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.