三维井地电阻率法有限差分数值模拟研究

Research on Finite-difference Numerical Simulation for 3-D Borehole-to-ground Resistivity Survey

井地电阻率法是在井中供电地表测量的一种方法。在井地电阻率法电法实际工作中电流源通常采用点状电流源和线状电流源,其中点状电流源适用于裸眼井中供电的情况,而线状电流源则适用于套管井供电的情况。结合野外实践工作,主要研究以下几个方面并得到了相应的结论:(1)电流源为点状时,针对电流源分别在异常体的上面、里面和下面3种模型进行正演数值模拟计算,结果表明地表的视电阻率响应变化很大;(2)电流源为垂直线源时,针对电流源分别在异常体的上部、延伸至异常体中间以及贯穿异常体3种模型进行正演数值模拟计算,结果表明地表视电阻率响应的幅值变化逐渐变大;(3)电流源为倾斜线源时,线源倾斜角度不断加大对应地表视电阻率的影响较大,随着线源倾斜角的加大,地表响应的幅值变小。这些结论为野外工作中设置井地电法仪器参数以提高其观测精度提供了理论依据,为初步判断异常体的埋深做出定性的分析,同时为井地电法三维反演奠定了基础。

Borehole-to-ground resistivity survey is a geophysical method by which an electric current is injected from the borehole,and is received on the ground with different kinds of power supplied.Usually,in the field through the borehole-to-ground resistivity,the current source is divided into point current source injected from the bare hole and the linear current source injected from the cased borehole.Based on the practical work in the field,this paper studies the following aspects and obtains the corresponding conclusions：（1） when the current source is point current,the results of three forward models（the current source above,inside and under the anomalous body）,show that the apparent resistivity response on the surface varies greatly;（2） when the current source is a vertical line source,the results of three forward models（current source in the upper part of the anomalous body,extending to the middle of the anomalous body,as well as throughout the anomalous body）,show that the apparent resistivity response amplitude changes gradually on the surface;（3） when the current source is inclined line source,the tilt angle of the line source has great effect on the apparent resistivity response on the surface,and the larger of the angle of inclination of the line source is,the smaller magnitude of the surface response is.These conclusions provide a guidance for field work by setting parameters of the apparatus in order to improve the accuracy of their observations,and make a qualitative analysis for the preliminary judging the depth of the anomalous body,and lay a solid foundation for the three-dimensional inversion of the borehole-to-ground resistivity as well.