Fundamentals of the Thermohydrogravidynamic Theory of the Global Seismotectonic Activity of the Earth

The article presents the fundamentals of the cosmic geophysics (representing the deterministic thermohydrogravidynamic theory intended for earthquakes prediction) based on the author’s generalized differential formulation of the first law of thermodynamics extending the classical Gibbs’ formulation by taking into account (along with the classical infinitesimal change of heat δQ and the classical infinitesimal change of the internal energy dU τ ) the infinitesimal increment of the macroscopic kinetic energy dK τ , the infinitesimal increment of the gravitational potential energy dπ τ , the generalized expression for the infinitesimal work δAnp,∂τ done by the nonpotential terrestrial stress forces (determined by the symmetric stress tensorT) acting on the boundary of the continuum region τ, and the infinitesimal incrementdG of energy due to the cosmic and terrestrial nonstationary energy gravitational influence on the continuum region τ during the infinitesimal time dt. Based on the established generalized differential formulation of the first law of thermodynamics, the author explains the founded cosmic energy gravitational genesis of the strong Chinese 2008 and the strong Japanese 2011 earthquakes.


Introduction
The problem of the long-term predictions of the strong earthquakes [1,2] is the significant problem of the modern geophysics.The analysis of the period 1977-1985 revealed [3] the strongly nonrandom tendencies in the earthquake-induced geodetic changes (owing to the mass redistribution of material inside the Earth) related to the change of the Earth's rotation and the Earth's gravitational field.The analysis of the period 1977-1993 (characterized by 11015 major earthquakes) revealed [4] the strong earthquakes' tendency to increase the Earth's spin (rotational) energy.The analysis of the same period 1977-1993 revealed [5] "an extremely strong tendency for the earthquakes to decrease the global gravitational energy" confirming the inherent relation of the earthquakes with the transformation of the Earth's gravitational energy into the seismic wave energy and frictional heat.The previous analysis of the principal geological features of the past 400 × 10 6 years revealed [6] the geological evidence for a pulsating gravitation related to periodic variation of the Earth's radius during the geological evolution of the Earth.The combination of satellite and gravimetric data revealed [7] the free-air anomalies of the Earth's gravitational field.
It is well known that "the deterministic prediction of the time of origin, hypocentral (or epicentral) location, and magnitude of an impending earthquake is an open scientific problem" [8].It was conjectured [8] that the possible earthquake prediction and warning must be carried out on a deterministic basis.However, it was pointed out [8] with some regret that the modern "study of the physical conditions that give rise to an earthquake and the processes that precede a seismic rupture of an ordinary event are at a very preliminary stage and, consequently, the techniques of prediction of time of origin, epicentre, and magnitude of an impending earthquake now available are below standard".The authors [8] argued that "a new strong theoretical scientific effort is necessary to try to understand the physics of the earthquake".It was conjectured [8] that the present level of knowledge of the geophysical processes "is unable to achieve the objective of a deterministic prediction of an ordinary seismic event, but it certainly will in a more or less distant future tackle the problem with seriousness and avoiding scientifically incorrect, wasteful, and inconclusive shortcuts, as sometimes has been done".Sgrigna and Conti conjectured [8] that "it will take long time (may be years, tens of years, or centuries) because this approach requires a great cultural, financial, and organizational effort on an international basis".It was conjectured [8] that a possible contribution to a deterministic earthquake prediction approach is related to observations and physical modelling of earthquake precursors to formulate, in perspective, "a unified theory able to explain the causes of its genesis, and the dynamics, rheology, and microphysics of its preparation, occurrence, postseismic relaxation, and interseismic phases".It was conjectured [8] that "the study of the physical conditions that give rise to an earthquake and of the processes that precede a seismic rupture is at a very preliminary stage and, consequently, the techniques of prediction available at the moment are below standard".However, Sgrigna and Conti believe [8] that "it should be better to pursue the deterministic prediction approach even if a reliable deterministic method of earthquake prediction will presumably be available only in the more distant future".
It was pointed out [9] that the gravity changes (derived from regional gravity monitoring data in China from 1998 to 2005) exhibited noticeable variations before the occurrence of two large earthquakes in 2008 in the areas surrounding Yutian (Xinjiang) and Wenchuan (Sichuan).A recent research [10] by Zhan and his colleagues demonstrated that significant gravity changes were observed before all nine large earthquakes that ruptured within or near mainland China from 2001 to 2008.It was pointed out [9] that the past experience and empirical data showed that "earthquakes typically occur within one to two years after a period of significant gravity changes in the region in question".It was concluded [9] that the "additional research is needed to remove the subjective nature in the determination of the timeframe of a forecasted earthquake".
The need of the thermohydrogravidynamic approach [11,12] is confirmed by previous studies [3][4][5]13] and by noticeable variations of gravitational field identified [9,10] before strong earthquakes in China from 2001 to 2008.The necessity to consider the gravitational field (during the strong earthquakes) is also related to the observations of the slow gravitational [14,15] ground waves resulting from strong earthquakes and spreading out from the focal regions [16,17] of earthquakes.Lomnitz pointed out [16] that the gravitational ground waves (related to great earthquakes) "have been regularly reported for many years and remain a controversial subject in earthquake seismology".Richter presented [18] the detailed analysis of these observations and made the conclusion that "there is almost certainly a real phenomenon of progressing or standing waves seen on soft ground in the meizoseismal areas of great earthquakes".Lomnitz presented [17] the real evidence of the existence of the slow gravitational waves in sedimentary layers during strong earthquakes.The fundamental connections of the geodynamics, seismicity, and volcanism with gravitation (and the slow gravitational ground waves resulting from strong earthquakes) are presented in the works [19][20][21][22].
It was conjectured [23] that the recent destructive earthquakes occurred in Sichuan (China, 2008), Italy (2009), Haiti (2010), Chile (2010), New Zealand (2010), and Japan (2011) "have shown that, in present state, scientific researchers have achieved little or almost nothing in the implementation of short-and medium-term earthquake prediction, which would be useful for disaster mitigation measures".It was conjectured [23] that "this regrettable situation could be ascribed to the present poor level of achievements in earthquake forecast".It was pointed out [23] that "although many methods have been claimed to be capable of predicting earthquakes (as numerous presentations on earthquake precursors regularly show at every international meeting), the problem of formulating such predictions in a quantitative, rigorous, and repeatable way is still open".It was formulated [23] that "another problem of practical implementation of earthquake forecasting could be due to the lack of common understanding and exchange of information between the scientific community and the governmental authorities that are responsible for earthquake damage mitigation in each country: they operate in two different environments, they aim at different tasks, and they generally speak two different languages".It was pointed out [23] that "the way how seismologists should formulate their forecasts and how they should transfer them to decision-makers and to the public is still a tricky issue".It was clearly formulated [23] that "the formulation of probabilistic earthquake forecasts with large uncertainties in space and time and very low probability levels is still difficult to be used by decision-making people".It was conjectured [23] that "in real circumstances the authorities deal with critical problems related to the high cost of evacuating the population from an area where the scientific methods estimate an expected rate of destructive earthquake as one in many thousand days, while they require much more deterministic statements".In the special issue [23] of the International Journal of Geophysics, Console et al. assessed the status of the art of earthquake forecasts and their applicability.They invited authors "to report methods and case studies that could concretely contribute or, at least seemed promising, to improve the present frustrating situation, regarding the practical use of earthquake forecasts" [23].
In this article, by accepting with gratitude the personal invitation from Dr. Reem Ali and Dr. Radwa Ibrahim (representing the Editorial Office of the International Journal of Geophysics) to submit an article to the special issue on "Geophysical Methods for Environmental Studies", the author presents the fundamentals of the thermohydrogravidynamic theory intended for deterministic prediction of earthquakes.The thermohydrogravidynamic theory is based on the established generalized differential formulation [11,12,[24][25][26] of the first law of thermodynamics (for moving rotating deforming compressible heat-conducting stratified macroscopic continuum region  subjected to the nonstationary Newtonian gravity): +   +   =  +  np, +  (1) extending the classical formulation [27] by taking into account (along with the classical infinitesimal change of heat  and the classical infinitesimal change of the internal energy   ) the infinitesimal increment of the macroscopic kinetic energy   , the infinitesimal increment of the gravitational potential energy   , the generalized expression for the infinitesimal work  np, done by the nonpotential terrestrial stress forces (determined by the symmetric stress tensor T) acting on the boundary of the continuum region , and the infinitesimal increment  of energy due to the cosmic and terrestrial nonstationary energy gravitational influence on the continuum region  during the infinitesimal time .
In Section 2 we begin by considering the inherent physical incompleteness of the classical expression [28,29] for the macroscopic kinetic energy per unit mass   defined (in classical nonequilibrium thermodynamics) as the sum of the macroscopic translational kinetic energy per unit mass   = (1/2)k 2 of the mass center of a continuum region and the macroscopic internal rotational kinetic energy per unit mass   = (1/2) 2 , where k is the speed of the mass center of a small continuum region,  is an angular velocity of internal rotation [29,30], and  is an inertia moment per unit mass of a small continuum region [28].The classical de Groot and Mazur expression has inherent physical incompleteness [24,31] related to the questionable assumption about the rigidlike rotation of a small continuum region.The classical de Groot and Mazur expression [28] does not consider the nonequilibrium component of the macroscopic velocity field related to the velocity shear defined by the rate of strain tensor   .In Section 2 the macroscopic kinetic energy per unit mass   is presented [31] as a sum of the macroscopic translational kinetic energy per unit mass   = (1/2)k 2 of the mass center of a continuum region, the classical macroscopic internal rotational kinetic energy per unit mass   [28], the new macroscopic internal shear kinetic energy per unit mass   [31], and the new macroscopic internal kinetic energy of shear-rotational coupling per unit mass  coup , [31] with a small correction.The presented expression for   and its particular form for homogeneous continuum regions of spherical and cubical shapes generalized [31] the classical de Groot and Mazur expression in classical nonequilibrium thermodynamics [28,29] by taking into account the new macroscopic internal shear kinetic energy per unit mass   , which expresses the kinetic energy of irreversible dissipative shear motion, and also the new macroscopic internal kinetic energy of shearrotational coupling per unit mass  coup , , which expresses the kinetic energy of local coupling between irreversible dissipative shear and reversible rigid-like rotational macroscopic continuum motions.
Following the "Statistical thermohydrodynamics of irreversible strike-slip-rotational processes" [11] and the "Thermohydrogravidynamics of the Solar System" [12], in Section 2.2 we present the generalized differential formulation of the first law of thermodynamics (in the Galilean frame of reference) for nonequilibrium shear-rotational states of the deformed finite one-component individual continuum (characterized by the symmetric stress tensor T) region  moving in the nonstationary gravitational field.In Section 2.3 we present the generalized differential formulation [11,12] of the first law of thermodynamics (in the Galilean frame of reference) for nonequilibrium shear-rotational states of the deformed finite individual region  of the compressible viscous Newtonian one-component continuum moving in the nonstationary gravitational field.We present the generalization [11,12] of the classical [27] expression  np, = − = − by taking into account (for Newtonian continuum) the infinitesimal works   and   , respectively, of acoustic and viscous Newtonian forces acting during the infinitesimal time interval  on the boundary surface  of the individual continuum region  bounded by the continuum boundary surface .Based on the generalized differential formulation of the first law of thermodynamics, in Section 2.4 we present the analysis [11,12] of the gravitational energy mechanism of the gravitational energy supply into the continuum region  owing to the local time increase of the potential  of the gravitational field inside the continuum region  subjected to the nonstationary Newtonian gravitational field.
Following the "Statistical thermohydrodynamics of irreversible strike-slip-rotational processes" [11] and the "Thermohydrogravidynamics of the Solar System" [12], in Section 3 we present the fundamentals of the cosmic energy gravitational genesis of earthquakes.Using the evolution equation of the total mechanical energy of the macroscopic continuum region  (of the compressible viscous Newtonian continuum), we demonstrate the physical adequacy [11,12] of the rotational model [2] of the earthquake focal region for the seismic zone of the Pacific Ring.We present the thermodynamic foundation [11,12] of the classical deformational (shear) model [1] of the earthquake focal region for the quasi-uniform medium of the Earth's crust characterized by practically constant viscosity.We present the generalized thermohydrogravidynamic shear-rotational model [11,12] of the earthquake focal region by taking into account the classical macroscopic rotational kinetic energy [28,29], the macroscopic nonequilibrium kinetic energies [24,31], and the external cosmic energy gravitational influences [12,25,26] on the focal region of earthquakes.
In Section 4 we present the fundamentals of the cosmic geophysics [12] applicable for the planets of the Solar System.In Section 4.1 we consider the energy gravitational influences on the Earth of the inner planets and the outer planets of the Solar System.In Section 4.1.1we present the relation for the energy gravitational influences (on the Earth) of the inner and the outer planets in the second approximation of the elliptical orbits of the planets of the Solar System.In Section 4.1.2we present the evaluation of the relative maximal planetary instantaneous energy gravitational influences on the Earth in the approximation of the circular orbits of the planets of the Solar System.In Section 4.1.3we present the evaluation of the relative maximal planetary integral energy gravitational influences on the Earth in the approximation of the circular orbits of the planets of the Solar System.In Section 4.2 we consider the energy gravitational influences on the Earth of the Moon.In Section 4.2.1 we present the evaluation of the relative maximal instantaneous energy gravitational influence of the Moon on the Earth in the second approximation of the elliptical orbits of the Earth and the Moon around the combined mass center  3,MOON of the Earth and the Moon.In Section 4.2.2.we present the evaluation of the maximal integral energy gravitational influence of the Moon on the Earth in the approximation of the elliptical orbits of the Earth and the Moon around the combined mass center  3,MOON of the Earth and the Moon.In Section 4.3 we demonstrate the reality of the cosmic energy gravitational genesis of preparation and triggering of earthquakes owing to the energy gravitational influence on the Earth of the Moon and the planets of the Solar System.In Section 4.3.1 we demonstrate the real cosmic energy gravitational genesis of preparation of earthquakes by considering the energy gravitational influence on the Earth of Venus.In Section 4.3.2we demonstrate the real cosmic energy gravitational genesis of triggering of the preparing earthquakes.In Section 4.4 we demonstrate the cosmic energy gravitational genesis of the seismotectonic activity induced by the nonstationary cosmic energy gravitational influences on the Earth of the Sun, the Moon, Venus, Jupiter, and Mars.In Section 4.4.1 we present the evaluations of the time periodicities of the maximal (instantaneous and integral) energy gravitational influences on the Earth of the Sun-Moon system, Venus, Jupiter, and Mars.In Section 4.4.2we present the empirical time periodicities of the seismotectonic activity for various regions of the Earth.In Section 4.4.3we present the set of the time periodicities of the periodic global seismotectonic (and volcanic) activity and the global climate variability of the Earth induced by the different combinations of the cosmic energy gravitational influences on the Earth of the Sun and the Moon, Venus, Jupiter, and Mars.In Section 4.5 we present the evidence of the cosmic energy gravitational genesis of the strong Chinese 2008 earthquakes.In Section 4.6 we present the evidence of the cosmic energy gravitational genesis of the strongest Japanese earthquakes near the Tokyo region.In Section 5 we present the summary of main results and conclusion.

