Nonlinear waves and solitons in models of fault block geological media

Abstract

This is an overview of theoretical research on solitons and other nonlinear waves induced by deformation in fault block (fragmented) geological media, including a brief description of available models with their geophysical and geodynamic applications. The cited models correspond to the classical and perturbed sine-Gordon equations and use the rotation angle and displacement of fault blocks as dynamic variables. The models simulate kinematics and dynamics of traveling deformation fronts (kinks and solitons) generated in faulted rocks. The sine-Gordon equation is presented in its seismological and geomechanic applications for description of earthquake data and modeling of strain waves, faulting patterns, and subduction processes, including slow earthquakes and periodic episodic tremor and slow slip (ETS) effects.

Reflection of Seismic and Solar Irregularities in Hydrogeological Fields of Kyrgyzstan

“…The basis of the analysis and interpretation of the obtained data is the theory of pulsating earth and the theory of reflection, as well as the multifactorial nature of the formation of hydrogeological fields. The fact is that, according to [7,8], medium-sized earthquakes represent the influence of deformation waves on the destroyed zones of the lithosphere when calculating the interval between seismic processes in real time. But this is instantaneous with respect to the geological evolution of structures.In [9], the relationships between the physicochemical parameters of the sources with the nature and intensity of neotectonic movements are shown using the example of the «Teskey hydrothermal line».…”

Two bullets to the head and an early winter: fate permits Kutuzov to defeat Napoleon at Moscow

“…Recently, the subject of canonization of Kutuzov was brought forward; however, the Russian Orthodox Church held that such a move was not appropriate because Kutuzov was a Freemason and had an ambiguous personality. 5 In 1831 the famous Russian poet Alexander Pushkin wrote an elegy, Before the Sacred Tomb, for Kutuzov. 10 In 1837 another famous Russian poet, Mikhail Lermontov, wrote his famous Borodino to honor Kutuzov, a poem recited by all Russian schoolchildren.…”

Moment of inertia for rock blocks subject to bookshelf faulting with geologically plausible density distributions

“…Thus, the MOI depends on the mass distribution inside a moving/deforming body (Batra 2016) that in turn is sensitive to any variations in density. Bykov (2014Bykov ( , 2015 used MOI in modeling seismicity related to rotation of fault blocks (also see Dahlen 1977). To be specific, Bykov (2014Bykov ( , 2015 presented a differential equation involving inertial rotation angle, displacement and the MOI that represented the rotation waves in the 'elastic fragmented massif'.…”

“…Bykov (2014Bykov ( , 2015 used MOI in modeling seismicity related to rotation of fault blocks (also see Dahlen 1977). To be specific, Bykov (2014Bykov ( , 2015 presented a differential equation involving inertial rotation angle, displacement and the MOI that represented the rotation waves in the 'elastic fragmented massif'. Dahlen (1977), on the other hand, presented an expression of Earth in mechanical equilibrium during its rotation involving its MOI, and demonstrated mathematically how far this equilibrium disturbs locally due to faulting.…”