Modifications of Schumann resonance spectra as an estimate of causative earthquake magnitude: The model treatment

Using a numerical model of the ELF radio wave scattering by seismogenic localized non-uniformity, we evaluate the earthquake (EQ) magnitude by using modifications in the power spectra of global electromagnetic (Schumann) resonance. The ionosphere non-uniformity is introduced as a disturbance in the vertical profile of atmosphere conductivity above the earthquake. Three types are considered of disturbance: the WHOLE, BOTTOM and TOP models, each depending on the EQ magnitude. The disturbance is axially symmetric; it varies along the radius according to the Gauss law with the scale corresponding to the EQ magnitude. The electromagnetic problem is solved by using the complex characteristic electric and magnetic heights relevant to conductivity profiles. These heights are found by solving the Riccati equation and are substituded into the two-dimensional telegraph equation (2DTE) for computing the vertical electric and two orthogonal magnetic fields in the Earth–ionosphere cavity. To avoid an impact of the field source coordinates, we apply the source model of independent lightning strokes uniformly distributed over the globe. The ionosphere non-uniformity is located above the North Pole, and the observer is positioned at the point of 63° N and 0° E, i.e., at 3 Mm distance from the disturbance. Comparison of power spectra in the regular and non-uniform cavities allowed us to single out their modifications at particular frequencies. Finally, equations are obtained connecting the EQ magnitude and the spectral modifications averaged over the frequency band covering four Schumann resonance modes. Computations indicate that reflections of radio waves from the localized seismogenic non-uniformity provide the noticeable impact when the EQ magnitude exceeds the M = 7 threshold. The BOTTOM model provides the highest impact on the Schumann resonance spectra, while the influence of the TOP model is the weakest one. The highest seismogenic effect exceeding the 20 dB level is observed in the meridional component HWE (the disturbance is found above the North Pole). Model data agree with available observations, and a further progress might be achieved in the case studies of particular EQs.