Using the multi-precision fast Hankel transformation to calculate the constant current field of wide-area layered earth

Abstract

The constant current field of wide-area layered earth has adverse effects on many industries. But it presents a high degree of numerical singularity, resulting in difficulty in solving. In this paper, the derivation of Green’s function and the fast Hankel transformation are presented based on the basic principle of linear filtering method for Green’s function of wide-area layered earth. A method of Multi-Precision Fast Hankel Transformation (MP-FHT) is proposed, which solves the problem of numerical singularity of integral kernel function in Green’s function by multi-precision algorithm, thus ensuring the accuracy of Hankel integral. The accuracy and reliability of the MP-FHT are proved by comparison of MP-FHT, commercial software CDEGS and improved version of high-order complex image method (HCIM). Compared with the existing algorithms, this method has high precision and low difficulty in algorithm implementation, which is a new method with high practical value.