This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY 1 Lightning Electromagnetic Fields and Their Induced Currents on Buried Cables. Part I: The Effect of an Ocean–Land Mixed Propagation Path Javad Paknahad, Keyhan Sheshyekani, Senior Member, IEEE, and Farhad Rachidi, Fellow, IEEE Abstract—We use a full-wave finite-element-based solution of Maxwell’s equations for the evaluation of lightning electromag- netic fields inside a vertically stratified, two-layer ground (ocean– land mixed propagation path) and their induced currents on the shield of buried cables. For “normal” incidence (with respect to the ocean–land interface), it is shown that the vertical electric field is the component most affected by the ocean–land mixed path when the observation point is close to the ocean–land interface (i.e., 5 m or so). For “oblique” incidence, however, depending on the angle of incidence and the distance between the observation point and the ocean, all the field components are reduced by the ocean–land interface. For the calculation of induced currents, and for the case of a parallel layout (cable laying in parallel to the ocean–land in- terface); 1) for a strike to the land, when the cable is buried in the soil and the distance to the ocean is greater than about 100 m, the effect of the ocean is negligible. 2) For a strike to the ocean, the induced current magnitudes are appreciable only when the cable is entirely within the land. For the case of a perpendicular layout (cable perpendicular to the ocean–land interface); 1) for a strike to the ocean, when the cable is totally buried in the ocean, the effect of ocean–land mixed propagation is negligible. However, when the cable extends into the land through one end, the induced currents increase at both ends with increasing length of underland portion. 2) For a strike to the land, when the cable is located entirely inside the land, the effect of ocean–land mixed path on the induced cur- rents at both ends is negligible. However, as the cable extends into the ocean, a remarkable enhancement in the induced currents is observed for the termination located inside the land. This enhance- ment can be as high as a factor of 2 with respect to the case of a cable in homogeneous soil characterized by the properties of the land. Index Terms—Cable modeling, finite-element method (FEM), induced currents, lightning electromagnetic fields, ocean–land mixed propagation path. I. INTRODUCTION T HE evaluation of lightning electromagnetic fields above and inside horizontally and vertically stratified grounds has been the subject of many investigations (e.g., [1]–[7]). For Manuscript received December 19, 2013; revised February 28, 2014; accepted March 6, 2014. J. Paknahad and K. Sheshyekani are with the Department of Electrical and Computer Engineering, Shahid Beheshti University, Tehran 1983963113, Iran (e-mail: javadpaknahad@gmail.com; k_sheshyekani@sbu.ac.ir). F. Rachidi is with the ´ Ecole Polytechnique F´ ed´ erale de Lausanne, Lausanne 1015, Switzerland (e-mail: farhad.rachidi@epfl.ch). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEMC.2014.2311923 a horizontally stratified ground, different approaches have ad- dressed the problem of the evaluation of lightning electromag- netic fields above [1]–[6], and inside the ground [7]. As far as identified by previous studies, stratified ground might have a significant effect on the lightning electromagnetic fields. There- fore, this effect can be important in the evaluation of the associ- ated lightning-induced voltages and currents on nearby overhead lines and buried cable. More recently, the effect of a horizontally stratified ground on the induced voltages on overhead lines and induced currents on buried cables has been partially investigated in [8] and [9]. In many practical situations, such as in offshore wind farm generating units where power cables are used as interarray ca- bles to connect the turbines within the wind farm, the buried cables crosses two different media (ocean–land mixed path or vertically stratified ground) characterized by different electrical properties. As known, the protection of cables against electro- magnetic transient surges caused by indirect lightning is of great importance as these surges significantly contribute to the cable aging and insulation breakdown [10]. This requires first, an ac- curate evaluation of the lightning electromagnetic fields inside a vertically stratified ground. Even though the effect of a vertically stratified ground on the above-ground lightning electromagnetic fields has been investigated in some studies (e.g., [11]–[13]), to the best of our knowledge, no effort has been made to study the effect of ocean–land mixed propagation path neither on under- ground electromagnetic fields nor on the induced currents on cables buried in a mixed propagation path. Within this context, this paper focuses on the analysis of the effect of a vertically stratified ground on the lightning radiated electromagnetic fields inside the ground at different distances from the lightning channel base as well as on their associated induced currents on buried cables. To this aim, we present a full- wave approach, which is based on the finite-element method (FEM) solution of Maxwell’s equations. Note that the effect of a horizontally stratified two-layer ground on the underground lightning electromagnetic fields and their induced currents on the shield of buried cables will be addressed in the companion paper (Paknahad et al., 2014). This paper is organized as follows. In Section II, we present briefly the full-wave finite-element modeling for the calcula- tion of lightning electromagnetic fields and induced currents. In Section III, the effect of a vertically stratified ground (ocean– land mixed propagation path) on the lightning electromagnetic fields inside the ground is discussed. Section IV evaluates the ef- fect of ocean–land mixed propagation path on lightning-induced 0018-9375 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.