电磁响应的互换原理及其在响应灵敏度计算中的应用

：在众多地球物理参数中，电阻率是评价储层含油气性的重要参数之一，利用电磁测量数据求取地下介质的 电阻率分布，是电磁测量数据处理和解释的基本任务。然而，由于电磁数据反演处理中，要求多次计算电磁响应 对电磁参数的灵敏度，计算量巨大，使电磁数据反演在实际测量资料中的应用受到限制。实际上，电磁响应灵敏 度的有效计算决定了电磁测量数据反演的精度和速度。从基本的Ｍａｘｗｅｌｌ方程出发，证明了电磁响应的互换原 理，并导出了基于互换原理的灵敏度计算方法。同时，利用调和方程方法推导出了电场和磁场对电导率灵敏度 的计算公式，分析了两者的等价性。借助单元块模型，利用波数域单个犓狔计算结果的对比及空间域多个波数 的积分结果的对比，证实了电磁场互换原理的灵敏度计算公式及调和方程计算公式的有效性和等价性。

Reciprocity of electromagnetic response and its application in sensitivity calculation

Resistivity is one of the most important parameters in evaluating water saturation among the other petrophysical parameters.It is a fundamental task to determine the resistivity distribution from electromagnetic measurements.In the inversion of electromagnetic data,we have to perform forward modeling and derivative calculation of the electromagnetic responses to resistivity or conductivity repeatedly.The process takes up formidable computing costs,which limits its use in field electromagnetic data processing.In fact,the computation of derivatives of the electromagnetic responses to resistivity largely determines the accuracy and efficiency of the inversion process.In this paper,the reciprocity of electromagnetic response between transmitter and receiver was validated mathematically on the basis of Maxwell equation.By using of the reciprocity of electromagnetic response,we have derived the sensitivity equation of the electromagnetic response to conductivity.We also derived an alternative sensitivity equation of electromagnetic response based on adjoint equation.The equality between the two equations has been analyzed through the reciprocity.In the numerical simulation on a single block,two kinds of sensitivity equations have been applied to evaluate the derivatives of electric and magnetic fields to conductivity.The effectiveness and equality of the two equations have been verified through the comparison of two numeric results.