The Generalized Formulation of the First Law of Thermodynamics for Moving Rotating Deforming Compressible Heat-Conducting Macroscopic
Individual Continuum Region  Subjected to the Nonstationary Newtonian Gravitational Field

The Generalized Expression for the Macroscopic Kinetic
Energy of a Small Continuum Region in Nonequilibrium Thermodynamics.De Groot and Mazur defined the macroscopic kinetic energy per unit mass   as [28] the sum of the macroscopic translational kinetic energy per unit mass   = (1/2)k 2 of a continuum region (particle) mass center and the macroscopic internal rotational kinetic energy per unit mass   = (1/2) 2 : where k is the speed of the mass center of a small continuum region,  is an angular velocity of internal rotation [29], and  is an inertia moment per unit mass of a small continuum region [28].Gyarmati's definition [29] of the macroscopic kinetic energy per unit mass is analogous to de Groot and Mazur's one.The classical de Groot and Mazur's and Gyarmati's definition (2) of the macroscopic kinetic energy per unit mass for a shear flows has some inherent physical incompleteness associated with the assumption about the rigid-like rotation of the continuum region with the angular velocity vector .This definition is based on the assumption of local thermodynamic equilibrium since it does not consider the nonequilibrium shear component of the macroscopic continuum motion related to the rate of strain tensor   .However, the assumption of local thermodynamic equilibrium, as noted by de Groot and Mazur [28], may be justified only by reasonable agreement of the experimental results with the theoretical deductions based on this assumption.
Landau and Lifshitz defined [32] the macroscopic internal energy of a small macroscopic continuum region as the difference between the total kinetic energy of the continuum region and kinetic energy of the translational macroscopic motion of the continuum region.According to Landau and Lifshitz's definition [32] of the macroscopic internal energy, the term (1/2) 2 in the expression (2) is the internal energy of the macroscopic (hydrodynamic) continuum motion.The classical definition [28,29] of the macroscopic internal rotational kinetic energy per unit mass (1/2) 2 is consistent with the Landau and Lifshitz's definition of the macroscopic internal energy.We shall use further the Landau and Lifshitz's definition [32] of the macroscopic internal energy.
Following the works [11,12,[24][25][26], we shall present the foundation of the generalized expression for the macroscopic kinetic energy in nonequilibrium thermodynamics.We shall assume that  is a small individual continuum region (domain) bounded by the closed continual boundary surface  considered in the three-dimensional Euclidean space with respect to a Cartesian coordinate system .We shall consider the small continuum region  in a Galilean frame of reference with respect to a Cartesian coordinate system  centred at the origin  and determined by the axes  1 ,  2 , and  3 (see Figure 1).
The unit normal -basis coordinate vectors triad  1 ,  2 , and  3 is taken in the directions of the axes  1 ,  2 , and  3 , respectively.The -basis vector triad is taken to be righthanded in the order  1 ,  2 , and  3 ; see Figure 1.g is the local gravity acceleration.
An arbitrary point  in three-dimensional physical space will be uniquely defined by the position vector r =     ≡ ( 1 ,  2 , and  3 ) originating at the point  and terminating at the point .The continuum region-affixed Lagrangian coordinate system   (with the axes  1 ,  2 , and  3 ) is centered to the mass center  of the continuum region .The axes  1 ,  2 , and  3 are taken parallel to the axes  1 ,  2 , and  3 , respectively: the axis   parallel to the axis   , where  = 1, 2, 3.The unit normal   -basis coordinate vector triad ^1, ^2, and ^3 is taken in the directions of the axes  1 ,  2 , and  3 , respectively.The   -basis vector triad is taken to be right-handed in the order ^1, ^2, and ^3.The mathematical differential of the position vector r, r ≡   ^ ≡ ( 1 ,  2 , and  3 ), expressed in terms of the coordinates   ( = 1, 2, 3) in the   -coordinate system, originates at the mass centre  of the continuum region  and terminates at the arbitrary point  of the continuum region.
The position vector r c of the mass center  of the continuum region  in the -coordinate system is given by the following expression: where is the mass of the continuum region ,  is the mathematical differential of physical volume of the continuum region,  ≡ (r, ) is the local macroscopic density of mass distribution, r is the position vector of the continuum volume , and  is the time.The speed of the mass centre  of the continuum region  is defined by the following expression: where k = r/ is the hydrodynamic velocity vector and the operator / = (/) + k ⋅ ∇ denotes the total derivative following the continuum substance [33].The relevant threedimensional fields such as the velocity and the local mass density (and also the first and the second derivatives of the relevant fields) are assumed to vary continuously throughout the entire continuum bulk of the continuum region .The instantaneous macroscopic kinetic energy of the continuum region  (bounded by the continuum boundary surface ) is the sum of the kinetic energies of small parts constituting the continuum region  when the number of the parts, , tends to infinity and the maximum from their volumes tends to zero [33]: where k is the local hydrodynamic velocity vector,  is the local mass density, and  is the mathematical differential of physical volume of the continuum region.We use the common Riemann's integral here and everywhere.
For the analysis of the relative continuum motion in the physical space in the vicinity of the position vector r c of the mass centre  we have the Taylor series expansion (consistent with the Helmholtz's theorem [30,34]) of the hydrodynamic velocity vector k(r) for each time moment : where ) is the hydrodynamic velocity vector at the position vector r, r ≡ r − r c ≡ ( 1 ,  2 ,  3 ) ≡ ( 1 ,  2 ,  3 ) is the differential of the position vector r, is the angular velocity of internal rotation (a half of the vorticity vector) in the -coordinate system at the position vector r, is the local vorticity in the -coordinate system at the position vector r, is the rate of strain tensor in the -coordinate system at the position vector r, (,  = 1, 2, 3), is the gradient operator, and is the small residual part of the Taylor series expansion (7), where   = ( 3  ), ( = 1, 2, 3),   = sup ,∈ √ (r(, )) 2 is the diameter of the continuum region  and the vector r(, ) originates at point  and terminates at point  of the surface .The linear of r terms of the Taylor series expansion (7) is presented in the classical form [33].
International Journal of Geophysics Substituting formula (7) into the formula (6) and integrating by parts, then we obtain the following expression [24,31]: where   is the mass of the continuum region  and   is the ik-component of the classical inertia tensor depending on the mass distribution in the continuum region  under consideration: where   ,   are the , -components of the vector r, respectively, in the   -coordinate system,   is the Kronecker delta tensor,   is the third-order permutation symbol, and   is the , -component classical centrifugal tensor depending on the mass distribution in the continuum region  under consideration: res = ( 7  ) is a small residual part of the macroscopic kinetic energy after substituting the Taylor series expansion (7) into formula (6).
Formula (13) states that the macroscopic kinetic energy   of the small continuum region  is the sum of the macroscopic translational kinetic energy   of the continuum region the macroscopic internal rotational kinetic energy   of the continuum region the macroscopic internal shear kinetic energy   of the continuum region and the macroscopic kinetic energy of shear-rotational coupling  coup The macroscopic internal rotational kinetic energy   is the classical [28,29] kinetic energy of reversible (equilibrium) rigid-like macroscopic rotational continuum motion.The macroscopic internal shear kinetic energy   expresses the kinetic energy of irreversible (nonequilibrium) shear continuum motion related to the rate of strain tensor   .The macroscopic internal kinetic energy of the shear-rotational coupling  coup , expresses the kinetic energy of the local coupling between irreversible deformation and reversible rigid-like rotation.
The deduced expression (13) for   confirms the postulate [35] that the velocity shear (  ̸ = 0) represents an additional energy source taking into account the Evans, Hanley, and Hess's extended formulation [35] of the first law of thermodynamics for nonequilibrium deformed states of continuum motion.The energies   ,   ,  coup , , and  res are the Galilean invariants with respect to different inertial -coordinate systems.
We obtained [31] from (13) the following expression for the macroscopic kinetic energy per unit mass   =   /  : where is the ik-component of the classical inertia tensor per unit mass of the continuum region , is the ik-component of the classical centrifugal tensor per unit mass of the continuum region , is the macroscopic translational kinetic energy per unit mass of the continuum region  (moving as a whole at speed V c of the mass center of the continuum region ), is the macroscopic internal rotational kinetic energy per unit mass of the continuum region , is the macroscopic internal shear kinetic energy per unit mass of the continuum region , is the macroscopic internal kinetic energy of the shear-rotational coupling per unit mass (of the continuum region ), and  res = ( For a homogeneous continuum region of simple form (sphere or cube) we have Formula ( 17) for the macroscopic internal rotational kinetic energy   is reduced to the classical expression [29] where  2 =  2 1 +  2 2 +  2 3 .Formula (18) for the macroscopic internal shear kinetic energy   is reduced to the expression [24,31] which is proportional to the local kinetic energy dissipation rate per unit mass  dis = 2](  ) 2 in an incompressible viscous Newtonian continuum, where ] is the molecular viscosity.The macroscopic internal kinetic energy of shear-rotational coupling  coup , vanishes for the homogeneous continuum region  of the form of the sphere or cube.The macroscopic kinetic energy   for the homogeneous continuum region  of the shape of sphere or cube is given by following expression [24,31] Hence, the macroscopic kinetic energy per unit mass   for the homogeneous continuum sphere or cube  is expressed as the sum of explicit terms [24,31] where   = (1/2)V 2 c is the macroscopic translational kinetic energy per unit mass of the continuum region ;  = /  ;  = /  ;   = (1/2) 2 is the classical [28,29] macroscopic internal rotational kinetic energy per unit mass of the continuum region ;   = (1/2)(  ) 2 is the macroscopic internal shear kinetic energy per unit mass of the homogeneous continuum sphere or cube  [24,31].
