Keywords:conductivity, magnetic storm
We estimated radial electrical conductivity distribution in the Earth using both vector geomagnetic observatory data and a forward solver in time-domain. The major difference between the time-domain and frequency-domain approach rests in the way of processing the finite-length time series of transient inducing and induced fields. In the frequency-domain, response functions are usually estimated at discrete frequencies, by splitting the time-series into multiple segments and applying Fourier transformation to each segment. As the periods increase, quality of response functions is reduced in the case of the frequency-domain approach. In addition, the frequency-domain approach should not be applied to the transient data since Fourier transformation premises periodicity for the time-series in concern. On the other hand, the time-domain approach exploits all the data in the time-series by fitting the entire waveform of the magnetic field including rapid variations such as sudden storm commencements. The quality of long period signals that are able to penetrate the deeper region of the Earth is not reduced in the time-domain. We can, therefore, estimate the deep distribution of conductivity using shorter time-series than in the frequency-domain. Specifically, we applied the time-domain approach to the vector geomagnetic observatory data with one minute sampling interval all around the globe. In order to extract the induced field, we subtracted the vector average for 5 quietest days of the month from the raw time-series. Contrary to the newly available data sets from recent low-Earth-orbiting satellite missions, the traditional ground-based data has biased distribution over the globe. We eliminated observatories in some congested places. We then separated the residual time-series into internal and external origin. The separated internal magnetic field can be reproduced using forward response of the radially symmetric conducting sphere to the separated external magnetic field. A heterogeneously conducting shell was placed at the top of the radially symmetric sphere so as to account for large scale surface contrast such as ocean-continent distribution. We solved an inversion problem with an objective function consisting of linear combination of data misfit and a regularization term that constrains the smoothness of the conductivities. Moreover, we estimated the internal Gauss coefficients' sensitivities for each shell of the radially symmetric conducting spheres by F-test and revealed that the lower mantle conductivity has a large influence on the magnetic field on the surface of the Earth after about more one day from the instance when the external magnetic field was applied. As a result, we estimated a conductivity profile of the Earth. This is the first profile that was estimated by a combination of inversion in time-domain and the vector geomagnetic observatory data over the globe. We will further discuss the necessary length of time-series in order to estimate the lower mantle conductivity accurately.