TO THE QUESTION OF ISOSTASIS OF THE EARTH`S CRUST AND UPPER MANTLE

A. G. Syromyatnikov and Yu. A. Zakoldaev

ABSTRACT

We discovered that intercommunications between gravity anomalies on the Earth surface and the Earth crust thickness for the Earth whole by R. M. Demenitskaya and so by G. P. Woollard and W. E. Strange confirm the function dependence of a gravydiffusion soliton of The geocosmic universal X – structure of the Earth crust and upper Mantle. It is allow to expline of the general form of the isostatic equilibrium. This results are used to the formulation of the task of a paleoisostatics of the Earth crust. It was considering ties to a global geochrnometric scale on a phase shift on a soliton movement.

Key words: rocks, Earth crust, high mantle, isostasis, geocosmic universal X – structure, gravidiffusion soliton, geotemperature gradient.

The gravitation is a moust universily information channel for the Earth`s inner structure investigation. A total value of the Earth`s gravity with whole features upon an arbitrarily features [1] formed on cosmic bodies influence from the Sun, Moon and planets and so from the galaxy potential which is varible along the motion to the galactic orbit [2] from ¼ to 0.45 of a Sun gravity potential value at the Sun disk edge. This differences gives definition from differences in a materic and ocean Earth construction and their subdivisions. This investigations are based on empiric dependences between gravitation anormalies and the relief heights and Earth crust thiknesses distribution (see [1], table 3, formulae 1 – 3 for the Earth whole):

where Δg – a Buge anormaly as a difference between an observable and normal values of gravitation with correction for the relief influence mGal; Δh – a height of relief, km; H – the Earth crust thickness, km. This an analitic dependence discribe the experimental points distribution on a plane (Δg, H) with an average deviation of the Earth crust thickness in oceans areals ± 1 – 2 км and in continents areals ±4.0 км. After them G. P. Woollard and W. E. Strange [3 – 6] got a depandence (1962) similar to the stochastic depandence [1]:

H_M – a depth from Mochorovichich`s surface, km.

Recalculation of the Earth crust thickness to depths of Mochorovichich`s border made on formular is known that

The analitic dependence for isostatics writes as

In the supposition about the existant of isostatic at a long geologic times this formular was being supposed by a paleoisostatic method (R. M. Demenitskaya, 1958) for the Earth crust thikness calculation in early epoches.

In another side a speed of vertical motion of the Earth crust according to [7] is very small – some mm in year. So their we operates the gravity mobility value [8] which is defindes in analogy with the ions mobility in electric fields by a way changing of an electric charge to ions mass. The ions motion in solids and liquides with a constant speed takes place in a compensation from field action (electric and gravitation) by force viscosity is proportional to a field srength and charge ore mass of ion correspodently. In gravitation field on Earth surface this velosity is equel to 1 mm/year. The solution of Newtonian gravity equestion with gravidiffusion equestions for atom – moleculares structures lead to a solition depandence take place

which is identical to empiric equestion for isostatic [1] as dependence from the height (depth ) with a vertial motion with a time t. A, B – an arbitrary constant, H = 2kT/MB, B – a gravity difference between a surface and in depth of Earth, , T - temperature, k – Boltsman`s costant, M – moleqular (atom) mass.

Discussion

This non-static depandence as quasystatic gravydiffusion soliton [9, 10] is asymptotic the most stable solution. Any initial diturbance by a time decay on a solitons superposition. Gravydiffusion soliton formed when a diffusion limitation to current take place, for example on a border of Earth nucleous, where it is strong fluid of Helium -3. The Earth crust thickness in a soliton dependence is defened due to Einstein`s correspondence generalizing (see for example in solid [17]) as propotional to temperature divided on a gravity jumping and it is constant on a time. So the soliton phase depandence is very variety. In an decompositon of many component system for fluid rock on a gravymobility as a small parameter (in analogy to [11] for electrodiffusion soliton) the most mobility moleculares as a rule is separated to one grope. So the solution have a form as for one – component system. It is take place there.

