多频电磁波测井数据的反演成像技术及应用

针对测井数据反演成像问题的不适应定性，采用了带不等式约束的正则化最小二乘迭代反演，模型响应的正演计算用有限元方法实现，模型响应对电阻率及介电常数的偏导数用格林函数和互换原理计算，对高低频电磁波测井数据的反演分两步进行，首先用低频数据得到电阻率的大致分布，再以此为初值，用高频电磁波数据同时反演电阻率和介电常数，通过对模型的数值模拟和某地热田1口井的实际资料的应用表明，电磁波测井数据的反演厉像能给出井周近旁介质的电性参数分布，而在离井较远的区域不能得到稳定可靠的解释结果，无论高频还是低频测井数据，要得到高质量的成像结果，工作频率的适当选择及接收器灵敏度的提高是至关重要的。

An Imaging Method to Inverse Multi-frequency Electromagnetic Logging Data and Its Application

Electromagnetic logging is one of the most efficient methods in evaluating electric and dielectric properties of formation. The paper studied an imaging method of inversing the multi-frequency electromagnetic logging data and its application in formation evaluation. It is assumed that formation is axis symmetric in respect of borehole axis, and a vertical magnetic dipole on the borehole axis is selected as a field source. With regarding to the ill-posedness of logging data inversion, the normalized least-square iterative inversion method is adopted with the inequality constraints. The forward modeling is implemented by finite element method. The partial derivatives of the electromagnetic responses with respect to resistivity and dielectric parameter are calculated by using Green function based on reciprocity principle. With respect to the high and low frequency electromagnetic logging data, the inversion is implemented in two steps:first, the low frequency data is used to obtain the rough distribution of resistivity, and then, the distribution is taken as an initial value, the resistivity and dielectric parameter are obtained simultaneously by inverting the high frequency data. Through application to numerical modeling and field data from one geothermal well, it is clarified that inversion of the electromagnetic logging data can provide appropriate images of electric parameters of medium near the borehole, whereas in the area far away from the borehole, we can not obtain a stable interpretation result. Whether it is high or low frequency data, if we hope to get a high quality image, it is very important to select appropriate working frequency and use high sensitive sensor.