Exact(7)
This assumes a single frequency independent factor, α = 0.27, relating the size of the primary to associated induced coefficients corresponding to an insulator overlying an infinitely conducting layer (Langel and Estes, 1985) at depth of 1200 km.
There are no constant or linearly dependent induced coefficients but c m are defined in the same way as b3,m.
The scheme is based on the analysis of time spectra of the internal (induced) coefficients of the SHE of the magnetic potential due to magnetospheric sources.
Given the resistivity ρ (r), and the source model, the forward solution is integrated from the initial condition, (7 to provide a time series of induced coefficients.
There is generally excellent coherency for the external coefficients (coh2 well above 0.95) and good coherence (coh2 > 0.8) for the induced coefficients, in particular for periods shorter than one month or so.
Details of the method, which involves Fourier transform of external field coefficients, evaluation of transfer matrices at discrete frequencies, and their spline interpolation in the frequency domain, and finally inverse Fourier transform of the induced coefficients back to time domain with 1 hr step, are given in Olsen and Kuvshinov (2004) and Kuvshinov and Olsen (2005).
Similar(53)
The impact of the fabrication tolerance induced coupling coefficients error on the figure of merits of the filter is considered.
Figure 9 shows squared-magnitude coherence (coh2) between the input and the estimated time series for external (red) and induced (blue) coefficients corresponding to Nmax = 3 and Mmax = 1.
A necessary condition for this approach is the determination of the time series of these and the corresponding external (inducing) coefficients.
Time series of internal and external (inducing) coefficients, whose determination is a prerequisite for this formulation, will be available as a Swarm Level-2 data product.
An ion bomdarment induced mixing coefficient is derived and experimentally evaluated for vanadium in silica.
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