“Detecting the Stress-Strain State of Lithospheric Plates and Certain Crustal Regions on the Basis of Inclinometer Data. Earthquake Prediction”
There are two main phases of tectonic movements for an earthquake to occur: slow (secular) and fleeting (saltatory). Secular movements can last over many decades, that is why they are quasi-static. As a result, deformations, being accumulated in lithospheric plates and certain crustal regions over years and reaching a critical value of 10−410−4, cause global destruction (an earthquake) (according to the data of the Japanese seismologist Rikitake, this value is 4,7⋅10−54,7·10−5). The major part of vast potential deformation energy accumulated over years releases as volume elastic longitudinal (primary) P-waves and shear (secondary) S-waves, and as Rayleigh-Love surface waves.
Fleeting (saltatory) movements are dynamic and result from foreshocks, the mainshock and aftershocks.
In the middle of the 20th century, seismologists recorded visible Earth’s surface deformations (point displacements) prior to an earthquake. Then, a logical idea was there to use these data both for determining the strain state of lithospheric plates and crustal regions and for monitoring their temporal changes using new information from further systematic measurements.
The asymptotic method for solving singular perturbation differential equations allowed coping with this problem.
To reduce the impact of external anomalous changes (mainly, atmospheric) on the real data within a layer (a lithospheric plate), seismologic measuring instruments (inclinometers, extensometer etc.) were put into the layer at a certain depth under the surface. At this seminar, the solutions of the corresponding non-classical quasi-static and dynamic problems were shown when measuring instruments were placed at the contact boundary between layers m and m+1. Moreover, the situations were described when the asymptotical solution becomes mathematically exact.
The obtained solutions to the quasi-statistic and dynamic problems make it possible to follow, on the basis of the regular measurements, the whole forerunning process resulting in an earthquake.