Two-Dimensional Whole Space Transient Electromagnetic Forward Response of Magnetic Moment in Arbitrary Direction

Abstract

In the two-dimensional Cartesian coordinate system, a transient electromagnetic forward algorithm of the magnetic moment in arbitrary direction is developed to simulate the electromagnetic response characteristics of the whole space geoelectric model. The magnetic moment <inline-formula> <tex-math notation= LaTeX >${\\mathbf {M}}_{r}$ </tex-math></inline-formula> in arbitrary transmitting direction is decomposed into <inline-formula> <tex-math notation= LaTeX >${\\mathbf {M}}_{x}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation= LaTeX >${\\mathbf {M}}_{y}$ </tex-math></inline-formula>. The transient electromagnetic fields excited by the magnetic moments <inline-formula> <tex-math notation= LaTeX >${\\mathbf {M}}_{x}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation= LaTeX >${\\mathbf {M}}_{y}$ </tex-math></inline-formula> are forwarded separately, and then synthesized to obtain the electric field excited by the magnetic moment <inline-formula> <tex-math notation= LaTeX >${\\mathbf {M}}_{r}$ </tex-math></inline-formula>. The time domain iteration’s results of the uniform whole space are compared with the analytical solutions to verify the correctness of algorithm. The comparison results show that the algorithm is reliable and can be used for whole space transient electromagnetic simulation in an arbitrary direction. The forward response of the magnetic moment in an arbitrary transmitting direction removes the shortcomings of the traditional two-dimensional whole space transient electromagnetic simulations where the magnetic moment can only be in the horizontal or vertical direction. The program code can be used for the forward response of other two-dimensional whole space geological mining models. It is of great significance to study the two-dimensional transient electromagnetic diffusion characteristics of different geological models by the sector sweeping method.