快速汉克尔变换及其在正演计算中的应用

The fast hankel transformation and its applications in forward calculations

在地球物理电(磁)法正演计算中常涉及贝塞尔函数积分,快速汉克尔数字滤波是最常用的计算方法之一.然而不同的汉克尔滤波系数,计算结果的精度也有所差异.本文对比了五组高精度快速汉克尔长滤波系数的计算精度,分析了不同核函数对计算精度的影响;同时将五种滤波系数应用于电阻率测深法、频域电磁测深法、瞬变电磁测深法的正演计算中,比较了不同滤波系数对响应和视电阻率模拟时精度的变化关系.经过大量的模型计算表明:滤波的精度并不单纯的只与滤波系数个数有关,而是多种因素综合作用的结果.本文的研究对于电(磁)法正演计算汉克尔滤波系数的选择具有指导作用,有利于节省计算机资源,提高计算效率.

In the forward calculation of active source electrical exploration methods,usually encounter the problem of the bessel integral calculations.Since fast Hankel transform being introduced in geophysical field,there have generated a lot of fast hankel filter coefficients. Different coefficients have different lengths and accuracy.This paper is a research about the the fast Hankel theory and application in electromagnetic exploration methods. Five groups coefficients with highprecision are selected,their accuracy are discussed,and being applied to the resistivity sounding method, frequency electromagnetic sounding method and transient electromagnetic sounding method,programming for many models,and calculate the response curves and apparent resistivity curves.On the analysis of the difference between curves,we know that the choose of coefficients is complicated,this research provide some advices about the selection of hankel coefficients in forward calculations.