We have the following expression for the macroscopic internal kinetic energy  int of the homogeneous continuum region  of the shape of sphere or cube [24,31] The macroscopic internal kinetic energy per unit mass  int for the homogeneous continuum region  of the shape of sphere or cube is given by the sum of explicit terms [24,31]: Compare formula (31) with the de Groot and Mazur's definition (2).Expression ( 31) is reduced to de Groot and Mazur's definition (2) under condition of local thermodynamic equilibrium.Therefore, we can conclude that the definition (2) of the macroscopic kinetic energy per unit mass   in classical nonequilibrium thermodynamics [28,29] is based on the assumption   = 0 of local thermodynamic equilibrium [24,31,35].
The obtained formula (20) for   and its particular form (31) (obtained for homogeneous continuum regions of spherical and cubical shapes) generalized [24,31] the classical de Groot and Mazur expression (2) in classical nonequilibrium thermodynamics [28,29] by taking into account the irreversible dissipative shear component of the macroscopic continuum motion related to the rate of strain tensor   .The expression (20) for   contains the new macroscopic internal shear kinetic energy per unit mass   , which expresses the kinetic energy of irreversible dissipative shear motion, and also the new macroscopic internal kinetic energy of the shearrotational coupling per unit mass  coup , , which expresses the kinetic energy of local coupling between irreversible dissipative shear and reversible rigid-like rotational macroscopic continuum motions.
The macroscopic internal shear kinetic energy per unit mass (for homogeneous continuum regions of spherical and cubical shapes) is proportional to the kinetic energy viscous dissipation rate per unit mass in an incompressible viscous Newtonian continuum characterized by the kinematic viscosity ].We have shown [24] that the proportionality is the basis of the established association [36,37] between a structure and an order (and, hence, the associated macroscopic kinetic energy), on the one hand, and irreversible dissipation, on the other hand, for the dissipative structures of turbulence in viscous Newtonian fluids.
International Journal of Geophysics Considering the graphical methods in the thermodynamics of fluids, Gibbs [27] formulated the first law of thermodynamics for the fluid body (fluid region) as follows (in Gibbs' designations): where  is the differential of the internal thermal energy of the fluid body,  is the differential change of heat across the boundary of the fluid body related to the thermal molecular conductivity (associated with the corresponding external or internal heat fluxes), and  =  is the differential work produced by the considered fluid body on its surroundings (surrounding fluid) under the differential change  of the fluid region (of volume ) characterized by the thermodynamic pressure .
The formulation [32] of the first law of thermodynamics for the general thermodynamic system (material region) is given by the equivalent form (in Landau's and Lifshitz's designations [32]) where  = −  is the differential work produced by the surroundings (surroundings of the thermodynamic system) on the thermodynamic system under the differential change  of volume  of the thermodynamic system characterized by the thermodynamic pressure ;  is the differential heat transfer (across the boundary of the thermodynamic system) related to the thermal interaction of the thermodynamic system and the surroundings (surrounding environment);  is the energy of the thermodynamic system, which should contain (as supposed [32]) the kinetic energy of the macroscopic continuum motion.We shall use the differential formulation of the first law of thermodynamics [28] for the specific volume  = 1/ of the compressible viscous one-component deformed continuum with no chemical reactions: where  is the specific (per unit mass) internal thermal energy,  is the thermodynamic pressure, Π is the viscous stress tensor, k is the hydrodynamic velocity of the continuum macrodifferential element [28], and  is the differential change of heat across the boundary of the continuum region (of unit mass) related to the thermal molecular conductivity described by the heat equation [28]: where J  is the heat flux [28].The viscous stress tensor Π is taken from the decomposition of the pressure tensor P [28]: where  is the Kronecker delta tensor.
Considering the Newtonian viscous stress tensor P V ≡ Π of the compressible viscous Newtonian continuum with the components [29] the differential formulation (41) of the first law of thermodynamics (for the continuum region (of unit mass) of the compressible viscous Newtonian one-component deformed continuum with no chemical reactions) can be rewritten as follows: where ] = / is the coefficient of the molecular kinematic (first) viscosity and ] 2 =  V / is the coefficient of the molecular volume (second) viscosity [38].The first and the second terms in the right-hand side of relation (45) are analogous to the corresponding respective first and second terms in the right-hand side of the classical formulations (39) and (40).The third term in the right-hand side of relation ( 45) is related to the "internal" heat induced during the time interval  by viscous-compressible irreversibility [24].The fourth term in the right-hand side of relation ( 45) is related to the "internal" heat induced during the time interval  by viscous-shear irreversibility [24].The differential formulation (45) of the first law of thermodynamics (for the continuum element of the compressible viscous Newtonian one-component deformed continuum with no chemical reactions) takes into account (in addition to the classical terms) the viscous-compressible irreversibility and viscous-shear irreversibility inside the continuum element of the compressible viscous Newtonian one-component deformed continuum with no chemical reactions.
International Journal of Geophysics 9 Using the differential formulation (41) of the first law of thermodynamics [28] for the total derivative / (following the liquid substance) of the specific (per unit mass) internal thermal energy  of a compressible viscous onecomponent deformed continuum with no chemical reactions, the heat equation ( 42) [28], the general equation of continuum movement [29] for the deformed continuum characterized by the symmetric stress tensor T of general form (in particular, with the components [29] for the compressible viscous Newtonian one-component continuum) and taking into account the time variations of the potential  of the nonstationary gravitational field (characterized by the local gravity acceleration vector g = −∇) inside an arbitrary finite macroscopic individual continuum region , we derived [11,12] the generalized differential formulation (for the Galilean frame of reference) of the first law of thermodynamics (for moving rotating deforming compressible heatconducting stratified macroscopic continuum region  subjected to the nonstationary Newtonian gravitational field): where is the differential work done during the infinitesimal time interval  by nonpotential stress forces (pressure, compressible, and viscous forces for Newtonian continuum) acting on the boundary surface  of the continuum region ; Ω n is the differential element (of the boundary surface  of the continuum region ) characterized by the external normal unit vector n; t = n⋅T is the stress vector [29], T = −P [29], where P is the pressure tensor characterized (in particular, for the model of the compressible viscous Newtonian continuum characterized by the coefficients of kinematic viscosity ] and the volume viscosity  V ) by components (obtained from (49)) is the differential change of heat of the macroscopic individual continuum region  related to the thermal molecular conductivity of heat across the boundary  of the continuum region , where J  is the heat flux [28] (across the element Ω n of the continuum boundary surface ); is the macroscopic potential energy (of the macroscopic individual continuum region ) related to the nonstationary potential  of the gravitational field; is the classical microscopic internal thermal energy of the macroscopic individual continuum region ; is the instantaneous macroscopic kinetic energy of the macroscopic individual continuum region .The instantaneous macroscopic kinetic energy   is given by the relation ( 13) [24,31] for the small macroscopic individual continuum region .
The generalized differential formulation (50) of the first law of thermodynamics can be rewritten as follows [11,12]: extending the classical [12] formulations ( 39) and ( 40) by taking into account (along with the classical infinitesimal change of heat  and the classical infinitesimal change of the internal energy   ≡ ) the infinitesimal increment of the macroscopic kinetic energy   , the infinitesimal increment of the gravitational potential energy   , the generalized infinitesimal work  np, done on the continuum region  by the surroundings of , and the infinitesimal amount  of energy [11,12] added (or lost) as the result of the Newtonian nonstationary gravitational energy influence on the continuum region  during the infinitesimal time interval .
The generalized differential formulation (50) of the first law of thermodynamics can be rewritten as follows [11,12]: International Journal of Geophysics The equivalent generalized differential formulations ( 50), (56), and (59) of the first law of thermodynamics take into account the following factors: (1) the classical heat thermal molecular conductivity (across the boundary  of the macroscopic continuum region ) related to the classical infinitesimal change of heat : (2) the classical infinitesimal change of the internal energy   of the macroscopic continuum region : (3) the established [11,12] infinitesimal increment of the macroscopic kinetic energy   of the macroscopic continuum region : (4) the established [11,12] infinitesimal increment of the gravitational potential energy   of the macroscopic continuum region : (5) the established [11,12] generalized infinitesimal work  np, done on the macroscopic continuum region  by the surroundings of : (6) the established [11,12] infinitesimal amount  of energy added (or lost) as the result of the Newtonian nonstationary gravitational energy influence on the macroscopic continuum region  during the infinitesimal time interval : The generalized differential formulations ( 50), (56), and (59) of the first law of thermodynamics (given for the Galilean frame of reference) are valid for nonequilibrium shearrotational states of the deformed finite individual continuum region (characterized by the symmetric stress tensor T in the general equation ( 48) of continuum movement [29]) moving in the nonstationary gravitational field.The generalized differential formulations ( 50) and ( 56) of the first law of thermodynamics [11,12] are the generalizations of the classical formulations (39) and ( 40 the time variations of the potential  of the nonstationary gravitational field inside the individual continuum region  due to the deformation of the individual continuum region  and due to the external (terrestrial and cosmic) gravitational influence on the individual continuum region  moving in the total (internal + external) nonstationary gravitational field.

