  Electromagnetic methods are increasingly being applied in settings with steel
infrastructure. These include applications such as monitoring of CO2
sequestration or even assessing the integrity of a wellbore. In this paper, we
examine the impacts of the magnetic permeability of a steel-cased well on
electromagnetic responses in grounded source experiments. We consider a
vertical wellbore and simulate time and frequency domain data on 3D cylindrical
meshes. Permeability slows the decay of surface electric fields in the time
domain and contributes to a phase shift in the frequency domain. We develop our
understanding of how permeability alters currents within, and external to, the
casing by focussing first on the time domain response and translating insights
to the frequency domain. Following others, we rewrite Maxwell's equations to
separate the response into terms that describe the magnetization and induction
effects. Magnetic permeability impacts the responses in two ways: (1) it
enhances the inductive component of the response in the casing, and (2) it
creates a magnetization current on the outer wall of the casing. The
interaction of these two effects results in a poloidal current system within
the casing. It also generates anomalous currents external to the casing that
can alter the geometry and magnitude of currents in the surrounding geologic
formation. This has the potential to be advantageous for enhancing responses in
monitoring applications.
