“…In other cases, the most significant physical property variations may conform to a cylindrical geometry, for example in settings where vertical metallic well-casings are present, or in the emerging topic of using geophysics to "look ahead" of a tunnel boring machine. In particular, understanding the behavior of electromagnetic fields and fluxes in the presence of steel-cased wells is of interest across a range of applications, from characterizing lithologic units with well-logs (Kaufman, 1990;Kaufman and Wightman, 1993;Augustin et al, 1989), to identifying marine hydrocarbon targets (Kong et al, 2009;Swidinsky et al, 2013;Tietze et al, 2015), to mapping changes in a reservoir induced by hydraulic fracturing or carbon capture and storage (Pardo and Torres-Verdin, 2013;Börner et al, 2015;Um et al, 2015;Weiss et al, 2016;Hoversten et al, 2017;Zhang et al, 2018). Carbon steel, a material commonly used for borehole casings, is highly electrically conductive (10 6 − 10 7 S/m) and has a significant magnetic permeability ( ≥ 100 µ 0 ) (Wu and Habashy, 1994); it therefore can have a significant influence on electromagnetic signals.…”