# A universal Theory about Earth's Changing Crust

## Heikki Ruohonen, M.Sc. (Eng.)

### Created: 15.8.2002, last update: 15.8.2007

Abstract

Paleomagnetic findings show that the North pole has changed its place several times. Charles H Hapgood suggested that the previous North pole was in Hudson Bay. Belcher Islands 56.2N 80W was a likely place for the pole. It is 33.80º from the North pole. There are two ways how the pole wandering could take place.

1. There is a stationary planet and the axis of rotation turns within it.

2. There is a stationary axis of rotation and the planet itself turns (gyroscopic effect).

In the case 1 the axial tilt of the Earth would have changed several times. However the Earth’s axial tilt 23,4º is close to the values of Mars 25,2º and Saturn 26,7º. In the beginning they have likely been equal ones. The difference of the values depends on different precessions. So the case 2 is more likely the true one. The latitude of the North pole has remained 90N. There has always existed arctic climate at the North pole.

When a fluid body rotates freely about its axis the gravity gives it a form of an ellipsoid of rotation. Its form depends on the mass and the speed of rotation. The Earth is such a fluid body with a chin crust. To research the consequences of the turn of the Earth we must use a mathematical ellipsoid of rotation instead of the real Earth. The error is not big as the Earth is already very close to an ellipsoid of rotation.. I call this mathematical body “the Globe” and the real planet “the Earth”.

I suppose that the planet Earth itself has turned an angle around one of its equatorial diagonals. Its axis of rotation has kept its position. Fig 1

In the figure 1 there is an ellipsoid of rotation, G, in an xyz co-ordinate. The x-axis is vertically to the figure. Let's turn the co-ordinate an angle δ around x-axis to a position XYZ. Now the ellipsoid G turns with the XYZ co-ordinate to a position G’. We give the ellipsoids the present values of the Earth, the equatorial radius is 6378388 meter and the polar one 6356912 meter, we get the Globes G and G’. The real Globe G turns to a position G’. The immaterial mathematical ellipsoid G remains. Its axis of rotation is jointed permanently with the z-axis. All elevations are measured from the Globe G. Hudson Bay was at the present geographical North pole. The latitude of Belcher Islands was 90N before the turn of the Earth. The latitude of a place before the turn of the Earth was its present distance from Belcher Islands. There was no interglacial warm period but a change of latitudes. Let’s take a piece of string and mark it with some color at 10°-intervals. Stick its other end with a pin at Belcher Island on a globe map. On the string you can find the latitude of the place before the last turn of the Earth. The Siberian mammoths lived on the latitudes of present Mediterranean and North Africa

Calculation of the elevation after the turn of the Earth. New York as an example.

the turn of co-ordinates
X=x
Y=y*cos(
δ)+z*sin(δ)
Z=-y*sin(
δ)+z*cos(δ)

change to the polar co-ordinate
x=r*cos(Φ)*cos(ψ)
y=r*cos(
Φ)*sin(ψ)
z=r*sin(
Φ)

an ellipsoid of revolution
x2/a2+y2/a2+z2/c2 = 1

equatorial radius of the Earth and the Globe in km
a=6378.388

polar radius of the Earth and the Globe
c=6356.912

the turning angle of co-ordinate
δ=33.8*π/180

latitude, negative if S e.g. New York 40.43N
la=40.43

latitude rad
Φ=la*π/180

longitude, negative if W e.g. New York 74.01W
lo= -74.01

longitude rad. Origin is 10E
ψ=π*(lo-10)/180

x=cos
Φ *cosψ
y=cosΦ *sinψ
z=sin
Φ

the basic Globe
r = a/( x2+y2+a2*z2/c2)

X=cos
Φ*cosψ

the turned co-ordinates
Y=cosΦ*sinψ*cosδ +sinΦ*sinδ
Z=sinΦ*cosδ-cosΦ*sinψ*sinδ

the turned Globe
R = a/( X2+Y2+a2*Z2/c2)

the elevation
e=R-r

New York sank 10.743km below sea level
e= - 10.743km Fig 2: Ice Age follows every turn of the Earth.

