Fast computation of Hankel Transform using orthonormal exponential approximation of complex kernel function

Journal of Earth system science

Neeta Chaudhary2¹  Pravin K Gupta1²  Sri Niwas1² 

[1] Oil and Natural Gas Corporation, Priyadarshini Building, Sion, Mumbai, India.$$;Department of Earth Sciences, Indian Institute of Technology Roorkee, Roorkee 247 667, India.$$

关键词: Electromagnetic response;    exponential approximation of kernel function;    Hankel Transform.;   

DOI  :  

学科分类：天文学(综合)

来源: Indian Academy of Sciences

【 摘 要 】

The computation of electromagnetic (EM)fields,for 1-D layered earth model,requires evaluation of Hankel Transform (HT)of the EM kernel function.The digital filtering is the most widely used technique to evaluate HT integrals.However,it has some obvious shortcomings.We present an alternative scheme,based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals.This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature.This expansion reduces the integral to a simple algebraic sum.The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated.The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method.The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital filtering technique with Anderson filters.The field curves for four types (A-,K-,H-and Q-type)of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson scheme.It is concluded that the present scheme is more accurate than the Anderson scheme.

【 授权许可】

Unknown