For fifty years, scientists from different countries in different regions of the Earth, using direct and indirect methods, discovered the migration of crustal deformation and earthquakes, and revealed its wave nature, and therefore proved the reality of the existence of slow strain waves in the Earth. This review presents a brief history of the development of the concept of strain waves in the Earth, the observation methods and properties of strain waves, and main types of the geological structures generating these waves, as well as the most prominent results of the theoretical, laboratory, and in-situ observations of slow strain migration.

The strongest earthquakes with magnitudes Mw 8–9 generate coseismic displacements of the Earth’s crust, covering entire regions of the world. These displacements can be recorded using observations provided by the independent geodetic GNSS networks. The data of these networks are processed using different algorithms and methods for analyzing satellite observations, methods for calculating the coseismic shift, and different implementations of the coordinate system. These factors lead to "inconsistency" of the combined displacement fields and the appearance of additional errors in the results of coseismic effects modeling. The paper proposes a method for combining the fields of coseismic displacements of the Earth's crust, obtained in the far-field zone from the source according to data from heterogeneous GNSS networks. The results of applying the proposed method are demonstrated by the example of combining the fields of coseismic displacements in China, South Korea and the south of the Far East of the Russian Federation, initiated by the catastrophic Tohoku earthquake on March 11, 2011, Mw 9.1, as well as the calculation and analysis of the unified field of coseismic deformations of the region under study.

The theoretical discovery of slow strain (tectonic) waves, the so-called strain waves in the Earth, served as a motivation to develop physical backgrounds of the mathematical theory of propagation of these waves and to search for methods of their experimental detection.For fifty years, scientists from different countries in different regions of the Earth, using direct and indirect methods, discovered the migration of crustal deformation and revealed its wave nature, and, therefore, proved the reality of the existence of strain waves of the Earth.This overview briefly describes the history of the development of the concept of strain waves on the Earth, the observation methods and properties of strain waves, and the main types of geological structures generating these waves.The most prominent results of the theoretical, laboratory, and in-situ observations of slow strain migration, including slow earthquakes and periodic Episodic Tremor and Slow (ETS) slip effects, are presented.In the near future, studies of slow strain waves may lead to a fundamental revision of the current concepts about the physics of the seismic process.

SUMMARY The objective of this study was to examine co- and post-seismic deformation following the 2011 Mw9.0 Tohoku–Oki earthquake and its impact on Northeast Asia. Large-scale, long-term post-seismic deformation caused by the earthquake was extracted according to the continuous Global Navigation Satellite Systems (GNSS) observation data for Japan, South Korea, Northeast China and the Far East Russia. The present research adopted a 2-D viscoelastic model to simulate the observed large-scale seismic deformation, considering the subducting slab in the western Pacific. The duration of the after-slip in the northwest of the main rupture area was found to be greater than that in the south of the main rupture area (approximately 6 yr). The steady-state viscosity coefficient of the continental mantle was found to be 8 × 1018 Pa·s. Post-seismic deformation in Northeast Asia was primarily caused by viscoelastic relaxation of the mantle, and observations on the west side of the Tan-Lu fault were smaller than simulation, revealing the heterogeneity in viscosity structures in NE China.

In this paper, we explore the Western Pacific subduction impact on the geodynamics of the Asian continent. The data on migration of slow strain and earthquakes from the Nankai, Japan and Kuril-Kamchatka segments of the Western Pacific subduction zone deep into mainland Asia are analyzed. The calculations performed on five profiles, crossing the Kuril Islands, the Japanese Archipelago and Sakhalin Island toward the Asian continent, have revealed the transverse migration of earthquakes from the Japan–Kuril-Kamchatka subduction zone. The velocities of hypocenter migration of M ≥ 4.5 earthquakes from the Kuril-Kamchatka Trench via northern and central Sakhalin vary from 6 to 17 km/year, on average, at different depths. The profiles crossing the islands of Hokkaido and Sakhalin show the M ≥ 4.earthquake migration from the Kuril and Japan trenches at velocities of 8–27 km/year.

