位的联合反演相比，单独考虑幅值或者相位的反演也能够取得相近的效果. 

Parametric Inversion on Complex Resistivity Mathematic Model of Chrome-Contaminated Soil

In order to promote the application of the complex resistivity detection method in the field of chrome-contaminated soil detection, a soil complex resistivity model should be established, which involves the adoption of a suitable model and its parametric inversion. The Optimization Toolbox of Matlab, including the least-squares curve-fitting method based on Trust-Region methods, provides a more convenient way for the actual application of optimization. Based on data obtained from a great deal of tests, the parameters of Cole-Cole Model were inverted by Trust-Region methods combined with constraint parameters. The results show that precise complex resistivity parameters can be obtained with the least-squares curve-fitting method based on Trust-Region methods under the condition that the initial value is provided precisely. Compared with union inversion of amplitude and phase, similar results can be obtained with the single inversion of amplitude or phase.