The difference between the radii of the two Globes, G and G’, gives the elevation at any place. In figure 2 there are the elevations over the entire Globe, calculated by C++. As you can see the surface of the Globe rises over 5000 meter in the most part of Asia and Europe and in Patagonia. Elevation maximum was close to 12 km.. It means that there was an Ice Age in these areas. I call pole meridians the meridian of Belcher Island (80W) and the meridian 170E,. They divide the globe into two symmetrical hemispheres. The origin of the co-ordinate in the figure 2 (and in all the next ones) is 10E as it is 90º from the pole meridians. The earth's surface rose within two Up-areas (the red areas ) and sank in two Down-areas (the blue and green areas). Sea level sank and uncovered large areas. The surface remains unchanged on the lines between these areas (zero lines). The zero lines intersect at the origins. The pole meridians pass through the points of elevation maximum and minimum (yellow points). The maximum elevations was 11.95 km at MAX1=61.78N 100E and MAX2=61.78S 80W and the minimum ones -11.95 km at MIN1=28N 80W and MIN2=28S 100E. The shape of the Earth differs now a lot from the Globe. The gravity forces the shape of the Earth change continuously towards the Globe. The Earth's surface must sink within Up-areas and rise within Down-areas, the sea level must rise. Fig 3: There is a symmetry as regards the origins.

If the theory is true there should be the corresponding symmetry on the real Earth too. The origin lies on the maps at the point 0N10E In figure 3 there is a red line that is a copy of the coastline of northwestern Africa. It is turned 180º around the point 0N 10E. It coincides with the coastline of southeastern Africa very well. It continues along Rift valley and Lake Tanganyika. There is indeed symmetry as regards the point 0N 10E. Fig 4: Flow paths

As the viscosity of magma is very great it is possible that the pressure can vary on the equipotential surfaces of the Earth. The local pressure depends on the elevation at the place. Magma flows from every point of the Earth to the direction of the lowest pressure. We have a point P on the surface of the Earth (fig 4) and we find the point P1 where the elevation is the minimum among all the points at a distance r from the point P. Magma flows now from the point P to the point P1 . I have used the points on the coordinate axes with 1º space as the starting points P, but it can be any point on the Earth's surface. I have used a step r =1º ( r = 111 km). If we proceed in the same way from the point P1 we will come finally to either point of minimum elevation Pmin (MIN1 or MIN2). If we proceed similarly from point P toward the maximum elevation, we will come finally to either point of maximum elevations Pmax (MAX1 or MAX2). We get lines that go from Pmax to Pmin (fig 4). I call them flow paths. Magma flows from every point of the Earth towards the points Pmin and the flow paths show the direction for the magma flow. For simplicity I have kept the Earth as a sphere, that it is very close to. However it brings about minor inaccuracy, especially in the Polar regions. Fig 5: Magma flow.

According to Bernoulli's equation the increase in the kinetic energy of frictionless fluids is equal to the consumption of its potential energy p1-p2 = c22/2g-c12/2g. The potential energy is proportional to the elevation difference p1-p2 = C*(e1-e2). As magma is far from frictionless, all the elevation difference is needed to sustain the velocity of magma, the rest of it converts into heat by friction. Thus the beginning velocity c1 = 0, so e1-e2 = c2/2g+heat. As the friction is usually proportional to the square of velocity, we get e1-e2 = C*c2. Thus the velocity of magma is v=C*(e1-e2) (fig 5). We have to use relative values of velocity instead of absolute ones as the proportion of the developed heat is unknown. Fig 6: Acceleration of magma flow (a=v2-v1).

The acceleration of the magma flow is positive in the red areas (fig 6) but negative in the blue ones. The acceleration of magma brings about stress in the crust. There is tension in the areas of positive acceleration but compression where the acceleration is negative one. The crust breaks up with tension and folds with compression. The brown stripes in the figure indicate the lines of equal velocity. I call them isovelos. Fig 7: Orientation of landscapes.

We have a line A-B, not parallel to isovelos I (fig 7). As the crust moves with magma along the flow paths tends the line A-B to turn parallel to the flow paths when the acceleration is positive one (7a), because the velocity is greater at a point B than at a point A. Line A-B tends to turn parallel to the isovelos when the acceleration is negative one (7b). The direction of the Andes is almost N-S up to latitude 16ºS and it turns then abruptly transversely (fig 6). Quite obviously they have turned along the flow paths as long as the acceleration has been positive one but transversely when acceleration has changed to negative. So a separate region can take a new orientation without that the entire continent turns. Thus the paleomagnetic theory is no liable method to show the place of the earlier Poles.  Fig 8: Accumulation of mass.

