Computations Using Artificial Intelligence to deploy the Green's Function of the Spherical Layered Earth

Currently, there are considerable challenges associated with the theoretical derivation and numerical calculation of Green’s function for spherical layered earths. In order to study the coupling effect between wide-area interconnected systems and the earth, this earth model is widely used. Artificial intelligence methods have been applied in order to overcome these challenges. First, Green’s function in the form of infinite Legendre series is derived using intelligent symbolic operations, and the weight function of Legendre series is recursively computed by means of a recursive algorithm. It is on this basis that the intelligent complex image method has been developed for solving spherical layered Green’s functions, which transforms the summation of infinite series of Green’s functions into the superposition of complex image potentials. Additionally, the upper error limit of the algorithm has been determined, and examples have been provided to demonstrate the accuracy of the algorithm. A solution based on multiple precision algorithms has been proposed to resolve the numerical singularity problem and the extremely slow convergence of the spherical layered Green’s function at the earth’s scale. It has been demonstrated that the intelligent complex image method has advantages in terms of computing speed and accuracy. A spherical layered Green’s function at the earth scale is presented in this paper as an effective and intelligent solution.