The basis factors of mass transference from deep to surface of Earth are (12):

– film mass transference;

– ions transference in an electric field;

– gradient of pressuare;

– diffusion.

So entrance of mass is 30 G/Tonna.

To a number of this factors we add the migration of chemikal elements in gravitation field that is characterized by their gravymobility. The value of gravymobility in water solutions in 18 °С for ions – in table 1.

Table 1

Gravimobility of ions in water solutions in 18 °С

Ion	H⁺	Li⁺	Na⁺	K⁺	Ag⁺	Mg²⁺	Ca²⁺	Sr²⁺	Ba²⁺
Gravimobility in 18 °С, [10^-15s]	3.65	2.808	12.04	30.05	69.807	13.5	24.93	46.26	62.16
Ion	Cu²⁺	Zn²⁺	La³⁺	OH^-	NH₄^-	CO(NH3)₆³⁺		Fe(CN)₆^3-
Gravimobility in 18 °С, [10^-15s]	35.88	36.23	100.9	35.12	69.807	138.6		223.7

The speed of Chemical Elements (CE) gravymigration is very small 1 mm/year in water solutions in caverns and splits of rock. Gravytansference of CE take place is not only in water but and in crystallic structure of depth rock.

Questions of transference of smalldipersion solution of rock in geologic scales aqre seen in [18] where it is shown that transference reach 30 G/T.

Conclusion:

So the gravydiffusion soliton of geocosmic X – structure confirmed by dates of isostatic of Eath crust.

It give possibility of generation of isostatic to geologic times with helpness of gravydiffusion soliton as paleoisostatic. In this article we are limited by a questions of stating this problem. We suppose show dates of superdepth borehole [13].

In general case with issue – fluids from depth and from space – meteors, dust, particles fluids from Sun etc. – gravydiffusion soliton have form

D – diffusion coefficient (as H_M and paleotemperature – may be time depandence), g₀(t) – time function.

From a condition on g₀(t) on a crust bottom we made calculation

where λ – termal conductivity, С – heat capacity, Q – heat flow from upper muntle. This formular we obtained by a way of differentiation on a time of upper part in brakets of a soliton depandence (at a crust border whole in brakets is equal to 1), *temperature (T). In result function g₀(t) is definded by derivative T on a time. Then transition of this dependence to g₀(t) from th give a formular of gravydiffusion velocity is proportional to mantle heat flow.

Due to this caculations the speed of vertical diplacement of Earth crust is proportional heat flow of litospere, as it was in [7]. It is noted that litospere convection we not see.

The physics model: frome correspondence of proportionality between speed of vertical displacement of Earth crust and litosphere heat flow, which is proportonal to derivative from temperature on time, lead that small displacement of Earth crust are proportional to temperature – as on heat extension. So such as heat transfering from more heat body to cold body then heat flows transfering to more cold crust which must pressing. Displacement of crust must go to the surface, such as it was obsirving in [7]. On a small heat flows from temperature fluctuations heat extention go in opposite directive, that was obsirving fractionally in [7] too. In another side here it is nececcery to take into account effect [9] of prolonged freezing ancient crust by gravydiffusion soliton. We supposed that this mechanism of crust displacements in continental scail speak about good using of isostatic formula.

All them due to that is gravity field oscillations with the period equal to paleotemperature period. In this time state much climate circle 1850 years. much climate circle 1850 years = 372 × 5 -10 (372 years – a period of oscillations of Kaspii sea level is in straight connection with climate) is in resonance with period of a galaxy year.