There are two points P1 and P2 on a flow path F (fig 8a). The distances of point P1 from the adjacent flow paths F1 and F2 are D11 and D12, and in the same way the distances of point P2 are D21 and D22 . If we connect points N1, N2 , N3 and N4 to the center of the Earth we get a pyramid (fig 8b) where D1 is the distance between F1 and F2 in the inflow site and D2 is the similar distance in the outflow site . Magma flows into this pyramid through a triangle A1 and leaves it through A2. As we use relative values of velocity we can take the average density ρ=1, then the mass inflow in a time unit is m1 = v1 * A1 and the outflow m2 = v2 * A2. There is accumulation of mass (positive or negative) inside the pyramid Ac = v1 * A1-v2 * A2. As the heights of the triangles A1 and A2 are practically equal, the distances D1 and D2 can substitute for the areas of the triangles. So we get Ac = v1 * D1-v2 * D2. The accumulation per a distance unit is ac = v1- D2/D1 * v2. If the elevation difference is very small the outflow v2 stops. The pressure in the pyramid grows and lifts magma up. There grows an uplift. That kind of situation is found along the zero lines. In fact we can find an uplift on the zero lines along the southwestern coast of Africa and its symmetrical counterpart, the eastern coast of New Zealand and further along Tonga-Kermadec Ridge, and along the northern coast of Horn of Africa (fig 2).

As the points N are with 1º space on the flow paths the distances D11 + D12 and D21 + D22 are longer than D1 and D2 but in the ratio D2/D1 it will be compensated more or less. Fig 9: Accumulation rate (ar).

Accumulation rate is the difference of adjacent values of accumulation along a flow path from Pmax to Pmin , ar = ac2 - ac1 (fig 9). In most cases the accumulation rate is positive even though the accumulation itself decreases in Up-areas. Both decr>.001 and incr>.001 mean the same accumulation rate. A positive accumulation rate decreases the elevation difference and slows down the magma flow. The earth's surface will rise in Down-areas. The yellow areas indicate a very great accumulation rate in Down-area. One result of it is a long uplift in Caribbean. The Greater Antilles and Yucatan are parts of it. It continues as Clarion Fracture Zone in the Pacific. In Australia there is a corresponding uplift from Exmouth Plateau to Barkly Tableland. Fig 10: Convergence of flow paths (c= D1/D2).

As all the flow paths pass from points Pmax to points Pmin , covering the entire earth, they have to diverge (c<1) in the Up-areas and converge (c>1) in the Down-areas. There are some exceptions anyway, red lines in the blue area.(figure 10). Fig 11: Length of flow paths.

The length of the flow path varies (fig 11) but as the departures and the arrivals are common for all of them, the average elevation difference is inversely proportional to the length of the flow path, i.e. amount of steps. So is the average velocity and the mass that has moved in a time unit. Fig 12: Distribution of the accumulation.

As the accumulation in a time unit is greater along a shorter flow path than along a longer one we must multiply the basic acceleration by a coefficient inversely proportional to the amount of steps, acc = (v1-D2/D1*v2)*100/amount. Its distribution over the Earth is shown in figure 12. The accumulation decreases along flow paths from the points Pmax toward zero line and increases then toward the points Pmin . The Earth approaches the shape of the Globe. This process makes the sea level rise. There has been a great negative accumulation in the beginning of flow paths, it means a strong flow of mass away. It has caused Grahamland and the southern end of South America to turn along with it. It has consumed the crust. That is to be seen in Scotia Sea and Scotia Basin. A similar consumption is noticed westward in South-east Pacific Basin too. A corresponding consumption is noticed on both sides of the point 61.78ºN 100ºE, The East Siberian plateau eastward and The West Siberian plain westward. Fig 13: Emerging continents.

All the previous cases represent the situation just after the turn of the Earth. If we add the accumulation, multiplied by a time related coefficient, to the elevation in figure 2, we get the elevation at the moment in question. E = e+(v1-D2 /D1*v2)*100/amount*TIME. If we select the time coefficient so that the sub-equatorial Africa rises above the sea-level (yellow areas in figure 13), we get the present situation. Then the chosen TIME coefficient is 335. The greatest part of Down-area will rise above the zero-level but the continental blocks only emerge above sea-level. Both the coast lines of northwestern Africa and southeastern Africa corresponds with the border line of the yellow area quite accurately. So does the western coast of North America. Its broken eastern coast is far inside the yellow area. It means that there is no continental block eastward. North America has obviously separated from Europe and moved westward, and so has done South America from Africa, as Wegener proposed. The large areas around the points Pmax cannot sink below zero level as figure 13 shows but the sinking stops at zero level. Fig 14: Changes in elevation difference.