The Generalized Differential Formulation of the First Law of Thermodynamics (in the Galilean Frame of Reference) for Nonequilibrium Shear-Rotational States of the Deformed Finite Individual Region of the Compressible Viscous Newtonian One-Component Continuum Moving in the Nonstationary
Gravitational Field.There is evidence [39] that the rocks of the Earth's crust at protracted loadings may be considered as fluids characterized by the very high viscosity.According to the classical viewpoint [39], the local mechanism of creation of the earthquakes is related to the release of the accumulated potential energy of the elastic deformation during the sudden local break (i.e., the discontinuous shear) of the Earth's crust (or the sudden increase of fluidity in the local region of the Earth's crust) accompanied by viscous relaxation and generation of seismic waves.It was conjectured [40] that "more punctual and refined methods of the mathematical analysis are obligatory" for "the practical assessment of the seismic hazard".
Taking into account the established [31] conception of the macroscopic internal shear kinetic energy (per unit mass)   related to the rate of medium deformation (i.e., with the rate of strain tensor   =   /, where   is the deformation tensor [30]), we have elucidated [41] from the viewpoint of nonequilibrium thermodynamics the mechanism of generation of seismic waves from the separate deformed finite zone of the Earth's crust.The proportionality (37) takes place also for deformed compressible finite region of the Earth's crust for sudden rise of fluidity (in a local region of the Earth's crust) related to the local sudden medium deformation in the separate seismic zones of the seismic activity.Taking into account the established [31] proportionality (37), we have assumed [31] that the accumulated potential energy of the elastic deformation (related to the deformation tensor   ) converts to the macroscopic internal shear kinetic energy   (related to the rate of strain tensor   ) in the seismic zone simultaneously with the damping of   by viscous dissipation and radiation of seismic waves during several oscillations.In Section 3 we shall evaluate this mechanism on the basis of the generalized differential formulation (50) of the first law of thermodynamics for nonequilibrium shear-rotational states of the deformed finite individual continuum region (characterized by the symmetric stress tensor T) moving in the nonstationary gravitational field.
Following the works [11,12,25,26], we shall present the foundation of the generalized differential formulation of the first law of thermodynamics for nonequilibrium shearrotational states of the deformed finite individual region of the compressible viscous Newtonian one-component continuum moving in the nonstationary gravitational field.The generalized differential formulation (50) of the first law of thermodynamics (formulated for the Galilean frame of reference) is valid for arbitrary symmetric stress tensor T, in particular for nonequilibrium shear-rotational states of the deformed finite individual region of the compressible viscous Newtonian one-component continuum moving in the nonstationary gravitational field.The coefficient of molecular kinematic (first, shear) viscosity ] = / and the coefficient of molecular volume (second) viscosity ] 2 =  V / are assumed to vary for each time moment  as an arbitrary continuous functions of the Cartesian space (three-dimensional) coordinates.
The differential work  np, for the Newtonian symmetric stress tensor T (characterized by the components ( 49)) is presented by three explicit terms [11,12]: where is the differential work of the hydrodynamic pressure forces acting on the boundary surface  of the individual continuum region  (bounded by the continuum boundary surface ) during the infinitesimal time interval ; is the differential work (related to the combined effects of the acoustic compressibility, molecular kinematic viscosity, and molecular volume viscosity) of the acoustic (compressible) pressure forces acting on the boundary surface  of the individual continuum region  during the infinitesimal time interval ; is the differential work of the viscous Newtonian forces (related to the combined effect of the velocity shear, that is, the deformation of the continuum region , and the molecular kinematic viscosity) acting on the boundary surface  of the individual continuum region  during the infinitesimal time interval .
Along with (45) the differential formulation of the first law of thermodynamics [28] for the total derivative / (following the continuum substance) of the internal thermal energy per unit mass  of the one-component deformed continuum with no chemical reactions, the thermohydrodynamic theory [28] contains additionally the equations of the mass and momentum balances: The generalized differential formulation (50) of the first law of thermodynamics (together with the generalized differential work  np, given by the expression (66)) is valid for nonequilibrium shear-rotational states of the deformed finite individual region of the compressible viscous Newtonian one-component continuum moving in the nonstationary gravity field.The coefficient of molecular kinematic (first, shear) viscosity ] = / and the coefficient of molecular volume (second) viscosity ] 2 =  V / are assumed to vary for each time moment  as an arbitrary continuous functions of Cartesian space (three-dimensional) coordinates.
The generalized differential formulation (50) takes into account the dependences of the hydrodynamic pressure on the hydrodynamic vorticity  V and on the rate of strain tensor   by means of the component   (in the expression (66) for  np, ) given by the expression (67).The presence of the third term   (given by the expression (69) and related to the combined effect of the molecular kinematic viscosity and the deformation of the continuum region  defined by the rate of strain tensor   ) in the expression (66) for  np, generalizes essentially the classical formulations (39) and (40) of the first law of thermodynamics by taking into account the differential work of the viscous Newtonian forces acting on the boundary continuum surface  of the individual continuum region .
The general equation ( 48) of continuum movement [29] for the compressible viscous Newtonian one-component continuum is reduced to the following equation: where (Grad ) ⋅ e is the internal multiplication of the vector (Grad ) and the rate of strain tensor e in accordance with the corresponding definition [29].Equation (72) generalizes the Navier-Stokes equation (71) (given for g = 0) by taking into account the dependences of the coefficient of molecular kinematic viscosity ] = / and the coefficient of molecular volume viscosity ] 2 =  V / on the space (three-dimensional) Cartesian coordinates.
The relevant example for illustration of the significance of the term   (in the expression (66) for the differential work  np, ) is related to the thermodynamic consideration [12] of the processes of the energy exchange [42] between the oceans and the lithosphere of the Earth.According to the expression (69) for the term   , the energy exchange between the oceans (and the atmosphere) and the lithosphere of the Earth is possible only under the presence of the medium acoustic compressibility (i.e., div k ̸ = 0) and the medium deformations (i.e.,   ̸ = 0) in the boundary regions of fluid (in the oceans), air (in the atmosphere), and the compressible deformed lithosphere of the Earth.According to the generalized expression (66) for the differential work  np, , International Journal of Geophysics the energy exchange between the oceans (and the atmosphere) and the lithosphere of the Earth is impossible for nondeformed (  = 0) and noncompressible (div k = 0) lithosphere.
We have the evolution equation for the total mechanical energy (  +   ) of the deformed finite individual macroscopic continuum region  [11,12]: obtained from the generalized differential formulation (50) for the compressible viscous Newtonian one-component continuum moving in the nonstationary gravitational field.In Section 3 we shall use the evolution equation (73) of the total mechanical energy to found the rotational, shear, and the shear-rotational models of the earthquake focal region.

Cosmic and Terrestrial Energy Gravitational Genesis of the Seismotectonic (and Volcanic) Activity of the Earth Induced by the Combined Cosmic and Terrestrial Nonstationary Energy Gravitational Influences on an Arbitrary Individual Continuum Region 𝜏 (of the Earth) and by the Nonpotential Terrestrial
Stress Forces Acting on the Boundary Surface  of the Individual Continuum Region .Following the works [11,12], we shall present the physical mechanisms of the energy fluxes to the continuum region  related to preparation of earthquakes.The equivalent generalized differential formulations ( 50) and ( 59) of the first law of thermodynamics show that the nonstationary gravitational field (related to the nonstationary gravitational potential ) gives the following gravitational energy power: associated with the gravitational energy power of the total combined (external cosmic and terrestrial and internal related to the macroscopic continuum region ) gravitational field.If the macroscopic continuum region  is not very large, consequently, it cannot induce the significant time variations to the potential  of the gravity field inside the continuum region .According to the equivalent generalized differential formulations ( 50) and ( 59) of the first law of thermodynamics and to the evolution equation ( 73) for the total mechanical energy (  +   ) of the deformed finite individual macroscopic continuum region , the energy power of the gravitational field may produce the fractures in the continuum region .We shall consider this aspect in Section 3.
The generalized differential formulation (59) of the first law of thermodynamics and the expression (74) for the gravitational energy power  gr () show that the local time increase of the potential  of the gravitational field is the gravitational energy mechanism of the gravitational energy supply into the continuum region .Really, the local time increase of the potential  of the gravitational field inside the continuum region  (/ > 0) supplies the gravitational energy into the continuum region .Consequently, according to the generalized differential formulation (59) and to the evolution equation ( 73), the total energy (  +   +   ) of the continuum region  and the total mechanical energy (  +  ) of the continuum region  are increased if / > 0.
According to the generalized differential formulation (59) of the first law of thermodynamics and to the evolution equation ( 73), the gravitational energy supply into the continuum region  may induce the formation of fractures in the continuum region  related to the production of earthquake.This conclusion corresponds to the observations [1, 3-5, 9, 10, 13] of the identified anomalous variations of the gravitational field before strong earthquakes.
According to the generalized differential formulation (59) of the first law of thermodynamics and to the evolution equation (73), the supply of energy into the continuum region  may occur also by means of the work done by nonpotential stress forces (pressure, compressible, and viscous forces for Newtonian continuum) acting on the boundary surface  of the continuum region  during the time interval ( −  0 ).The considered mechanisms of the energy supply to the Earth's macroscopic continuum region  should result in the irreversible process of the splits formation in the rocks related to the generation of the high-frequency acoustic waves from the focal continuum region  before the earthquake.Taking this into account, the sum   +   in the expression ( 45) is interpreted [11,12] as the energy flux (related to the compressible and viscous forces acting on the boundary surface  of the continuum region ) [38]  vis, =   +   (76) directed across the boundary  (see Figures 2 and 3) of the continuum region .
The considered mechanisms of the energy supply to the Earth's macroscopic continuum region  should result in the significant increase of the energy flux  vis, of the geo-acoustic energy from the focal region  before the earthquake.The deduced conclusion is in a good agreement with the results of the detailed experimental studies [43].

Generalized Thermohydrogravidynamic
Shear-Rotational and Classical Shear and Rotational Models of the Earthquake Focal Region

The Generalized Thermohydrogravidynamic Shear-Rotational and the Classical Shear (Deformational) Models of the Earthquake Focal Region Based on the Generalized Differential Formulation of the First Law of Thermodynamics.
Following the works [11,12], we shall present the foundation of the generalized thermohydrogravidynamic shear-rotational model of the earthquake focal region based on the generalized differential formulation (59) of the first law of thermodynamics.Using the evolution equation (73) of the total mechanical energy of the subsystem  (the macroscopic continuum region ) of the Earth, we shall show now that the formation of fractures (modeling by the jumps of the continuum velocity on some surfaces) is related to irreversible dissipation of the macroscopic kinetic energy and the corresponding increase of entropy.We consider at the beginning the analysis of formation of the main line flat fracture (associated with the surface  1 () of the continuum velocity jump) inside the macroscopic continuum region  (bounded by the closed surface ).The macroscopic continuum region  may be divided into two subsystems  1 and  2 by continuing mentally the surface  1 () by means of surface  1 () crossing the surface  of the macroscopic region .The surface of the subsystem  1 consists of the surface () 1 (which is the part of the surface ) and the surfaces  1 () and  1 ().The surface of the subsystem  2 consists of the surface () 2 (which is the part of the surface ) and the surfaces  1 () and  1 ().
Using the formulation (73), we have the evolution equations for the total mechanical energy of the macroscopic subsystems  1 and  2 : where  1 is the external unit normal vector of the surface (of the subsystem  1 ) presented by surfaces  1 () and  1 () and − 1 is the external unit normal vector of the surface (of the subsystem  2 ) presented also by surfaces  1 () and  1 ().
Adding (77) (by using the equality Σ  1 = Σ − 1 of the elements of area of surfaces  1 () and  1 ()) we get the evolution equation for the total mechanical energy (  +   ) = (  1 +   2 +   1 +   2 ) of the macroscopic region  consisting of subsystems  1 and  2 interacting on the surface  1 () of the tangential jump of the continuum velocity: where k 1 ( 1 ) is the vector of the continuum velocity on the surface  1 () in the subsystem  1 , and k 1 ( 2 ) is the vector of the continuum velocity on the surface  1 () in the subsystem  2 .
The evolution equation (78) takes into account the total mechanical energy (  +  ) of the macroscopic region  consisting of subsystems  1 and  2 interacting on the surface  1 () of the tangential jump of the continuum velocity.The first term in the right-hand side (of (78)) describes the evolution of the total mechanical energy of the macroscopic continuum region  due to the continuum reversible compressibility; the second and third terms express the dissipation of the macroscopic kinetic energy by means of the irreversible continuum compressibility and the velocity shear.The forms of three primary terms in the right-hand side (of (78)) are related to the considered model of the compressible viscous Newtonian continuum.The fourth, fifth, and sixth terms in the right-hand side (of (78)) are the universal terms for arbitrary model of continuum characterized by symmetrical stress tensor T. The fourth term expresses the power of external (for the continuum region ) nonpotential stress forces acting on the boundary surface  of the macroscopic continuum region .The fifth term expresses the power of external (for the continuum region ) forces on different sides of the surface   () characterized by the velocity jump during the fracture formation.The sixth term in (78) presents the power of the total mechanical energy added (or lost) as the result of the Newtonian nonstationary gravitational energy influence on the macroscopic continuum region  related to variations of the potential  of the combined gravitational field in the continuum region .Consider (78) for one continuum velocity jump on the nonstationary surface  1 () during the time interval (, +Δ).Taking into account the form of the fifth term on the righthand side of the evolution equation (78), we obtained [11,12] the expression for the work  np, 1 () (done during the time interval (, +Δ) by the external (for the continuum region ) nonpotential stress forces acting on different sides of the velocity jump on the surface  1 ()): which is reduced to the following expression: To test the formula (81), let us calculate the energy  np,ΔΣ , which dissipates during formation of the surface dislocation on the small surface ΔΣ during the time interval (,  + Δ).Using the theorem about the average value and integrating the internal integral on time, we obtained from relation (81) for  1 () = ΔΣ the following relation [11,12]: where ⟨( 1 ⋅ T)⟩ is the average value of the stress vector for the element of area Σ  1 of the two-side surface ΔΣ, and w( 1 ,  + Δ) and w(− 1 ,  + Δ) are the vectors of the continuum displacement on different sides of the element of area Σ  1 of the two-side surface ΔΣ in the points characterized by normal unit vectors  1 and − 1 .Using the obvious expression for "linear" time average ⟨( as the arithmetical average of the values of the stress vectors p on the different sides from the surface of the jump of the continuum velocity, we obtained [11,12] the expression for the elementary work of the external nonpotential stress forces on the two-side surface ΔΣ of dislocation: This expression was obtained [44] in the frame of the classical linear approach to formation of surface dislocations in rigid compressible continuum on the small area of surface ΔΣ.It is clear that the assumption (83) is valid only for weak tangential jumps of the continuum displacement.Consequently, we can consider the expression (80) as the natural nonlinear generalization of expression (84) for arbitrary surface  1 () of dislocation and for strong tangential jumps of the continuum displacement on the surface  1 () of dislocation.The work (80) of the external (for the continuum region ) nonpotential stress forces should be negative.The sufficient energy  , 1 () needed for formation of the surface  1 () of dislocation is equal to the work of the internal forces in the macroscopic continuum region .The energy  , 1 () should be positive and equal to the expression (80) with the sign "−": The formulae (80), (84), and (85) are obtained (taking into account the generalized differential formulation (50) of the first law of thermodynamics) for the model of continuum characterized by an arbitrary symmetrical stress tensor T. The macroscopic internal shear kinetic energy (  )  1 (of the subsystem  1 ), the macroscopic internal rotational kinetic energy (  )  1 (of the subsystem  1 ), and the macroscopic kinetic energy of shear-rotational coupling ( coup , )  1 (of the subsystem  1 ) are the significant components of the macroscopic internal shear-rotational kinetic energy ( - )  1 [11,12,24,31]: taken into account (along with the classical internal thermal energy   1 of the macroscopic continuum region  1 , the macroscopic potential energy   1 of the macroscopic continuum region  1 , and the macroscopic translational kinetic energy (  )  1 = (1/2)  1 (V  ) 2  1 of the continuum region  1 (of a mass   1 ) moving as a whole at speed equal to the speed (V  )  1 of the center of mass of the continuum region  1 ) in the generalized differential formulation (50) of the first law of thermodynamics for the macroscopic continuum region  1 .
The macroscopic internal shear kinetic energy (  )  2 (of the subsystem  2 ), the macroscopic internal rotational kinetic energy (  )  2 , and the macroscopic kinetic energy of shearrotational coupling ( coup , )  2 are the significant components of the macroscopic internal shear-rotational kinetic energy ( - )  2 [11,12,24,31]: taken into account (along with the classical internal thermal energy   2 , the macroscopic potential energy   2 , and the macroscopic translational kinetic energy (  )  2 = (1/2)  2 (V  ) 2  2 of the continuum region  2 (of a mass   2 ) moving as a whole at the speed (V  )  2 of the center of mass of the continuum region  2 ) in the generalized differential formulation (50) of the first law of thermodynamics for the macroscopic continuum region  2 .
The macroscopic internal shear kinetic energy (  )  1 (of the subsystem  1 ), the macroscopic internal rotational kinetic energy (  )  1 , the macroscopic kinetic energy of shear-rotational coupling ( coup , )  1 , the macroscopic translational kinetic energy 1 , the macroscopic potential energy   1 , the macroscopic internal shear kinetic energy (  )  2 (of the subsystem  2 ), the macroscopic internal rotational kinetic energy (  )  2 , the macroscopic kinetic energy of shear-rotational coupling ( coup , )  2 , the macroscopic translational kinetic energy (  ) 2 , and the macroscopic potential energy   2 are the significant energy components taken into account in the presented thermohydrogravidynamic shear-rotational model described by the evolution equation (78) for the total mechanical energy (  +   ) of the macroscopic region  consisting of interacting subsystems  1 and  2 .

