Numerical simulation of the electromagnetic field in layered media applicable to high-frequency scenarios

In geophysical exploration, the expression of the electromagnetic field in homogeneous layered media involves Hankel integrals, and the kernel function can be simplified into a combination of zero- and first-order Bessel functions. Owing to the complex nature of the electromagnetic field, only a few analytical expressions for the Hankel integrals of the electromagnetic field in layered media exist. Moreover, as the argument of the Bessel functions increases, the Hankel integrals exhibit rapid oscillations and slow decay, making it difficult for the computation of the electromagnetic field to achieve high accuracy, especially for high-frequency and long-range transmission and reception scenarios. To address this issue, we propose a fully analytical integration method applicable to both high and low frequencies and long and short transmission and reception distances. The study used quadratic function interpolation for the coefficient part of the Hankel integrals in the expression of the electromagnetic field in layered media. The interpolated results within each element, multiplied by the Bessel functions, could derive analytical expressions. Then, by summing up all the discrete elements, the numerical solution of the Hankel integrals could be obtained, resulting in a high-precision numerical simulation of the layered media. The fully analytical integration algorithm was tested using the expressions of the electromagnetic field in the entire space with different forms of Bessel function integrals. The computational results demonstrated the correctness and high accuracy of the algorithm. The proposed algorithm exhibited high computational accuracy in different frequency ranges and transmission and reception distances, especially in high-frequency and long-distance scenarios, where its accuracy exceeds that of the four selected digital filtering algorithms by over two orders of magnitude, indicating its strong universality..