The changes in elevations change the elevation difference as well. If we use the same TIME coefficient as in the previous chapter, we will get the present situation (fig 14). When the elevation difference diminishes enough the magma flow slows down and stops finally and there will grow an uplift (blue stripes in the figure 14). One of these uplifts begins from Corsica and Sardinia continuing as Atlas mountains in Northwest Africa. Its symmetrical counterpart begins from Cape Rise and continues as Drakensberg in South Africa. The largest of these uplifts are the Mid-Atlantic Ridge and its counterparts. According to the Archimedes' law the highest mountain chains grows always in seas.

Ocean effect
The sinking of crust increases toward the points of elevation minimum (fig 2), so does the sea bottom too. The oceans grow deeper and deeper as approaching these points along the flow paths. It decreases the elevation difference. This ocean effect has not taken account in this study. It brings about a moving of the mountain changes in figure 14 toward the points of elevation maximum. It means that the Mid-Atlantic Ridge in South Atlantic moves westwards but eastwards in North Atlantic its most northern part turns toward Iceland because the flow paths under the ocean are very long there. Fig 15: The past of the Earth.

By choosing some smaller value for the TIME coefficient we can survey the past of the Earth. If we chose the value 170 we get the moment when Novaya Semliya took its shape. Lesser Antilles emerge at the same time but we must bear in mind the later effect of the orientation (fig 7). Its influence has been very significant in Lesser Antilles.

We can also predict a future situation by choosing the TIME coefficient greater than 335. Fig 16: Trapped magma.

An interesting case is the Tibetan plateau. A diagrammatic drawing 16 illustrates the case. The elevation of the Tibetan plateau was very high just after the turn of the Earth (figure 16a) and it remained high. Magma flow met higher pressure A former high mountain chain, Himalayas blocks the advance. The magma had no possibility to move forward but to take other ways. When the elevation in Siberia had sunk to lower level than in Tibet (figure 16b) the magma began flow from the high plateau back towards Siberia, bringing about an uplift Kunlun Shan. A similar case but in smaller scale is going on in Europe. The Scandinavian mountain chain stopped the magma flow that now is reversing and lifts the crust in West Finland. South of Himalayas the magma goes on flowing towards the point of elevation minimum. So the elevation sink there. It increases the elevation difference and pressure against the mountain chain. When the pressure grows big enough it breaks Himalayas at 100E making the mountain chains turn southward. In this event erupts enormous amount magma. It had brought about peninsula Malaya and Sumatra island. It caused the disastrous tsunami too. It will be repeating. There was a great eruption in the western end of Himalayas too. Fig 17: Negative accumulation rate.

There are stripes where the accumulation rate is negative. The surface sinks there (fig 17). It brings about rifts and ridges. One of them has created the Greater Antilles (notice the bend of Cuba Island). It continues as Clarion Fracture Zone in the Pacific. In the Atlantic it brings about Puerto Rico Trench. As these rifts alternate with high uplifts they bring about a very unstable crust like the stripes from Altai through Pamir to Iran and another one through Korea and Japan. Fig 18: Changes in the Earth's moment of inertia.

As mass moves from one place to another the moment of inertia of the Earth changes. The principal axes of the ellipsoid of inertia changes too. As the Earth spins about one of the principal axes the spin axis must also change. In accordance with the "Law for conservation of angular momentum" the spin angular momentum is constant. We have a body, composed of all the pyramids (fig 8b) along a flow path from Pmax to Pmin (fig 18). It consists of two parts B1 and B2. B1 is composed of all the pyramids that have lost mass. B2 is composed of all the pyramids that have gained mass. These moving of mass change the moment of inertia. These changes will be compensated so that the center of mass of the body B1 (point c1) rises and the center of mass of the body B2 (point c2) sinks. It takes place so that heavy material from the core rises (case c1) and sinks (case c2). So the moment of inertia remains unchanged. If every layer inside the bodies B1 and B2 is homogeneous, the centers of gravity of areas A1 and A2 , points c'1 and c'2 , lie on the same radius of the earth as points c1 and c2 . We can now compute their coordinates on the Earth's surface. Fig 19: The correction stripes of moment of inertia.

