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在计算水平层状地层上由电、磁偶极子产生的电磁场分量的公式中,涉及一积分限为无穷大的积分。其被积函数是两个函数的乘积。一个称为核函数,它和地电断面的参数、频率及积分常数λ有关,在数字滤波计算中被视为输入函数。另一个是不同阶数的第一类贝塞耳函数。由于它们具有振荡性质且衰减很慢,故用数值方法求这一积分是很费时间的。在用数字滤波方法时,这一部分构成数字滤波器系数。由于此滤波器系数只与装置的类型有关,不随地电断面的性质变化,故对各种装置只需计算一次,因而,使用起来比较方便。与数字积分方法相比,数字滤波方法大约可以提高功效四倍。本文包括三部分内容:第一部分总结了文献中用数字滤波器计算垂直磁偶极子场的方法;第二部分给出了利用已有的数字滤波器计算水平电偶极子的电场;第三部分介绍具体实现步骤及计算结果的对比。
The formula for calculating the component of the electromagnetic field produced by the electric and magnetic dipoles on a horizontal stratigraphic formation involves the integration of an integral limit to infinity. The integrand is the product of two functions. One is called the kernel function, which is related to the parameter, frequency and integral constant λ of the geoelectric section, and is regarded as the input function in the digital filter calculation. The other is the first order Bessel function of different order. Because of their oscillatory nature and slow decay, it is time-consuming to find this point numerically. In the digital filtering method, this part constitutes the digital filter coefficients. Since the filter coefficient is only related to the type of device, it does not change with the nature of the electrical section, so it only needs to be calculated once for each device. Therefore, it is more convenient to use. Compared with the digital integration method, digital filtering method can improve the efficiency of about four times. This paper includes three parts: the first part summarizes the literature using digital filters to calculate the vertical magnetic dipole field method; the second part gives the use of existing digital filters to calculate the horizontal electric dipole electric field; the third The part introduces the concrete realization steps and the comparison of calculation results.