The Rotational Model of the Earthquake Focal Region
Based on the Generalized Differential Formulation of the First Law of Thermodynamics.Following the works [11,12], we shall present the foundation of the rotational model [2] of the earthquake focal region for the seismic zone of the Pacific Ring.It was noted [2] that the studies of the dislocation models of the focal regions of strong earthquakes showed the bad correspondence with the model of flat endless dislocation in the uniform continuum [45][46][47].The analysis [2] showed that the conditions exist to realize the rotational mechanism related to the rotation of the geoblocks by means of the stress forces related to the Earth rotation in the vicinity of the seismic zone of the Pacific Ring.It was noted [2] that the rotational mechanism can be more real compared to the conventional mechanism related to the formation of the main line flat fracture inside the focal region.
Let us consider the energy thermodynamic analysis of the rotational mechanism [2] of the earthquake focal region, related to formation of the circular continuum velocity jump revealed in the form of circular dislocation after relaxation of the seismic process in the earthquake focal region.The developed and tested (in this section) mathematical formalism of description of the main line flat fracture may be generalized on the closed surfaces of the continuum velocity jumps.Following the rotational model [2] of the earthquake focal region, we consider the separate geoblock  int of the seismic zone.If the external influences of the nonstationary gravitational forces (on the geoblock  int ) and the nonpotential stress forces (on the boundary   of the geoblock  int ) exceed the certain critical value then the geoblock may rotate and slip relative to the surrounding fine plastic layer (subsystem)  ext with the tangential continuum velocity jump on the boundary surface   of the geoblock  int .We assume that fine plastic layer (subsystem)  ext is limited by external surface  of the considered thermodynamic system  consisting of the macroscopic subsystems  int and  ext .
Using the evolution equation (73) of the total mechanical energy of the subsystem , we obtained [11,12] the evolution equations for the total mechanical energy of the macroscopic subsystems  int and  ext : where m is the external unit normal vector of the surface   of the subsystem  int , −m is the internal unit normal vector of the surface   , n is the external unit normal vector of the surface , k int (  ) are the velocities vectors on the inner side of the surface   in the subsystem  int , and k ext (  ) are the velocities vectors on the outer side of the surface   in the subsystem  ext .
Adding the evolution equation (88) and using the condition of equality Σ m = Σ −m of the area elements of the surface   , we get the evolution equation for the total mechanical energy of the macroscopic continuum region  consisting of the subsystems  int and  ext interacting on the surface   of the continuum velocity jump: Equation ( 89) is analogous to (78).The energy needed for formation of the continuum velocities jumps (on the surfaces  1 () and   ) is related to the penultimate terms in the righthand sides of (78) and (89).Similar to expression (85), we have the expression for the sufficient energy  ,  needed to rotate and slip (for the subsystem  int ) during the time interval (,  + Δ) relative to the surrounding fine plastic layer (subsystem)  ext (with the tangential continuum velocity jump (k int (  ) − k ext (  )) on the boundary surface   of the geoblock  int ): Taking into account the information [2] that the critical continuum stresses (required for rotation of the geoblock  int weakly coupled with the surrounding plastic layer  ext ) are less than the critical continuum stresses required to split the mountain rock by forming the main line flat fracture, we concluded [11,12] that the required energy  ,  (given by the expression (90)) is less than the required energy  , 1 () (given by the expression (85)) if the displacements of the rock continuum on different sides of the analyzed different jumps of the continuum displacements (the closed dislocation and the main line flat fracture) have the same order of magnitude and the ratio of the surfaces area of the closed dislocation to the surfaces area of the main line flat fracture does not exceed 10.
This thermodynamic energy consideration showed [11,12] the preferable realization of the rotational motion of the geoblock  int (under condition that exists the surrounding plastic layer around the geoblock  int ) as compared with formation of the of the main line flat fracture inside the geoblock  int .This result explains the rotational motions of the geoblocks in the seismic zone of the Pacific Ring [2] and the vortical structures of the lithosphere of Earth [48] and the lithospheres of the planets [49] of the Solar System.
Using of the generalized differential formulation (50) of the first law of thermodynamics for the macroscopic continuum region  of the quasi-uniform medium of the Earth's crust characterized by practically constant viscosity, we obtained [11,12] the thermodynamic foundation of the classical deformational (shear) model [1] of the earthquake focal region for the quasi-uniform medium of the Earth's crust characterized by practically constant viscosity.

The Instantaneous Energy Gravitational Influences on the Earth of the Planets of the Solar System in the Approximation
of the Elliptical Orbits of the Planets.We shall consider the movements of the Earth  3 and the outer (or inner) planet   in the ecliptic plane  (see Figure 4) around the Sun  0,0 in the approximation of the elliptical orbits of the planets.The mass center  3 of the Earth  3 , the mass center  of the Sun, and the mass center   of the inner ( = 1, 2) and the outer ( = 4, 5, 6, 7, 8, 9) planet   are located on the direct coordinate axis  at a certain initial time moment  = 0 characterized by the minimal distance between the mass center   of the inner ( = 1, 2) and the outer ( = 4, 5, 6, 7, 8, 9) planet   and the mass center  3 of the Earth  3 .The fixed mass center  of the Sun is considered as the right focus of the elliptical orbits of the inner ( = 1, 2) planet   , the outer ( = 4, 5, 6, 7, 8, 9) planet   , and the Earth  3 .
The combined maximal contribution of these additional two terms is of the order for the inner ( = 1, 2) planet   and of the order for the outer ( = 4, 5, 6, 7, 8, 9) planet   .Consequently, the contribution of the first term in the figured brackets of the expression (96) is (1/  , 1/ 3 ) times larger than the contribution of the additional two new terms related to the eccentricities   and  3 .Using the maximal eccentricity  1 = 0.206 of Mercury's orbit, we have that the contribution of the first term in the figured brackets of the expression (96) is approximately 5 times larger than the contribution of the additional two new terms (in the figured brackets of the expression (96)) related to the eccentricities  1 = 0.206 and  3 = 0.017 of the elliptical orbits of Mercury  1 and the Earth  3 , respectively.We have that the first term (in the figured brackets of the expression (96)) is significantly larger than the contribution of the additional two new terms for the other planets (of the Solar System) having the small eccentricities of the elliptical orbits.
Thus, the obtained [12,25,26] evaluation (97) (for the circular orbits of the planets) of the relative maximal energy gravitational influences on the Earth (of the planets of the Solar System) may be considered as the first sound approximation for the evaluation of the relative maximal energy gravitational influences of the inner ( = 1, 2) and the outer ( = 4, 5, 6, 7, 8, 9) planets on the Earth.