An experimental study of the dynamics of the BOLD (blood oxygen level dependent) signal by functional magnetic resonance imaging was carried out. It was found that the dynamic responses of the BOLD-signal, have a biphasic character. Through kinetic modeling methods, it was shown that the biphasic nature of the hemodynamic response is based on negative feedback, with Ca2+ pulse inhibited by vasodilation products (NO and prostaglandin). The effect of thermoheliox (inhalation of a mixture of helium and oxygen at 70 degrees C) on functional hemodynamics was studied. It was shown that preliminary inhalation of thermoheliox stimulates and prolongs hemodynamic impulses.

The interaction between the India-Eurasia collision and the Western Pacific subduction and their contribution to recent geodynamics of the Asian continent are discussed. We perform a comparative analysis of the data available from world literature and new data on the slow strain and earthquake migration from the India-Eurasia collision and the Western Pacific subduction zones. Based on the concepts of wave dynamics of the deformation processes, a localization scheme is constructed illustrating the migration of slow strain fronts in central and eastern Asia, and the wave geodynamic impact of collision and subduction on the Asian continent is shown.

A kinetic model of the dynamics of a multipathway mechanism of neurovascular coupling induced by nerve impulses was constructed. The model calculations were compared with experimental data on the changes in the blood oxygen level dependent signal during sensory-motor and visual excitation before and after the use of the nonsteroidal anti-inflammatory drug indomethacin. The influence of the catalytic activity of key enzymes on the dynamics of the neurovascular response in the proposed model is shown. The multipathway mechanism of the biochemical reactions provides stability of the neurovascular coupling during various possible catalytic activities of the key enzymes in the process.

An analysis of data on the migration of earthquakes and slow deformations from the Indo–Eurasian collision and the Western Pacific subduction zones is given and the wave “geodynamic impact” of these tectonic processes on the Amurian plate and adjoining structures is demonstrated. The interaction of collision and subduction, and their relative contribution to the recent geodynamics of the Amurian plate are discussed. A scheme illustrating localization of slow strain wave manifestations in central and eastern Asia has been constructed. Calculations were performed aimed at revealing the transverse migration of earthquakes (M ≥ 6.5) directed from the Japan and Kuril–Kamchatka trenches toward the Asian continent in the time period from 1960 to 2015. The migration of earthquakes along the profile crossing Hokkaido Island is transferred at velocities of 15 and 23 km/yr, whereas the migration velocity from the Kuril–Kamchatka Trench via Sakhalin Island is estimated to be from 20 to 40 km/yr at various depths. We focus on the insufficient study of the impact of the Western Pacific subduction on the generation of the deformation field in mainland Asia.

The locus of real and complex roots of algebraic equations are constructed in this paper. Calculations of specific equations show that the location of their roots depends on the type of equation.

Обсуждается проблема современной геодинамики Дальневосточного региона на основе мониторинга разномасштабных деформаций и сейсмичности в области сочленения Евразийской, Североамериканской, Тихоокеанской, Амурской и Охотской литосферных плит с применением современных методов космической геодезии и широкополосной сейсмологии. Дан краткий обзор этапов развития Единой сети геодинамических наблюдений ДВО РАН, основных результатов сейсмологических и GPS/ГЛОНАСС-наблюдений, полученных в рамках целевой комплексной программы научных исследований ДВО РАН «Современная геодинамика, активные геоструктуры и природные опасности Дальнего Востока России (2009–2013 гг.)» и проектов ДВО РАН 2014, 2018, 2019 гг., а также достигнутых позиций ДВО РАН в области геодинамики. The problem of the recent geodynamics of the Far East region is discussed based on monitoring of different-scale deformations and seismicity in the articulation of Eurasian, North American, Pacific, Amurian and Okhotsk lithospheric plates using modern methods of space geodesy and broadband seismology. We present a brief overview of the development stages of the Unified Network of Geodynamic Observations of the Far Eastern Branch of the Russian Academy of Sciences, the main results of seismological and GPS/GLONASS observations obtained within the framework of the Targeted Comprehensive Research Program of the Far Eastern Branch of the Russian Academy of Sciences for 2009–2013 «Recent geodynamics, active geological structures and natural hazards of the Far East of Russia», Projects of the Far Eastern Branch of the Russian Academy of Sciences (2014, 2018, 2019) and the achievements of FEB RAS in the field of geodynamics.