According to autor`s (Syromyatnikov A. G.) approach all geologic events without exception in geochronology of Zakoldaev Yu. A. And Spitalnaya A. A. scale in 4500 Ma are in resonance with ¼ period of displacement of perigelium of the Earth Т_п = 33.7517 Ma according to autor`s mekhanism of resonanse acceleration of magnetic dipole (Earth) in rotating magnetic fields (Sun – in orbital motion according to conformal gauge theory of gravitation`s equations). Т_p = 34 Ma – longitude of part of galazy year and 13/2 T_p = 219.39 Ma in limits of fluctuations 2.5 Ma (217 Ma – in average on planets) is definded obsirvable value of galaxy year 217 Ma. Necessary push for start of the mechanism supposed the action of a new interaction influencing on beta – decay.

In another side it is stated (Syromyatnikov A. G., 2006) by a method of Evolution Invariants (EVI) [10] when week non-homogeneous of himself time motion total period 372 years generation of a seismic energy (½ of this value 186 years correspond to planet circles Yu S). So a period of oscillations of Kaspii sea level. Usually it is equal near 400 years. This period is known on ancient.

We have a question about possibility of resonance coonection between this two seismic periods: - on displacement of perigelium of Earth orbit 5/4 Т_p = 42 Ma and – and period 372 years. It was accaused that this periods are in resonance connection: 5/4 T_p = 113413.0 × 372 = 42 Ma.

The whole number of resonance has following simple parts: 113413.0 = 2 × 2 × 3 × 13 × 5² × 29.006. Due to them are significant periods on 2, 3, 5 and13-14 (on 372 years).

Table 2

Correlations of borders of geologic systems of Phanerozoi and periods of displacements of perigelium of Earth

Systems	N	data according to period of displacements of perigelium of Earth NT_З – 0.272, Ma	data of system begining [2], Ma	Distortion [2], Ma	N	data according to period of displacements of perigelium of Earth NT_З –0.272, Ma	data of system begining [14], Ma	Distortion [14], Ma
1	2	3	4	5	6	7	8	9
Neogene	¾	25	21 ± 3	-4	¾	25	23 ± 1	-2
Paleogene	2	66.8	66 ± 3	-0.8	1 ¾	58.7	61.7	3
Cretaceous	4	135.3	136 ± 5	0.7	4 ¼	143.1	145.5 ± 4	2.4
Jurassic	5 ¾	193.7	192 ± 5	-1.7	6	202.3	199.6	-2.7
Triassic	6 ¾	227.8	227 ± 10	-0.8	7 1/2	252.8	251	-1.8
Permian	8 ¼	278.1	283 ± 10	4.9	9	294.5	299	4.5
Carbonic	10 ¼	345.7	353± 10	7.3	10 ½	354.2	359.2 ± 2.5	5
Devonian	12 ¼	413.4	409 ± 10	-4.4	12 1/4	413.5	416 ± 2.8	2.5
Silurian	13 ¼	447.2	444 ± 10	-3.2	13 1/4	448	443.3	-3.7
Ordovician	14 ¾	497.8	500 ± 15	2.2	14 ½	489.1	488	-1.1
Cambrian	17	573	570 ± 15	-3	16	540	542 ± 1	2
	Average (publication year 1993)			-0.26 ± 3.0	Average (publication year 2006)			0.7 ± 3.1

From Table 2 lead to dates of system beginning on [2] and [14] are coinsided in limit ± 2σ, but displacement in bottom for [2] less then [14].

The same have place so for borders of gelogic system of Docambry [14]: in that case average distorsion on periods of displacements of perigelium of Earth is equal to 1 ± 3.5 Ma, and on Table 2 0.0 ± 2.45 Ма. It is significantly – in 1.44.

Additionally, Neruchev`s point have age 10 Ma – ¼ of resonance period. Calculations of resonance points on periods of displacements of perigelium of Earth we may beginning and in modern time. As result on another beginning in No2 (table 2) we have

¼, 1 ½, 3 ½, 5 ¼, 6 ¼, 7 ¾, 9 ¾, 11 ¾, 12 ¾, 14 ¾, 16 ½; but in No6:

¼, 1 ¼, 3 ¾, 5 ½, 7, 8 ½, 10, 11 ¾, 12 ¾, 14, 15 ½.