The Evaluation of the Relative Maximal Planetary Instantaneous Energy Gravitational Influences on the Earth in the Approximation of the Circular Orbits of the Planets of the Solar
System.Following the monograph [12], we shall consider the movement of the Earth  3 and the inner planet   around the Sun  0,0 in the first approximation of the circular orbits of the planets.The planets revolve in the ecliptic plane  (see Figures 5 and 6).The mass center of the Sun is located at the fixed point  of the origin of the coordinate system.The mass center  3 of the Earth, the mass center  of the Sun, and the mass center   of the inner planet   are located on the direct coordinate axis  at a certain initial time moment  = 0 characterized by the minimal distance between the Earth and the inner planet   (see Figure 5).
We have the following expressions for the angles   and  3 : which describe the positions of the mass centers of the planet   and the Earth  3 during the time .We shall consider the gravitational potential  3 ( 3 , int) created by the inner planet   in the mass center  3 of the Earth.We have the distance  3 ( 3 ) between the mass center   of the inner planet   and the mass center  3 of the Earth (see Figure 7): The relation (101) can be rewritten as follows [12]: We derived [12] the expression for the partial derivative (/) 3 ( 3 , int): which is reduced to zero for the time moments  *  (, 3) = (1/2)(   3 /( 3 −   )) (for  = 1, 2;  = 0, 1, 2, . ..), when the mass centers of the Sun, the Earth, and the inner planet   are located on the direct line.
We have (for configuration of the Earth and the outer planet   shown on Figure 8) the distance  3 ( 3 ) between the mass center   of the planet   and the mass center  3 of the Earth: The gravitational potential created by the outer planet   at the point  3 (for configuration shown on Figure 8) is given by the following expression: We derived [12] the expression of the partial derivative (/) 3 ( 3 , ext) for the expression (106): We used [25,26] the maximal positive value max(/ ) 3 ( 3 , int) (of the partial derivative (/) 3 ( 3 , int) International Journal of Geophysics of the gravitational potential  3 ( 3 , int) created by Mercury at the mass center  3 of the Earth) as a scale of the energy gravitational influence of the planets of the Solar System on the Earth in the considered first approximation of the circular orbits of the planets.To evaluate the relative energy gravitational influence of the inner planet   (Mercury or Venus) at the mass center  3 of the Earth, we considered [25,26] the ratio (,  3 ) of the maximal positive value max(/) 3 ( 3 , int) (of the partial derivative (/) 3 ( 3 , int) of the gravitational potential  3 ( 3 , int) created by the inner planet   at the point  3 ) and the maximal positive value max( 31 ( 3 , int)/) (of the partial derivative  31 ( 3 , int)/ of the gravitational potential  31 ( 3 , int) ≡  3 ( 3 , int) created by Mercury at the mass center  3 of the Earth): We obtained [25,26] from expression (108) the obvious value (1,  3 ) = 1 for Mercury  1 .Using the formula (108) for Venus ( = 2), we calculated [25,26] the numerical value (2,  3 ) = 37.69807434 for the following numerical values [35]: the mass   = 0.06 3 of Mercury, where  3 is the mass of the Earth, the mass   =  2 = 0.82 3 of Venus, the time period  3 = 365.3days of the Earth's circulation around the Sun, the time period   = 88 days of Mercury's circulation around the Sun, the time period   =  2 = 224.7 days of the Venusian circulation around the Sun, the average radius   =  1 = 57.85⋅ 10 6 km of Mercury's orbit, around the Sun, the average radius  3 = 149.6 ⋅ 10 6 km of the Earth's orbit, and the average radius   =  2 = 108.1 ⋅ 10 6 km of Venusian orbit around the Sun.The power of the maximal energy gravitational Venusian influence (on the unit mass at the mass center  3 of the Earth) is (2,  3 ) = 37.69807434 times larger than the power of the maximal energy gravitational influence of Mercury (on the unit mass at the mass center  3 of the Earth).
To evaluate the relative energy gravitational influence of the inner planets   (Mercury and Venus) and the outer planets   (Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto) at the surface point  3 (which is the intersection of the direct line (connecting the mass center  of the Sun and the mass center  3 of the Earth) with the surface of the Earth), we obtained [12] the gravitational potential  3 ( 3 , int): created by the inner planet   in the surface point  3 of the Earth.We derived the expression for the partial derivative (/) 3 ( 3 , int) of the gravitational potential (110): International Journal of Geophysics

21
The gravitational potential created by the outer planet   at the surface point  3 (for configuration shown on Figure 8) is given by the following expression [12]: We derived [12] the expression of the partial derivative (/) 3 ( 3 , ext) of the gravitational potential (112): which is reduced to the relation (111) owing to the equalities sin(  − 3 ) = − sin( 3 −  ) and cos(  − 3 ) = cos( 3 −  ).However, we take into account that the expression ( 113) is given for the outer planet   , but the expression ( 111) is given for the inner planet   .
We used [12,25,26] the maximal positive value max(/ ) 3 ( 3 , int) (of the partial derivative (/) 3 ( 3 , int) of the gravitational potential  3 ( 3 , int) created by Mercury at the surface point  3 of the Earth) as a scale of the energy gravitational influence of the planets of the Solar System on the Earth in the considered first approximation of the circular orbits of the planets.
Taking into account the calculated powers of the maximal energy gravitational influences of the planets on the unit mass of the Earth (at the mass center  3 of the Earth and at the surface point  3 of the Earth), we obtained [12,25,26] the following order of signification of the planets of the Solar System (Venus, Jupiter, Mercury, Mars, Saturn, Uranus, Neptune, and Pluto) with respect to the planetary power of the maximal energy gravitational influences on the unit mass of the Earth.
The revealed [25,26] small difference of the maximal energy gravitational influence of each planet at the surface point  3 and at the mass center  3 of the Earth must lead to the small difference of the combined maximal energy gravitational influences of the planets of the Solar System at the points  3 and  3 of the Earth.It was recognized [25,26] that the small difference of the combined planetary maximal energy gravitational influences at the surface point  3 and at the mass center  3 of the Earth can contribute to the following related geophysical phenomena: the small oscillatory motion of the rigid kernel of the Earth relative to the fluid kernel of the Earth; the small oscillation of the Earth's pole (i.e., the Chandler's wobble of the Earth's pole); the small oscillations of the boundary of the Pacific Ocean (i.e., the seismic zone of the Pacific Ring); the oscillations, rotations, and deformations of the geoblocks weakly coupled with the surrounding plastic layers in all seismic zones of the Earth and the formation of fractures related to the strong earthquakes and the planetary cataclysms.

The Evaluation of the Relative Maximal Planetary Integral Energy Gravitational Influences on the Earth in the Approximation of the Circular Orbits of the Planets of the Solar
System.We assume that  03 and  0 are the initial phases of the Earth  3 and the planet   , respectively.Consequently, the positions of the center of the Earth  3 and the center of the planet   (inner or outer) for the time moment  are given (instead of the relation (100)) by the following expressions: Taking into account the initial phases  03 and  0 , the expressions (104), ( 107), (111), and (113) can be generalized as follows: We obtained [12] the integral energy gravitational influence Δ   3 (  ,  0 ,  03 , ,  0 ) on the Earth  3 owing to the nonstationary instantaneous energy gravitational influence of the planet   (inner or outer) during the time interval ( 0 , ): where  3 is the mass of the Earth.Substituting (119) into (121), we obtained [12] The result of integration of the expression (122) is given by the relation [12]: characterized by the following coefficients: Using the initial phases  03 = 0 and  0 = 0 for the initial time moment  0 = 0, the expression (123) gives the more simple relation [12]: used for calculation of the maximal integral energy gravitational influence of the planet   (inner or outer) on the Earth  3 .Consider the expression (125) by taking into account that the mass center   of the inner planet   , the mass center  3 of the Earth  3 , and the mass center  of the Sun are located on the axis  for the initial time moment  0 = 0 as it is shown on Figure 6.Considering the time duration we obtain that the mass center   of the inner planet   , the mass center  3 of the Earth  3 , and the mass center  of the Sun will be localized again on the same straight line and the distance between the mass centers of the inner planet   , and the Earth  3 will be maximal.We have from relation (125) the positive integral energy gravitational influence on the Earth's continuum during the time  * 1 (, 3): We obtained [12] from relation (125) that the integral energy gravitational influence on the Earth of the inner planet   is equal to the zero during the time duration when the distance between the mass centers of the inner planet   and the Earth  3 will be minimal.
We tested [12] the relation (125) for the outer planet   and the Earth  3 assuming that the mass centers of the outer planet   and the Earth  3 and the mass center  of the Sun are located on the axis  for the initial time moment  0 = 0 as it is shown on Figure 6.Considering the time duration , ( = 4, 5, we have that the mass center of the outer planet   , the mass center  3 of the Earth  3 , and the mass center  of the Sun will again be located on the same straight line, and the distance between the mass centers of the outer planet   and the Earth  3 will be maximal.We obtained [12] from relation (125) the negative integral energy gravitational influence on the Earth of outer planet   during the time  * 1 (3, ): Considering the time duration we obtained [12] from relation (125) the zero integral energy gravitational influence on the Earth from the outer planet   during the time  * 2 (3, ): Using the expression (124), we established [12] that the expressions (127) and (131) give the following extreme values: of the integral energy gravitational influences (respectively, the positive maximal integral energy gravitational influence from the inner planet   and the negative minimal integral energy gravitational influence from the outer planet   ) for the given initial phases  03 = 0 and  0 = 0 (for the initial time moment  0 = 0) corresponding to the initial configurations shown on Figures 5 and 6.
Using relation (134), we obtained [12] for Mercury ( = 1) and for Venus ( = 2) the following expressions of the maximal positive integral energy gravitational influences on the Earth: Considering the mass   of the macroscopic continuum region near the surface point  3 (instead of the mass  3 of the Earth) in relations ( 136) and (137), we obtained [12] the following expressions for the positive integral energy gravitational influences of Mercury ( = 1) and Venus ( = 2) on International Journal of Geophysics the macroscopic continuum region of the mass   near the surface point  3 of the Earth: We shall use the expression (136) as a measuring unit for evaluations of the maximal absolute values of the integral energy gravitational influences on the Earth of the planets of the Solar System and the Moon.
Considering the ratio of the extreme value max  Δ   3 (  , 0, 0, , 0) (given by expression (134)) and the maximal positive integral energy gravitational influence max  Δ   3 ( 1 , 0, 0, , 0) (given by the expression (136)) of Mercury on the Earth, we obtained [12] the relative values () of the maximal integral energy gravitational influences on the Earth of the inner planets: We have the obvious value (1) = 1 for Mercury ( = 1).We calculated [12] the value (2) = 89.6409for Venus ( = 2) based on the planetary numerical values [50] of the average radii of the orbits, the time periods of circulations around the Sun, and the masses of the Earth, Venus, and Mercury.
We established [12] that Venus and Jupiter induce the main maximal integral energy gravitational influences on the Earth.Mars, Saturn, and Mercury induce the combined maximal integral energy gravitational influence on the Earth, which is one order of the magnitude smaller than the maximal integral energy gravitational influence of Jupiter.The maximal integral energy gravitational influences on the Earth of Uranus, Neptune, and Pluto are two, three, and seven orders of the magnitude, respectively, smaller than the maximal integral energy gravitational influence of Mercury.

The Evaluation of the Relative Maximal Instantaneous Energy Gravitational Influence of the Moon on the Earth in the
Second Approximation of the Elliptical Orbits of the Earth and the Moon around the Combined Mass Center  3, of the Earth and the Moon.We shall consider the movement of the Earth  3 and the Moon along the elliptical orbits around the combined mass center  3,MOON of the Earth and the Moon.
We have the following relations (see Figure 9): We obtained [25,26] from the relation (146) the expression for the partial derivative (/) between the mass center  MOON of the Moon and the mass center  3 of the Earth  3 .We have the expression for the gravitational potential  3,MOON ( 3 ) created by the Moon at the mass center  3 of the Earth  3 : We obtained [25,26] from the relation (149) the expression for the partial derivative: We can obtain the focal parameter  MOON of the elliptical orbit of the Moon in terms of the average distance  3 (between the mass centers of the Earth and the Moon) and the eccentricity  MOON =   of the elliptical orbits of the Moon and the Earth around the combined mass center  3,MOON of the Earth and the Moon.Using the relation (143), we have the relation for the large semiaxis  MOON of the elliptical orbit of the Moon: which gives the relation for the focal parameter  MOON of the elliptical orbit of the Moon: We can obtain the large semiaxis  MOON of the elliptical orbit of the Moon in terms of the average distance  3 (between the mass centers of the Earth and the Moon) and the eccentricity  MOON of the elliptical orbit of the Moon.Defining the average distance  3 (between the mass centers of the Earth and the Moon) as the average arithmetic value of the large semiaxis  MOON and the small semiaxis  MOON of the elliptical orbit of the Moon International Journal of Geophysics and using the definition of the eccentricity  MOON of the elliptical orbit of the Moon we obtained [25,26] the relation for the average distance  3 : which leads to the relation for the large semiaxis  MOON : Using the relations ( 152) and ( 156), we obtained [25,26] the relation for the focal parameter  MOON of the elliptical orbit of the of the Moon: Using the relation (157) and the relations the relation (150) can be rewritten as follows [25,26]: Taking sin( MOON ()) = 1 and equating evaluating  MOON ()/ to  MOON (for the corresponding hypothetical circular orbits of the Earth and the Moon), we obtained [25,26] the characteristic maximal positive value of the partial derivative (/) (160) To evaluate (in the second approximation) the relative power of the energy gravitational influence of the Moon on the Earth, we obtained the ratio  MOONM ( 3 , second approximation) of the maximal characteristic maximal positive value char.max .pos.(/) 3,MOON ( 3 , second approximation) and the maximal positive value max(/) 3 ( 3 , int): The corresponding numerical value  MOONM ( 3 , second approximation) = 19.44083was calculated [25,26] by taking into account the following numerical values:  MOON = 0.05,  MOON =  3 /81,   = 0.06 3 ,  MOON = 29.5306days, and   = 88 days.
The calculated numerical value  MOONM ( 3 , second approximation) is 19.44083 times larger than the maximal power of the energy gravitational influence (on the unit mass at the mass center  3 of the Earth) of Mercury moving around the mass center  of the Sun along the hypothetical circular orbit.

