The Scaling Law of The Near-Field Coseismic Ionospheric Disturbances

Coseismic ionospheric disturbances (CIDs) appear shortly after relatively large earthquakes as a result of ionospheric irregularity associated with passing atmospheric waves excited by the earthquakes. CIDs appearing approximately 10 minutes after earthquakes are caused by acoustic waves generated by coseismic vertical movements of the crust or the sea surface, and they propagate as fast as ~1 km/second over the distance of hundreds of kilometres. Here we collected past examples of CID detected in Total Electron Content (TEC) by GPS observations for 21 earthquakes 1994-2012 distributed worldwide. Their moment magnitudes (Mw) range from 6.6 to 9.2, and include two normal fault earthquakes that occurred in the outer rise region of the trenches (2007 January central Kuril earthquake, and 2012 December Tohoku-oki earthquake), and two strike-slip earthquakes (the main shock and the largest aftershock of the 2012 North Sumatra earthquakes). The rest are all reverse-fault earthquakes. We tried to select the pair of GPS satellite and station showing the largest CID amplitudes. Due to the directivity, the ionospheric piercing point (IPP) of line-of-sight (LOS) should be on the southern/northern side for earthquakes in the northern/southern hemisphere. We also selected GPS stations lying on the same side of IPP and located farther than IPP, to enable shallow-angle LOS penetration with the CID wavefront. We also selected CIDs with (1) appearance time not later than 15 minutes after earthquakes, and (2) sharp peaks. The first ensures that IPPs are close to the epicentres and geometric decays are insignificant. The second condition is the manifestation of the shallow angle penetration of LOS. The peak amplitudes were derived by (1) finding the peak TEC value, (2) going back in time from the peak by 90 seconds, and (3) calculating the TEC difference at the two epochs. We also obtained background vertical TEC from Global Ionospheric Maps (GIM), and expressed the CID amplitudes as percents relative to the background TEC. When we plot relative CID amplitudes as a function of seismic moment in the double logarithmic plot, data are distributed roughly around a line, suggesting that they obey a certain scaling law. The slope of the line shows that the CID amplitudes increase by two orders of magnitude as Mw increases by three. We speculate that this reflects the scaling law governing the maximum uplift in relatively large shallow-angle reverse faultings. This scaling law and its empirical factor-two uncertainty in CID amplitude imply that we can determine Mw with an uncertainty of ×0.45 by measuring CID amplitudes. This is useful for early warning in a region where tsunamis arrive at the coast later than acoustic waves arrive at the ionospheric F layer, and this is the case for the Pacific coast of NE Japan. There are two earthquakes deviating negatively beyond the factor 2 uncertainty. They are the 2012 North Sumatra earthquake (Mw8.6), the largest strike-slip earthquakes ever recorded, and its largest aftershock (Mw8.1). This negative deviation would possibly reflect the smaller vertical crustal movements in strike-slip earthquakes than dip-slip events.