Fat we signed beginning lead presicely to mechanism of resonance acseleration. Such periods in case 1- 8, so in case 2 – 5.

Impact craters date which coinside with signed (fat) periods:

15 Ma (neogenic) – there are 3 (15 Ма and 270 Ма displacing on ¼ of period relatively of beginning of neogene and permian periods give precise resonance periods ¼ and 7 ¾ correspondly), 130 Ma (end of jurassic – cretaceous), 270 Ma (permian) – there are 2, 440 Ма (silurian), 570 Ма (cambrian) – on the beginning of phanerozoic there are 3. 144 Ма, 450 Ма.

Drop of meteors is not connection with borders of geologic systems but as see mechanism of resonance accelerations interact and for it. There is major in first case -10 case, so in second case – 5, which may be connected and with first case. On impact craters majority have events [2], in 9 from 11.

In Table 3 periods of displacements of perigelium of Earth on dates of superdepth borehole [13] with helpness of uran clock [15].

Table 3

U - point

Depth, m

Age of bottom border, Ма

Age of U Point (UP), Ма

data according to period of displacements of perigelium of Earth NT_З – 0.272, Ma

Distortion UP on [2],

4600

6840

9750

10250

11100

11790

11840

11850

11900

12100

1000

2620 ± 20

2640 ± 10

2650 ± 10

2660 ± 10

2670 ± 10

2680 ± 10

2690 ± 40

2730 ± 40

2810 ± 80

1004

2616

2647

2678

2709

2740

2802

1004

2632.4

2671*

2704*

2776*

-12

-11

-1

-14

-46

average

0.7 ± 21 Ма

*) addition periods.

Table 4

Correlations of borders of geologic systems of Phanerozoi on Global Standart Section and Point Phanerozoic (GSSP, 2004) and periods of displacements of perigelium of Earth

System	N	data according to period of displacements of perigelium of Earth NT_З – 0.272, Ma	data of system beginning, Ma	Distortion, Ma
Neogene	¾	25	23	-2
Paleogene	2	66.8	65.5 ± 0.3	-1.3
Cretaceous	4 ¼	143.4	145.5 ± 4	1.1
Jurassic	5 ¾	193.7	199.6 ± 0.6	5.9
Triassic	7 ½	253.1	251 ± 0.4	-2.1
Permian	8 ¾	295.3	299 ± 0.8	3.7
Carbonic	10 ½	354.4	359.2 ± 2.5	4.8
Devonian	12 ¼	413.4	416 ± 2.8	-4.4
Silurian	13 ¼	447.2	443.7 ± 1.5	-3.2
Ordovician	14 ½	489.4	488.3 ± 1.7	-1.1
Cambrian	16	540	542 ± 1	-2
	Average (publication year 2004)			-0.06 ± 3.5 Ма

from Table 4 lead to that date of beginning of borders of geologic systems of Phanerozoic on Global Standart Section and Point Phanerozoic (GSSP, 2004) exactly centering on periods of displacements of perigelium of Earth in limits ± 3.5 Ма.

Table 5

Correlations of borders of geologic systems of precambrian on (GSSP, 2004)

and periods of displacements of perigelium of Earth

System	N	data according to period of displacements of perigelium of Earth NT_З – 0.272, Ma	data of system beginning, Ma	Distortion, Ma
Neoproterozoic	29 ¾	1004	1000	-4
Mesoproterozoic	47 ¼	1595	1600	5
Paleoproterozoic	74 ¼	2506	2500	-6
Neoarchean	83	2801	2800	-1
Mesoarchean	94 ¾	3198	3200	2
Paleoarchean	106 ¾	3603	3600	-3
Eoarchean
	Average (publication year 2004)			-1.2 ± 4.1Ма

From Table 5 lead to that near all dates of borders of precambrian (2004) corresponde to mechanism of resonance acceleration but within limits ±4 Ма.

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