The Evaluation of the Maximal Integral Energy Gravitational Influence of the Moon on the Earth in the Approximation of the Elliptical Orbits of the Earth and the Moon around
the Combined Mass Center  3, of the Earth and the Moon.We evaluated [25,26] the maximal integral energy gravitational influence of the Moon on the Earth in the approximation of the elliptical orbits of the Earth and the Moon around the combined mass center  3,MOON of the Earth and the Moon.We have the integral energy gravitational influence of the Moon on the Earth  3 (characterized by the mass  3 ) during the time interval ( 0 , ): Substituting the expression (159) into (162) and integrating, we obtained [25,26] the following analytical relation: Considering the following phases:  MOON () =  and  MOON ( 0 ) = 0, we have from relation (163) the maximal positive value of the integral energy gravitational influence of the Moon on the Earth: To evaluate the maximal integral energy gravitational influence of the Moon on the Earth, we consider the ratio (Moon, second approximation) of the maximal positive value (164) and the maximal positive value (136) (of the integral energy gravitational influence of Mercury on the Earth): Using the relation (165), we calculated [25,26] the numerical value (Moon, second approximation) = 13.0693 for the following numerical values: the eccentricity  MOON = 0.05 of the elliptical orbits of the Moon and the Earth around the combined mass center  3,MOON , the mass  1 =   = 0.06 3 aof Mercury, the mass  MOON =  3 /81 of the Moon, the average distance  3 = 384400 km between the mass centers of the Earth and the Moon, the time period  3 = 365.3days of the Earth's circulation around the Sun, the time period  1 =   = 88 days of Mercury's circulation around the Sun, the average radius  OM =  1 = 57.85⋅ 10 6 km of Mercury's orbit around the Sun, and the average radius  3 = 149.6 ⋅ 10 6 km of the Earth's orbit around the Sun.
Thus, considering the aspect of the cosmic gravitational preparation of the strong earthquakes, we have demonstrated the Venusian ((2) = 89.6409)and Jupiter's ((5) = 31.319)energy gravitational predominance [12] in supplying of the cosmic planetary gravitational energy to the focal region of the preparing earthquakes.We have demonstrated the significant maximal integral energy gravitational influence of the Moon ((Moon, second approximation) = 13.0693)[25,26] on the Earth.Venus, Jupiter, and the Moon induce the main combined (planetary and lunar) integral energy gravitational influence on the Earth.The combined maximal integral energy gravitational influence on the Earth of Mars ((4) = 2.6396), Saturn ((6) = 1.036), and Mercury ((1) = 1) is one order of the magnitude smaller than the maximal integral energy gravitational influence of Venus.The combined maximal integral energy gravitational influence on the Earth of Uranus ((7) = 0.0133), Neptune ((8) = 0.003229), and Pluto ((9) = 1.4495 ⋅ 10 −7 ) is two orders of the magnitude smaller (i.e., negligible) than the maximal integral energy gravitational influence of Mercury.Taking into account the obtained [12] numerical values () for the planets of the Solar System and the numerical value (Moon, second approximation) = 13.0693 for the Moon [25,26], we can recognize the established [25,26] predominant significance of the Moon (along with the minor significance of Venus, Jupiter, and Mercury) as the predominant lunar cosmic trigger mechanism of earthquakes preparing by the combined (planetary and lunar) integral energy gravitational influences on the Earth of Venus, Jupiter, the Moon, Mars, and Mercury.

The Demonstration of the
It was suggested in [51] the hypothesis that the Chandler's wobble of the Earth's pole can be generated by the motion of the rigid kernel of the Earth induced by the disturbances in the Sun-Earth-Moon system.The presented results of Sections 4.1, 4.2, and 4.3 support the stated [25,26] conclusion that the related geophysical phenomena (the small oscillatory motion of the rigid kernel of the Earth relative to the fluid kernel of the Earth [51]; the small oscillation of the Earth's pole (i.e., the Chandler's wobble of the Earth's pole); the small oscillations of the boundary of the Pacific Ocean (i.e., the seismic zone of the Pacific Ring [2]); the oscillations [42], rotations, and deformations [1,2] of the geoblocks weakly coupled with the surrounding plastic layers in all seismic zones of the Earth and the formation of fractures related to the strong earthquakes [1-5, 9-12, 23] and the planetary cataclysms [25,26]) are induced by the combined nonstationary cosmic energy gravitational influence on the Earth of the planets of the Solar System, the Sun, and the Moon.

The Cosmic Energy Gravitational Genesis of the
Considering the different approximation of the ratio  3 / MOON , we obtained [12] the successive approximations for the time periodicities:

International Journal of Geophysics
(2) The Time Periodicities of the Maximal (Instantaneous and Integral) Energy Gravitational Influences on the Earth of Venus.If the configuration of the Earth and Venus is characterized at any time moment by the maximal (instantaneous or integral) energy gravitational influence on the Earth, then the Earth and Venus will have the recurrence of the same configuration (in the frame of the real elliptical orbits of the Earth and Venus) after  ,3 circulations of Venus around the Sun and  3, circulations of the Earth around the Sun to satisfy the following condition [12]: Following the known method [52], we present the ratio  3 /  by the following mathematical fraction: Considering the different approximation of the ratio  3 /  , we obtained the successive approximations for the time periodicities [12]: of recurrence of the maximal (instantaneous and integral) energy gravitational influences of Venus on the Earth in the first and second approximations, respectively.We can verify that the time periodicity may be considered as the third approximation of recurrence of the maximal (instantaneous and integral) energy gravitational influences of Venus on the Earth.
(3) The Time Periodicities of the Maximal (Instantaneous and Integral) Energy Gravitational Influences on the Earth of Jupiter.If the configuration of the Earth and Jupiter is characterized at any time moment by the maximal (instantaneous or integral) energy gravitational influences on the Earth, then the Earth and Jupiter will have the recurrence of the same configuration (in the frame of the real elliptical orbits of the Earth and Jupiter) after  ,3 circulations of Jupiter around the Sun and  3, circulations of the Earth around the Sun to satisfy the condition [12]  ,3   =  3,  3 .
Following the known method [52], we present the ratio   / 3 by the following mathematical fraction: (182) Considering the different approximation of the ratio   / 3 , we obtained the successive approximations for the time periodicities [12]: Following the known method [52], we present the ratio  MARS / 3 by the mathematical fraction: Considering the different approximation of the ratio  MARS / 3 , we obtained the successive approximations for the time periodicities [12]:

Empirical Time Periodicities of the
Seismotectonic Activity of the Earth.It was pointed out [1] that the sinusoidal "saw-like" form of the graphic dependence of growth and recession of the seismotectonic activization of the separate geological structure is related to the following empirical time periodicities: It was pointed out [2] that the strongest earthquakes in the all boundary region of the Pacific Ocean are characterized by the established tendency for recurrence on average once during the following time period [53][54][55][56][57][58][59][60][61]: It was pointed out [2] also that the close values for recurrence of the strongest earthquakes were established for different seismic belts of the Earth: 90÷140 years for the Caucasus [62] and 150 years for the Anatolian fault zone [63].We present the data of the monograph Based on the data presented in the monograph [2] concerning the recurrence of the strongest earthquakes in different regions of the Earth, Dr. A. V. Vikulin made the valid conclusion that the seismic processes have the global nature for the Earth.In the next section we shall explain the considered empirical time periodicities by the different combinations of the cosmic energy gravitational influences on the Earth of the Sun-Moon system, Venus, Jupiter, and Mars.

The Time Periodicities of the Periodic Global Seismotectonic (and Volcanic) Activity and the Global Climate Variability of the Earth Induced by the Different Combinations of the Cosmic Energy Gravitational Influences of the Sun-Moon
System, Venus, Jupiter, and Mars.We have shown [12] that the periodic recurrence (characterized by the time periodicity  energy ) of the maximal integral energy gravitational influences on the Earth (defined by the planetary combination of the Sun-Moon system and the arbitrary combination of the planets: Venus, Mars, and Jupiter) leads (according to the generalized differential formulations (50) applied for the Earth) to the periodic recurrence of the maximal tectonic activity (characterized by the same time periodicity  tec =  energy ) of the geospheres of the Earth and each geoblock of Earth.We have shown [12] that the periodic recurrence (characterized by the time periodicity  tec =  energy ) of the maximal tectonic (and volcanic) activity of the geospheres of the Earth and each geoblock of the Earth (defined by the combination of the Sun-Moon system and the arbitrary combinations of the planets: Venus, Mars, and Jupiter) leads to the periodic recurrence (characterized by the time periodicity  tec =  energy ) of the maximal concentration of the atmospheric greenhouse gases owing to the periodic increase (characterized by the time periodicity  tec =  energy ) of the output of the greenhouse gases related to the periodic tectonic-volcanic activization of the Earth.We have shown [12] that the periodic increase (characterized by the time periodicity  tec =  energy ) of the average planetary concentration of the atmospheric greenhouse gases leads (as a consequence of the greenhouse effect produced by the gravity-induced periodic tectonic-volcanic activization accompanied by increase of the atmospheric greenhouse gases) to the periodic global planetary warming related to the increase (characterized by the time periodicity  tec =  energy ) of temperature of the atmosphere-ocean system of the Earth.The periodic decrease (characterized by the time periodicity  tec =  energy ) of the average planetary concentration of the atmospheric greenhouse gases leads (as a consequence of the decreased greenhouse effect) to the periodic global planetary cooling [12] related to the fall (characterized by the time periodicity  tec =  energy ) of temperature of the atmosphere-ocean system of the Earth.The time periodicity  energy of the periodic recurrence of the maximal integral energy gravitational influences on the Earth (defined by the combination of the Sun-Moon system and the arbitrary combinations of the planets: Venus, Mars, and Jupiter) corresponds to different two time periodicities of the Earth's climate variability [12]: the first time periodicity  clim1 =  tec =  energy (related to the periodic tectonicvolcanic activity of the geospheres of the Earth induced by the cosmic nonstationary combined energy gravitational influences on the Earth of the Sun-Moon system, Venus, Mars, and Jupiter) and the second time periodicity  clim2 =  endog =  energy /2 related to the periodic tectonic-endogenous heating (of the geospheres of the Earth, the atmosphere, and the oceans of the Earth) induced by the periodic continuum deformation (characterized by the time periodicity  energy ) owing to the periodic cosmic nonstationary combined energy gravitational influences (characterized by the time periodicity  energy ) on the Earth of the Sun-Moon system, Venus, Mars, and Jupiter.
Table 1: The time periods  1 (given in years) of recurrence of the strongest Japanese earthquakes [2] and the obtained [12,25,26] corresponding time periodicities (given in years) determined by the following cosmic combinations.

Region
The occurrence of two large earthquakes in 2008 in the areas surrounding Yutian (Xinjiang) and Wenchuan (Sichuan) confirmed the proposed [12,25,26] cosmic energy gravitational genesis of the strong Chinese earthquakes.

