不同装置下点源球体的近似解与精确解对比

针对利用简单加倍的方法求解点源球体解析解的局限性,采用双球坐标系,通过镜像法求解点源下球体的精确解,将其与简单加倍求得的近似解进行对比,给出了简单加倍方法的适用条件,从而在实际中能够更准确地使用简单加倍的方法.研究结果表明:对于二极装置,当球心埋深h≤1.5r0时,利用简单加倍方法求得的近似解与精确解的误差已达到10％以上；对于中梯装置,当球心埋深h≤1.7r0时,二者的误差达到10％；二极装置的视电阻率曲线随着极距AM的增加会出现反向异常的现象,且极距越大,反向异常越明显.

Comparison of approximate solution and exact solution of buried sphere model at point source with different arrays

In order to overcome the limitation of general method for the problem of a buried sphere with point source,based on bispheroid coordinate system,the exact solution was solved by image method.Through comparing the exact solution with approximate solution,the using condition of approximate solution was achieved and the general method could be better used in practice.The results show that the error between exact solution and approximate solution is more than 10% when the depth of sphere is less than 1.5r0 and being measured with pole-pole array.The error is more than 10% when the depth of sphere is less than 1.7r0 and being measured with schlumberger array.With the increase of electrode distance,the phenomenon of reversed anomaly appears in apparent resistivity curves of pole-pole array and the bigger the electrode distance is,the more obvious the phenomenon is.