The paper investigates a modelsimulating crustal fault dynamics and strain wave generation ina fault block geological medium, the parameters determiningsliding regimes in faults, and the physics of transitionsbetween different deformation regimes. The model comprises themost important mechanisms responsible for the interaction offault walls: friction, geometric irregularities (roughness andasperities on the fault surface), and external load, whichgovern sliding along the fault. The results of field andlaboratory studies of deformation migration on themacro/mesoscale are consistent with the concept of localizeddeformation propagation in the form of solitary waves (kinks,solitons) and autowaves. The conditions are defined which makepossible the transition from the model simulating solitary wavesin a conservative medium with low “friction” (soliton-likebehavior of the system) toward the model of solitary waves in anactive medium with diffusion (autowave-like behavior of thesystem). Two possible deformation regimes of the fault blockstructure in the high-friction limit are considered. The faultwall displacement is stopped due to this friction, but theadjacent blocks move relative to each other in the core of thefault. It is shown that in the high-friction limit a perturbedsine-Gordon equation applied for fault dynamics modeling isreduced to a reaction-diffusion equation, whereas the systemgoes from the soliton regime to the autowave regime. In the caseof high friction and a lack of energy supply to the fault froman external source, the transfer of localized deformation ischanged by a diffusive dissipation of stress.

ВВЕДЕНИЕКонцепция направленной миграции землетрясений предполагает наличие разломов -границ плит, блоков и других структурных элементов, в которых при динамической подвижке происходит генерирование сейсмических волн, вызывающих землетрясения.Однако в сейсмоактивных районах довольно часто связь сейсмических событий с разломами, выделенными по геологическим данным, не фиксируется, и поэтому возникает проблема выделения скрытых разломов.Выявление тектонической нарушенности в виде скрытых разломов, т.е.не вышедших на поверхность Земли, но способных генерировать интенсивные сейсмические колебания и опасные геологические явления [17], является актуальной задачей.При этом отсутствует общепринятая методика обнаружения сейсмогенерирующих разломов

The detection of tectonic fracturing zones in the form of hidden faults, which are not exposed at the surface but are capable of generating intense seismic oscillations and causing hazardous geological phenomena, is a vital problem to be solved in the Priamurye region. We propose a comprehensive approach following which the earthquake migration data are taken as a basis for the detection of hidden faults, while the geophysical and morphostructural data are involved as the additional information for validating the obtained results. In our study, we detail the earthquake migration tendencies and estimate the migration direction and velocity. Based on these data, tectonic fracturing zones are identified and the hidden faults and their segments where persistent earthquake migration is manifested are revealed in the Priamurye region. The data that establish the direction and velocity of the earthquake epicenter migration will provide forecasting and assessment of natural hazards in the Priamurye region.

A kinetic model of the process response of nervous tissue to an external signal stimulus is proposed. The model is based on the multistage and non-linear nature of the dynamic process of changes of N-acetylaspartate concentration. The existence of multiple steady states explains the trigger effect of the system. The effect of substrate inhibition for this system was studied as a necessary factor of N-acetylaspartate’s autostabilization as a key metabolite in the brain. The appearance of N-acetylaspartate’s “anti-peak” causes a wave of its hydrolysis products, such as aspartic acid and acetic acid.