Small momentary changes in the great moment of inertia of the Earth will be corrected by changes in the liquid core as shown in the previous chapter. These corrections are seen on the surface as uplifts (red stripes) and subsidence (blue stripes). We can see that the red stripe follows the northern coast of Asia lifting it above sea-level. The lifting is especially clear along Tien Shan. James Bay, by Hudson Bay, is the place of the strongest subsidence. The blue stripe crosses the Rocky Mounts along the Valley of Colorado. It crosses the coast line at Los Angeles. Basins are typical on the blue stripes. The "trans Atlantic cable break" was caused presumably by this phenomenon too. During a serious Earth quake a considerable motion of mass takes place. That will be compensated by another Earth quake at some place on the opposite site of the Earth.

These kind of corrections of the moment of inertia are like a house of cards resting on nothing, only the spinning of the Earth keeps it up. The higher it rises the more uncertain is the balance, especially when the spinning is slowing down. Finally the house of cards will collapse. So the correction of the moment of inertia is possible only to a certain limit. When that limit is exceeded the deformities of the core disappear and the principal axes take their proper stand and the Earth turns. Fig 20: Isostasy.

J.H. Pratt's idea of isostasy implies that there is a certain level of compensation where the pressure due to the weight of the overlying mater is same everywhere. If we have a continental column and an oceanic one lying on this level their weights are equal. But the center of mass of the continental column is situated higher as its average density is smaller (fig 20). Thus its moment of inertia is greater . As the distribution of the continents on the Earth is uneven, the principal axes never coincides with the geometrical axes of the ellipsoid (the Globe).

Summary

1. The Earth is a liquid heavenly body.

2. When it cooled off enough it got a solid crust that uniformly covered the entire planet. All was covered by a shallow sea.

3. There is left only 40% of that original crust, the continental plates. Another heavenly body approached near enough to tear 60% of the crust off. Water filled the hole uncovering a continent Pangaia on the opposite side of the Earth. Now the terrestrial life was possible.

4. Since then the Earth was not an ellipsoid any more. The moment of inertia changed and with it the Earth turned.

5. Whenever the Earth differs from a shape of rotation ellipsoid the gravity moves its masses so that its shape approaches an ellipsoid again. The gravity is the only force needed. It is a real force. It is capable to move continents, contrary to fictitious convection forces. The moving of masses change the moment of inertia of the Earth, I=mr². As the angular momentum, L=Iω is constant, the angular velocity ω ought to change. But as the Earth is a liquid body, the small changes in the moment of inertia will bee compensated by inner changes in the Earth. That distort however the shape of the Globe. Finally the abnormality grows big enough and the ellipsoid of inertia turns with its principal axes. As the rotation axis must join one of them the Earth turns so that a principal axis meets the rotation axis. Because of the uneven distribution of continents the Earth is unable to get the shape of an exact ellipsoid before than the continents had broken into pieces that are scattered evenly over the Earth.

The last turn of the Earth take place about 12000 years ago.

1. Platon told that Atlantis sank 9000 years before Solon, it is 11300 years ago.

2. Russians found a frozen mammoth in Siberia, at Beresovka. It was nothing if not decayed. It had suffocated 12000 years ago. A very interesting thing was a flowering butter cup in its mouth. So it had been grazing in summer-time, suffocated and not decayed! It is hard to find any other explanation but it had been moved from Mediterranean latitudes to present Siberia and lifted suddenly to an altitude of several thousand meters.

3. Mankind's collective memory about a great catastrophe. The common knowledge of deluge. Psalm 114 tells: “The Red Sea hurried out of their way, the mountains skipped like rams”. An old Finnish ballad tells that when we go to the Last Judgement the stars are dancing on the sky. It is really the dancing stars one can see at the moment of turning the Earth.

The Theory of Continental Drift has gained almost an indisputable approval. According to this theory, among other things, an Indian plate is pushing below an Eurasian plate lifting it several kilometers. The thickness of the solid crust within continents is about 50 Km. Its density is circa 2.7 g/cm3. In that case the pressure under the continental plate is about 13500 bars. It would be impossible to push there any Indian plate. Especially when there the dominating temperature is so high that all material melts. So would happen to the pushing Indian plate too. The ancient truth tells:” You can’t push with a rope”.

E-mail: heikki.ruohonen@pp.inet.fi

Heikki Ruohonen
MSc Engineering
Elotie 1 A 10
Fin-20780 Kaarina
Finland