Cosmic Energy Gravitational Genesis of the Strongest
Japanese Earthquakes near the Tokyo Region.We have shown [12,25,26] the cosmic energy gravitational genesis of the strongest ( ≥ 7.9) Japanese earthquakes near Tokyo region and southwest from Tokyo.To confirm the proposed cosmic energy gravitational genesis of the strongest ( ≥ 7.9) Japanese earthquakes, we present in Table 1 the time periods  1 (given in years) of recurrence of the strongest Japanese earthquakes [2] and the obtained [12,25,26] corresponding time periodicities (given in years) determined by the following planetary combinations.
Taking into account the time periodicity 83 years (given by (185)) and the year 1927 AD of Jupiter's opposition with the Earth, respectively, and the time periodicity 88 years = 8 × 11 years (determined by the Sun-Moon system, Venus, Jupiter, and Mars) and the year 1923 AD of the last strongest Japanese earthquake in the Tokyo region, we predicted [25,26]  of the next sufficiently strong Japanese earthquake near the Tokyo region".The powerful 6.6-magnitude (on Richter scale) Japanese earthquake (that occurred on 14 March, 2010) near Tokyo (with the epicenter in the Fukushima Prefecture) gets into the predicted time range 2010 ÷ 2011 AD [25,26].The powerful 6.8-magnitude (on Richter scale) Japanese earthquake (that occurred on 11 March, 2011) near Tokyo gets also into the predicted time range 2010÷2011 AD [25,26].The occurrence of the strong Japanese earthquakes on 14 March, 2010, and on 11 March, 2011, confirmed the previous predictions [1,25,26] and the proposed cosmic energy gravitational genesis [12,25,26] of the strongest Japanese earthquakes.

Summary of Main Results and Conclusion
We have developed in this article the fundamentals of the thermohydrogravidynamic theory intended for the longterm deterministic predictions of the strong earthquakes.The deterministic thermohydrogravidynamic theory is based on the established generalized formulation [11,12] of the first law of thermodynamics for moving rotating deforming compressible heat-conducting stratified macroscopic continuum region  subjected to the nonstationary Newtonian gravitational field.
Using the classical continuum-mechanical theoretical approach [29,33], we have presented in Section 2.1 the generalized expression [24,31] for the macroscopic kinetic energy of a small continuum region.The generalized expression [24,31] is the generalization of the classical expression [28,29] in classical nonequilibrium thermodynamics for the macroscopic kinetic energy per unit mass of a small macroscopic continuum region (considered in a stratified threedimensional shear flow) by taking into account the irreversible shear component of the hydrodynamic velocity field related to the rate of strain tensor   .The macroscopic kinetic energy (of the small macroscopic continuum region) is presented as a sum of the macroscopic translational kinetic energy and three Galilean invariants: the classical macroscopic internal rotational kinetic energy [28,29], the established macroscopic internal shear kinetic energy [24,31], and the established macroscopic internal kinetic energy of shear-rotational coupling [24,31] with a small correction.The generalized formula (20) for the macroscopic kinetic energy per unit mass   and its particular form (31) for homogeneous continuum regions of spherical and cubical shapes generalize the classical de Groot and Mazur expression (2) in classical nonequilibrium thermodynamics [28,29] by taking into account the established [24,31] macroscopic internal shear kinetic energy per unit mass   , which expresses the kinetic energy of irreversible dissipative shear motion, and also the established [24,31] macroscopic internal kinetic energy of shear-rotational coupling per unit mass  coup , , which expresses the kinetic energy of local coupling between irreversible dissipative shear and reversible rigid-like rotational macroscopic fluid motions.The generalized expression (20) confirms the postulate [35] that the velocity shear (  ̸ = 0) represents an additional energy source.
Based on the postulates of thermodynamics [27,28], continuum mechanics [29,30] and hydrodynamics [33,38], we have presented in Section 2.2 the equivalent generalized differential formulations ( 50), (56), and (59) (given for the Galilean frame of reference) of the first law of thermodynamics [11,12] for nonequilibrium shear-rotational states of the deformed finite one-component individual continuum region (characterized by the symmetric stress tensor T) moving in the nonstationary Newtonian gravitational field.The equivalent generalized differential formulations ( 50), (56), and ( 59) are valid for moving rotating deforming compressible heat-conducting stratified macroscopic continuum region  subjected to the nonstationary Newtonian gravity.The generalized differential formulation (56)   +   +   =  +  np, +  (208) generalizes the classical [27,32] formulations (39) and ( 40 by taking into account (along with the classical infinitesimal change of heat  and the classical infinitesimal change of the internal energy   ≡ ) the infinitesimal increment of the macroscopic kinetic energy   , the infinitesimal increment of the gravitational potential energy   , the generalized expression [11,12,24] for the infinitesimal work  np, done on the continuum region  by the surroundings of , and the additional [11,12] infinitesimal amount  of energy added (or lost) as the result of the Newtonian nonstationary energy gravitational influence on the continuum region  during the infinitesimal time interval .The presented (in Section 2.3) generalized expression [11,12] for infinitesimal work  np, (done on the continuum region  by the surroundings of ) generalizes the classical [27] expression  np, = − = − by taking into account (for Newtonian continuum) the infinitesimal work   (given by expression ( 68)) of the acoustic forces and the infinitesimal work   (given by expression (69)) of the viscous forces acting during the infinitesimal time interval  on the boundary surface  of the individual continuum region .
Based on the equivalent generalized differential formulations (50), (56), and (59) of the first law of thermodynamics and the obtained expression (74) for the gravitational energy power  gr (), we have presented in Section 2.4 the established [11,12] gravitational energy mechanism of the gravitational energy supply into the continuum region  owing to the local time increase of the potential  of the gravitational field inside the continuum region  subjected to the nonstationary Newtonian gravitational field.The revealed gravitational

Figure 1 :
Figure 1: Cartesian coordinate system  of a Galilean frame of reference and the continuum region mass center-affixed Lagrangian coordinate system   .
) of the first law of thermodynamics taking into account: (1) the generalized expression (51) for the differential work  np, done during the infinitesimal time interval  by nonpotential stress forces acting on the boundary surface  of the individual continuum region  and (2)

Figure 2 :
Figure 2: The macroscopic continuum region  containing two subsystems  1 and  2 interacting on the surface  1 () of the tangential jump of the continuum velocity.

Figure 3 :
Figure 3: The macroscopic continuum region  consisting of the subsystems  int and  ext interacting on the surface   of the continuum velocity jump.

Figure 4 :
Figure 4: The geometric sketch of circulation of the outer planet   (Mars or Jupiter, Saturn, Uranus, Neptune, and Pluto) and the Earth  3 around the mass center  of the Sun.

Figure 5 :
Figure 5: The initial ( = 0) planetary configuration characterized by the opposition of the inner planet   (Mercury or Venus) and the Earth  3 .

Figure 6 :Figure 7 :
Figure 6: The initial planetary configuration of the outer planet   (Mars or Jupiter, Saturn, Uranus, Neptune, and Pluto) and the Earth  3 .

Figure 9 :
Figure 9: The geometric sketch of circulation of the mass center  3 of the Earth  3 and the mass center  MOON of the Moon around the combined mass center  3,MOON of the Earth-Moon system.

(𝑇 𝐽, 3 ) 3
= 83 years (185) of recurrence of the maximal (instantaneous and integral) energy gravitational influences of Jupiter on the Earth in the first, second, and third approximations, respectively.(4) The Time Periodicities of the Maximal (Instantaneous and Integral) Energy Gravitational Influences on the Earth of Mars.If the configuration of the Earth and Mars is characterized at any time moment by the maximal (instantaneous or integral) energy gravitational influence on the Earth, then the Earth and Mars will have the recurrence of the same configuration after  MARS,3 circulations of Mars around the Sun and  3,MARS circulations of the Earth around the Sun to satisfy the following condition [12]:  MARS,3  MARS =  3,MARS  3 .

Magnitude
= 8 × (11 ÷ 12)-Sun-Moon-Venus-Jupiter Ruichang 2005, and Yanjin 2006 earthquakes were not forecasted also using the warning omens.Using the results of previous sections and the presented set of the Chinese earthquakes (Luhuo 1973, Haicheng 1975, and Tang Shan 1976; Bachu 2003, Ruichang 2005, and Yanjin 2006), we predicted (Simonenko, 2007) the nearest (to the Yanjin 2006 earthquake) Chinese 2008 earthquakes by considering the following arguments.The difference equal to 3 years between the times of the Luhuo 1973 and Tang Shan 1976 earthquakes means that the Tang Shan 1976 earthquake may be induced by the integral energy gravitational influence of the Sun-Moon system or Venus (characterized by the same time periodicity 3 years of recurrence of the maximal integral energy gravitational influence on the Earth in the first approximation) or by the combined integral energy gravitational influence on the Earth of the Sun-Moon system and Venus.If the Tang Shan 1976 earthquake was induced by the integral energy gravitational influence of the Sun-Moon system then the Bachu 2003 earthquake can be explained by the recurrence of the integral energy gravitational influence of the Sun-Moon system (characterized by the time periodicity 27 years of recurrence of the maximal integral energy gravitational influence on the Earth in the fourth approximation):1976 + 27 = 2003-Bachu 2003 earthquake.(202)The Tang Shan 1976 earthquake can be induced by the participation of the integral energy gravitational influence of Venus (characterized by the time periodicity 8 years of recurrence of the maximal integral energy gravitational influence on the Earth in the second approximation) since it is easily to explain the Ruichang 2005 earthquake by the recurrence of the maximal integral energy gravitational influence of Venus on the Earth.Considering[12] 1973+   8 = 2005,(203)which should be solved for integer number   , we obtained[12] the integer number   = 4 confirming the Venusian genesis of the Tang Shan 1976 and the Ruichang 2005 earthquakes: 1973 + 4 × 8 = 2005-Ruichang 2005 earthquake.(204) Taking into account the Chinese Yanjin 2006 earthquake (explained [12] by the sum 1973 + 3 × 11) and considering the Venusian genesis of the Tang Shan 1976 earthquake, we obtained the time of the Chinese 2008 earthquake from the following inequality [12]: 0 < 1976 +   8 − 2006 < ( ,3 ) 1 = 3, (205) which should be solved for integer number   .The obtained solution   = 4 founded the time of the several (owing to the participation of Mars characterized by the time periodicity 32 years of recurrence of the maximal integral energy gravitational influence on the Earth in the second approximation) distinct Chinese 2008 earthquakes [12]: 1976 + 4 × 8 = 2008.
The geometric sketch of circulation of the outer planet   (Mars or Jupiter, Saturn, Uranus, Neptune, and Pluto) and Earth  3 around the mass center  of the Sun.
[12,25,26]formula (139), we evaluated[12,25,26]the numerical value   ( 2 ,  3 ,   ) of the integral energy gravitational influence of Venus on the macroscopic continuum region  (the focal region of the preparing earthquake) of mass   near the surface point  3 of the Earth during the time  of the Earth.Using the expression (139) for the maximal positive integral energy gravitational influence   ( 2 ,  3 ,   ) of Venus ( = 2) on the macroscopic continuum region  of mass   near the surface point  3 of (Moon, second approximation) = 13.0693) for Mars;   (5) = 199.4705days and (5) = 2.3182 (which is smaller significantly than (Moon, second approximation) = 13.0693) for Jupiter;   (6) = 189.069days and (6) = 0.0809 (which is significantly smaller than (Moon, second approximation) = 13.0693) for Saturn;   (7) = 184.8506days [52] Periodicities of the Seismotectonic Activity Induced by the Nonstationary Cosmic Energy Gravitational Influences onthe Earth of the Sun, the Moon, Venus, Jupiter, and Mars If the configuration of the Sun and the Moon is characterized at any time moment by the maximal combined (instantaneous or integral) energy gravitational influence on the Earth, then the Sun and the Moon will have the recurrence of the same configuration after different integer numbers of circulations ( MOON,3 circulations of the Moon around the Earth and  3,MOON circulations of the Earth around the Sun) to satisfy the following condition[12]: MOON,3  MOON =  3,MOON  3 .(173)Followingtheknownmethod[52], we present the ratio  3 / MOON by the following mathematical fraction: