One-dimensional parallel forward modeling for geophysical electromagnetic fields excited by sagging overhead transmission lines

Geophysicists often regard the 50/60 Hz electromagnetic (EM) waves and their harmonics, excited by overhead transmission lines, as noise that interferes with geophysical prospecting. However, some researchers view them as effective signals for geophysical exploration. Forward modeling can be used to study the characteristics of EM fields generated by overhead transmission lines. It can help in either eliminating or utilizing power-frequency EM fields. Nevertheless, current research on the forward modeling of EM fields excited by transmission lines neglects the sagging shape and direction of the actual transmission lines, simplifying them into infinitely long straight lines. In this research, we develop a one-dimensional forward modeling algorithm specifically designed for overhead transmission lines, which can accurately calculate the EM fields excited by realistic overhead transmission lines considering the three-phase system, design parameters, sag, and orientation of the transmission lines. To construct an accurate transmission line model, we represent the sagging shape of a single transmission line within a span by a catenary equation. We then derive analytical expressions for the EM fields excited by sagging overhead transmission lines. During forward modeling, an appropriate number of Gauss points must be selected to balance accuracy and speed. The optimal number of Gauss points is determined based on the distance between the observation point and the transmission line source, as well as the type of fields being calculated. OpenMP parallelization is used to improve computational speed. The forward modeling results reveal significant differences between the forward responses of a single infinitely long straight line and realistic transmission lines. This highlights the importance of fully incorporating the three-phase system, design parameters, and geometric shapes of transmission lines in the forward modeling process. Moreover, the inversion test demonstrates the potential utility of EM fields radiated by transmission lines for geophysical exploration.