The fundamental assumption underlying the magnetotelluric (MT) method is that external source fields have wavelengths that are large compared to the fundamental length scale characterizing electromagnetic (EM) induction in the Earth—that is, the skin depth (e.g., Weidelt and Chave 2012). With the assumption of a quasi-uniform source, the impedance (transfer function, TF, relating electric to magnetic fields at a point on the Earth’s surface) is well defined and independent of the actual (large-scale) spatial structure of the source fields. Because EM induction in a conductor is a diffusive process, the impedance and other uniform source TFs used in MT (e.g., vertical magnetic field TFs) should be very smooth functions of frequency (Weidelt 1972). Indeed, excessively rapid variations in TF curves estimated from field data are often taken as evidence of source complications, most often due to relatively short-wavelength anthropogenic EM signals such as electric trains (e.g., Larsen et al. 1996; Egbert 1997; Egbert et al. 2000). Possible biases in MT TFs due to complications in naturally occurring external sources are also occasionally considered, but generally only at long periods (> 1000 s) and near the auroral or equatorial electrojets (e.g., Viljanen 2012, and references therein).
As part of the EarthScope USArray project (http://www.usarray.org/researchers/obs/magnetotelluric), long-period (~ 101–104 s) MT data have been acquired since 2006 in a series of short (20–30 day) deployments on a quasi-uniform 70 km grid. As of this writing, approximately 1000 sites across about half of the continental USA have been occupied (Fig. 1). A significant fraction of the impedances from this dataset displays unphysical “humps” that significantly deviate from the smooth trend of the TF over a narrow range of periods, typically much less than half a decade in width, between 10 and 100 s (Fig. 2). A conservative marking of sites where impedances clearly exhibit these unphysical features is shown in Fig. 1. A larger fraction of sites, perhaps as great as 15%, show at least some evidence for similar biases of smaller amplitude. The affected sites are most common in, or on the edges of, areas where the Earth is relatively resistive (Fig. 1). As increasing resistivity increases the skin depth and makes the quasi-uniform assumption easier to violate, this observation suggests that these humps reflect source bias. In this paper, we provide further evidence for this conclusion and demonstrate that short-wavelength natural sources associated with geomagnetic pulsations (Pc’s) can explain the observed biases.
The possibility that Pc’s, which in the ~ 10–100-s period band usually result from geomagnetic field-line resonance (and hence exhibit rapid variations meridionally), might violate the quasi-uniform source assumption has been discussed previously from a theoretical perspective by Pilipenko and Fedorov (1993, 1994). Our results demonstrate with a large collection of MT impedance estimates that such source effects can indeed cause problems for the MT method, at least in resistive areas.
The quasi-uniform source assumption in the magnetotelluric method
Mathematically, the external magnetic field satisfies the quasi-uniform source (“plane-wave”) assumption when the skin depth δ for induced currents is much less than the spatial scale of the source, i.e.,
$$\lambda \left( T \right) \gg \delta = \frac{{\sqrt {\rho T} }}{2}$$
(1)
where T is the period (in s) of the exciting source harmonic component; λ is the spatial wavelength (in km) of the source; and ρ is the electrical resistivity (in Ωm) of the region of the Earth in question.
For a one-dimensional Earth, a rigorous mathematical treatment is possible. Dmitriev and Berdichevsky (1979) showed that if the source magnetic field varies linearly over a distance of at least three times the skin depth, the local relationship between electric and magnetic fields will be nearly identical to that obtained with an exactly uniform source. (See also Wait 1954, 1982.) When there are lateral variations in resistivity, a rigorous analysis is not possible, and there is some evidence that source effects may be stronger (e.g., Egbert and Booker 1989). Nonetheless, the fundamental physical intuition remains the same: the inducing external magnetic field should not vary significantly over length scales that are several times the skin depth in the Earth.
Geomagnetic pulsations and field-line resonances
In the ~ 10–100-s period band, geomagnetic pulsations are a dominant component of the geomagnetic power spectrum measured on the Earth’s surface (e.g., McPherron 2005). These signals originate beyond the magnetosphere (in the foreshock, bowshock, and/or magnetopause) as ULF hydromagnetic waves that propagate into the magnetosphere through a variety of mechanisms (Hughes 1994; Clausen et al. 2009; Menk 2011). Within the magnetosphere, these hydromagnetic disturbances can excite standing Alfvén waves along geomagnetic field lines (Hughes 1994). A single field line can be pictured as a forced, damped harmonic oscillator (Waters et al. 1991), with the amplitude of the response greatly enhanced at the natural resonant frequency of the field line. (See Additional file 1: Fig. S1 for a graphical summary.) Although this model of field-line resonance (FLR) is very simple, it explains many observed characteristics of Pc’s (Hughes 1994).
FLRs drive electrical currents in the ionosphere at the ends of the field lines (McPherron 2005). Ionospheric Pedersen currents (parallel to driving electric field) cancel out the magnetic field of the FLRs, thereby screening their direct signature at the Earth’s surface, but east–west ionospheric Hall currents (perpendicular to driving electric and magnetic fields) produce electromagnetic radiation that is observed on the ground as dominantly north–south magnetic oscillations (McPherron 2005). The FLR signature at the Earth’s surface is therefore the result of ionospheric screening processes (Hughes and Southwood 1976; McPherron 2005). Because geomagnetic field lines have distinct resonant frequencies, the resulting magnetic disturbances observed on the ground are nearly monochromatic and highly sinusoidal; they are therefore identified as a type of continuous pulsation (Pc). Pulsations associated with FLRs are generally in the Pc3-4 band (~ 10–150 s) (McPherron 2005).
The resonant period of geomagnetic field lines depends on the length of the field line, the magnetic field strength along the field line, and the plasma density along the field line (Hughes 1994; Waters et al. 2006; Menk 2011). Field-line length increases with geomagnetic latitude, so the fundamental FLR period generally increases geomagnetically poleward. Because magnetic field strength and plasma density are highly dynamic, the FLR period fluctuates in time; for example, daily variations in plasma density cause daily variations in FLR period (Poulter et al. 1988).
On the Earth’s surface, the width of a given FLR is of order 100 km (Hughes 1994; Menk 2011; Chi et al. 2013). As can be seen from the simple harmonic oscillator model of an FLR as well as from more complex theoretical and empirical treatments, amplitudes will be enhanced over a limited range of latitudes centered on the main resonant field line (several hundred kilometers), and there will be a 180° phase shift moving geomagnetically north–south through this zone (Waters et al. 1991; Hughes 1994; Chi and Russell 1998; Kawano et al. 2002; see also Additional file 1: Fig. S1). Although large-scale magnetospheric perturbations (fast-mode compressional waves) are also observed on the ground in this same period range (Kawano et al. 2002; Chi et al. 2013), when FLRs are excited, their effects typically dominate the total incident field at the Earth’s surface (Ádám et al. 2005). Therefore, near the (latitude-dependent) resonant frequency, the total source magnetic field can vary rapidly over only a few hundred kilometers in the geomagnetic north–south direction. Where the Earth is in bulk moderately conductive (~ 100 Ωm), from Eq. 1 the skin depth at an FLR period of 30 s will be ~ 30 km, still relatively small compared to Pc source wavelengths. However, if the Earth is in bulk relatively resistive (~ 1000 Ωm or more), the skin depth at 30 s will be ~ 90 km or more, comparable to source wavelengths expected for Pc’s. More resistive Earth or a longer-period FLR will make the skin depth an even larger fraction of the spatial scale of the Pc’s. Clearly, over resistive Earth the quasi-uniform source assumption of the MT method can be violated in the Pc3-4 band.