On the solution stability in the problem of determining the time variations of the tidal responses of a medium in the vicinity of the sources of severe earthquakes

In (Molodenskii M.S. et al., 2016), the data from horizontal pendulums recording the tilts in the closest vicinity of the Great Tohoku earthquake of March 11, 2011 in Japan were analyzed. A significantly improved method for statistical analysis of the observational data enabled the authors to reveal a slow growth in tidal tilts during a period of six years before the earthquake, which was superseded by an instantaneous drop in the amplitudes at the time of the earthquake. After this, during the subsequent four years, the tidal amplitudes have remained at a significantly lower level than their average values before the earthquake. These changes in tidal amplitudes testify to the nonlinear character of the tidal response of the medium in the presence of large tectonic stresses: as is well known, the linear relationship between stresses and strains in a real medium is only the case for stresses that are far below the yield stress. When the stresses approach the failure limit, two counteracting effects come into play: (1) the shear moduli in some areas decrease as a result of the avalanche growth of the crack formation processes, and (2) the moduli increase due to the compression in the other areas. Irrespective of which particular effect of these two is predominant, in either case the linearity of the relationship between the stresses and strains should be violated. This violation cannot but affect the amplitudes of the tidal tilts and strains characterizing this relationship in the presence of fairly low additional tidal stresses (i.e., the derivative of the off-diagonal stress tensor components with respect to the same components of the strain tensor). Since there is presently a sufficiently dense network of the horizontal pendulums recording the tilts (the global IRIS network and the particularly dense F-NET network in Japan), monitoring the changes in the amplitudes of tidal tilts can be considered as a key instrument for capturing the signs of the approach of tectonic stresses to their critical values. The increase in tidal amplitudes before the Tohoku earthquake and their drop at the moment of the earthquake, which were revealed by us, as well as the constancy of the amplitudes during four years after the event, unambiguously indicate that the accumulation of tectonic stresses caused the growth in tidal amplitudes, whereas the stress release by the earthquake caused their diminution. This does not however mean that stress accumulation is accompanied by a decrease in the elastic moduli and that the release of stresses is accompanied by the growth of elastic moduli all over the source area. As was shown in (Molodenskii M.S. et al., 2012), even in the simplest model of spatially homogeneous variations of elastic modules, the variations in tidal tilts are an odd function of the distance from the epicenter. Therefore, irrespective of whether the elastic moduli decrease or increase, the amplitudes of tidal tilts should decrease in some areas and increase in other areas. Hence, the very fact of the growth of tidal tilt amplitudes with time cannot be considered as a sign of the growth of tectonic stresses. To be positive about the latter, one should make sure that the consistent (unidirectional) changes have been observed during a sufficiently long time interval and that their magnitudes were significantly larger than the measurement errors. Hence, it is important to reliably estimate the errors of the observational data.