The interaction between the Amur, Pacific and Eurasian tectonic plates initiates seismic activity at the plate margins as well as in the plate periphery, as evidenced by intracontinental earthquakes. In the Amur plate, the dynamics of intercontinental seismicity is controlled by deformation wave fronts comprising a regular pattern of equidistant zones [Sherman, 2013]. According to [Trofimenko et al., 2015a, 2015b, 2016], maximum values of seismic activity in the range of magnitudes 2≤M≤4 also form a sequence of spatial cells in the form of seismic clusters from the east (Sakhalin – Sakh) to the west (the western boundary of the Baikal rift zone – BRZ ) (Fig. 1). One of the main characteristics of the seismic process is seismic activity migration given as sequential activation of seismogenic structures within the seismically active zones and on the global scale [Vikulin et al., 2012; Khain, Khalilov, 2008]. Direct observations show that crust deformation migrates from the Japan-Kuril-Kamchatka subduction zone towards the continent, and the estimated migration rates range from 10 to 140 km per year (e.g. [Ishii et al., 1978; Kasahara, 1979; Harada et al., 2003; Yoshioka et al., 2015]). In the Baikal and Amur regions (107–140°E), the fronts of deformation waves migrate at a rate of 5–20 km per year [Sherman, 2007, 2013]. Considering the order of magnitude, this rate is comparable to the rates of crust deformation migration from the Japan-Kuril-Kamchatka zone (10–100 km per year). Our studies show that the sequential activation of the seismic clusters in the northeastern segment of the Amur plate (Sakh – TanLu – Al-St) occurs at a rate of 1000 km per year [Trofimenko et al., 2015a] (Fig. 1). In the meridional tectonic structures, the shifting chains of maximum seismicity values are sequentially replaced by minimum values (i.e. inversion zones). Based on the spatial cycles with the phase shift of the maximum seismic activity values at the rate of 1000 km per year, it is possible to represent the dynamics of seismicity in the form of a process initiated by long-period stress waves/deformations. According to [Mogi, 1968; Kasahara, 1979; Malamud, Nikolaevskii, 1989; Saprygin et al., 1997; Harada et al., 2003; Bykov, 2005, 2014; Sherman, 2007, 2013, 2014; Milyukov et al., 2013], slow deformation waves of the global and regional scale are generated at the margins of lithospheric plates. Under this concept, the migration rate of seismic activity and the spatial extent of seismic cycles can be identified as the velocity and length of deformation waves. Using the data on seismicity of the most active region of the Baikal rift zone – the northwestern segment of the Amur plate, we have studied the periodic components of seismicity along the entire northern boundary of the Amur plate. An indirect evidence of the existence of deformation waves is the migration of anomalies of geophysical fields and its correlation with the migration of seismic activity. The space-time anomalies of the magnetic and gravity fields were studied in the South Yakutian geodynamic polygon [Trofimenko, 1990; Trofimenko, Grib, 2003, 2016], and the indicators of deformation waves were revealed in the seismic regime and the geophysical fields at the northern margin of the Amur plate. The sequential manifestation of anomalies in the magnetic and gravity fields is associated with the activation of latitudinal tectonic structures. Our estimations show that the geophysical anomalies migrate at different rates, from 100 to 1000 km per year. Based on the results obtained in our study and their comparison with other available data, the dynamics of seismicity along the northern margin of the Amur plate is identified as a wave process.

The theoretical prediction of strain waves in the Earth is one of the most significant achievements in geophysics of the last third of the 20th century. Using the strain wave theory, the physical foundations were developed for the mathematical theory of strain wave propagation, and the search for methods that could detect the strain waves in experiment and simulation has commenced. This article provides an overview of the history of the strain wave theory and describes the observation methods, the main types of geological structures generating strain waves, and the properties of strain waves. It presents the most important results of the theoretical, laboratory and field studies of slow migration of strain. Future studies based on the strain wave theory may initiate a fundamental revision of the current concepts of the seismic process.

The modeling results are presented on the annual dynamics of seismicity in the northeastern segment of the Amur plate, which are obtained from statistical studies of the number of earthquakes with magnitudes 2 ≤ М ≤ 6 in different phases of variations in the Earth’s rotation rate. We have calculated a degree of relationship between the observed seismicity variations and phases of decrease and increase in the Earth’s rotation rate for the magnitude ranges between 2 ≤ М < 4 and 4 ≤ М < 5 using rank correlation methods. It has been established that epicenters of earthquakes with magnitudes 5 ≤ М ≤ 6 are spatially grouped into a sequence of homogeneous equally spaced, 3.5°–4°, on average, east-westerly oriented clusters.

In this paper, we aimed to investigate the statistical distributions of shallow earthquakes with 2 ≤ М ≤ 4, located in 13 rectangular areas (clusters) bounded by 120°E and 144°E along the northern boundary of the Amurian microplate. As a result of our study, the displacement of seismicity maxima has been determined and three recurrent spatial cycles have been observed. The clusters with similar distribution of earthquakes are suggested to alternate being equally spaced at 7.26° (360–420 km). A comparison of investigation results on the structure of seismicity in various segments of the Amurian microplate reveals the identity between the alternation pattern observed for meridional zones of large earthquakes and a distinguished spatial period. The displacement vector for seismicity in the annual cycles is determined, and the correspondence between its E-W direction and the displacement of the fronts of large earthquakes is established. The elaborated model of seismic and deformation processes is considered, in which subsequent activation of clusters of weak earthquakes (2 ≤ М ≤ 4), tending to extend from the Japanese-Sakhalin island arc to the eastern closure of the Baikal rift zone, is initiated by the displacement of the strain wave front.