Time causal operational estimation of electric fields induced in the Earth's lithosphere during magnetic storms

Abstract

In support of projects for monitoring geomagnetic hazards for electric power grids, we develop a simple mathematical formalism, consistent with the time causality of deterministic physics, for estimating electric fields that are induced in the Earth's lithosphere during magnetic storms. For an idealized model of the lithosphere, an infinite half‐space having uniform electrical conductivity properties described by a galvanic tensor, we work in the Laplace‐transformed frequency domain to obtain a transfer function which, when convolved with measured magnetic field time series, gives an estimated electric field time series. Using data collected at the Kakioka, Japan observatory, we optimize lithospheric conductivity parameters by minimizing the discrepancy between model‐estimated electric field variation and that actually measured. With our simple model, we can estimate 87% of the variance in storm time Kakioka electric field data; a more complicated model of lithospheric conductivity would be required to estimate the remaining 13% of the variance. We discuss how our estimation formalism might be implemented for geographically coordinated real‐time monitoring of geoelectric fields.

Reproducing electric field observations during magnetic storms by means of rigorous 3-D modelling and distortion matrix co-estimation

“…We want to note that the issue of estimating the distortion matrix at a geomagnetic observatory was recently also addressed by Love and Swidinsky (2014). In contrast to us, the authors employed a local approach, i.e.…”

“…However, both studies can reliably reproduce the measured time series of both E x and E y . Indeed, Love and Swidinsky (2014) state that they can reproduce 87% of the measured variations (although it is not entirely clear from the description how this value is calculated). We reach coefficients of determination of 76% for E x and 81% for E y .…”

Observatory geoelectric fields induced in a two-layer lithosphere during magnetic storms

“…Optimal parameters (#4 in Table 1) for the two-layer model leave a misfit residual of only ε 2 = 0.0686; this means that the model accounts for 93% of the variance in the 2003 Halloween storm 1-s Kakioka E m data. These results are an improvement over those of Love and Swidinsky (2014), whose minimal half-space model accounted for 87% of the variance in the Kakioka electric field data for the Halloween storm but where high-frequency variation was not as well estimated. Still, even with the two-layer model presented here, some small residual signal remains, much of which varies over an approximate diurnal timescale.…”

“…A model with just two horizontal layers is a reasonable incremental extension of the half-space model considered by Love and Swidinsky (2014). For this, the C-function at the Earth's surface reduces to:…”

“…7), previously used by Love and Swidinsky (2014) in their analysis of storm-time induction. From these observations, we recognize that induction within the top layer modifies induction within the lower half-space, but the total inductive effect is not simply an additive superposition: T R 0 depends on both σ 1 h 1 and σ 2 , while H R 0 only depends on σ 2 .…”