USE OF THE CONCEPT OF AN OFFSET INNER CORE IN THE EARTH

TO SOLVE TECTONIC PROBLEMS

AND TO DETERMINE GENERAL REGIONS OF POTENTIAL MINERALISATION

By T. Frank Lee, geologist.

The following paper was suggested to the author by the then Associate Professor W. Peck of the Geology Department of RMIT University as a topic of interest for geologists and miners.

ABSTRACT

PART A: It is argued that the inner core of the Earth is offset from the Earth’s figure centre and that it is exerting a radial, outwardly directed pressure on the rest of the body. With the core centre defined, and using three simple assumptions, the intersections of the principal and shear planes of the resulting stress field at the Earth’s surface are given. Major straightline tectonic features are shown to coincide or closely parallel parts of the surface traces of the planes.

Other major but curved features are shown to be related to circles with centres at the poles of two of the principal axes of the stress figure. It is argued that the circular features are Earth-surface expressions of "cones" of stress, inside which is horizontally circulating mantle material. A cone exception, that termed the Aleutian cone, is given of which the cone axis does not coincide with a principal axis.

Using the above data it is shown how a simple explanation can be given for the Pacific "Ring of Fire", and the location of regional mineral zones related to it predicted.

PART B: It is also explained how the hypothesis is used to determine a simple formula for permitting the plotting back in time of any continental plate using only palaeomagnetic poles of that plate. Examples are given of plate relationships to show that the formula is valid.

PART C: Three examples are given of the combined use of plate path plotting and Earth planes and cones of stress to show how explanations of major geological events can be derived and regional mineral zones predicted. The three examples are of the Deccan Traps of India, the Mesozoic kimberlites of southern Africa, and the Mesozoic-Cainozoic development of the Andes of Peru.

Lastly, it is shown that continental lineaments are the product of stress in a moving plate moving over a three-dimensional body, the Earth. A lineament, if one forms, develops parallel to the movement path of the plate.

PART A.

INTRODUCTION

There is much argument in geological circles as to the causes of continental plate movements, linear tectonic zones, continental lineaments, and the regional controls of mineralisation. At present the concepts of mantle currents and hot spots hold centre stage, with a number of other hypotheses such as Earth expansion being actively supported by minorities. Though not any of the minorities may presently have sufficient evidence to have its ideas accepted by mainstream geologists they all have some data which casts doubt on the mantle current "theory". And the doubt is greater than many of the knowledgeable supporters of mantle current tectonics like to admit.

The author of this paper is one of the minority. A study of mantle current theory has caused him to reject it. And so he has developed a new hypothesis which, as this paper will show, can give simple explanations, show simple relationships, and allow predictions of physical phenomena in a way no other "theory" can do.

The paper explains the basically simple hypothesis of the author, gives a little of much evidence supporting it, and shows how it can be developed to explain and predict various mineral-bearing regimes.

THE HYPOTHESIS

The lithosphere is undergoing, and has undergone over its whole existence, a radial, outwardly directed stress regime exerted by a displaced inner core. In fact, the following argument does not require the inner core to be displaced but it seems the most reasonable condition, particularly as other terrestrial bodies, viz. Mars and the Moon, have been argued as having offset cores (Reasenburg, 1973; Ransford and Sjogren, 1972), almost all the solid bodies of the Solar System have offset centres of mass, and almost all, including the Earth, have triaxial shape. The alternative to an offset core is to assume a point of expansion and then develop an identical argument to what is to follow here.

To test the hypothesis it is necessary to define the following:

  1. the position of the inner core centre relative to the Earth’s body centre;

  2. the orientation and condition (perfect or ductile) of the stress field; and

  3. the life of the stress field.

With these conditions defined the hypothesis can be tested by comparing the theoretical stress field, which can be constructed using the conditions, with various physical properties of the Earth. Coincidence or close parallelism of several of the physical properties with the stress field is support for the hypothesis and will allow predictions to be made in those properties. The hypothesis is codified as follows:

The Earth’s inner core is offset from the Earth’s body centre, its centre lying on the straight line joining the North and South Magnetic Poles at the point where the line is cut by the 6°N latitudinal plane. The poles’ join line forms a common line of intersection for two of the principal planes and two of the principal shear planes of the radial inner core stress field. The planes are spaced equiangularly, i.e. 45° between adjacent planes, and one of the principal planes passes through the figure centre of the Earth. The above conditions have persisted for the life of the planet, though the stress intensity probably has varied.

CONSTRUCTION FROM THE HYPOTHESIS

The hypothesis allows the position of the stress field’s three principal axes, three principal planes, and six shear planes to be located both within the Earth and as Earth-surface traces. The pole positions of the three principal axes are:

N – long. 100°W, lat. 73°N S – long. 139°E, lat. 65°S

P – long. 155°W, lat. 6°N A – long. 027°E, lat. 6°N

E – long. 124°E, lat. 23½°N W – long. 073°W, lat. 10½°S

where N and S are the present Magnetic Poles;

P is the pole lying in the Pacific;

A is the pole lying in Africa;

E is the pole lying in the "East Indies";

W is the pole lying in the West Indies;

While the plane N-P-S-A has been labelled the a-plane;

the plane N-E-S-W has been labelled the b-plane;

and the plane P-E-A-W has been labelled the c-plane.

The "vertical" shear plane between planes a and b and passing north-south through the Atlantic Ocean has been labelled as s1, the other passing north-south through the Indian Ocean as s2. The "horizontal stress planes between planes a and c are labelled f1 and f2 while those between planes b and c are labelled g1 and g2. See figure 1 for the locations of the principal poles, principal planes, and the two "vertical" shear planes.

TESTING THE HYPOTHESIS

For the hypothesis to be correct major straight-line Earth-surface tectonic and physiographical features should coincide with or closely parallel surface traces of the nine stress planes developed from the hypothesis. And they do. Other physical phenomena can also be shown to be related to the stress planes or, in some cases, to the principal stress axes poles. For example, isoporic contours for magnetic declination and inclination, seismic anomaly contours for the lower mantle, isostatic anomaly contours of the Earth’s gravity field, the triaxiality of the Earth’s shape, and the heat flow pattern of the Earth all show spatial relationships to planes or poles.

Although many Earth-surface features show lineal relationships to the Earth-surface traces of the nine planes, a number of very prominent major features, both tectonic and physiographic, appear not to be. Curved features such as the Java Trench, the Aleutian Archipelago, and the right lateral fault system stretching from the Gulf of Hormuz to the Bosphorus, when viewed on an Earth globe will be found to lie on very slightly elliptical "circles" having centres coinciding with the Earth-surface poles of the two "horizontal" principal axes. Where these circles intersect, the paralleling or coinciding curved features on the Earth’s surface tend to be bent or warped. This suggests that the circles are the Earth-surface expressions of cones of rotating or spiralling mass movement, and that mass movement is of different speed in each cone. (See Figure 2 for those parts of the planes and cones of stress with related physiographic and tectonic structures.)

The circle which the Aleutian arc parallels is the lone exception to relationship to a principal pole. In this case the circle centre is at about the first point of collision of the Asian-North American continental plates and, as will be shown below, it has a close relationship with several of the other stress planes.

The radii of the circles are not the same but, excluding the Aleutian, are all near either 30° or 60° of arc, where the distance is measured in degrees equivalent of latitude. The few degrees difference from these two figures can be shown to be related to the difference in distance of the surface circle centres from the inner core centre. Because of this it has been assumed that the surface circular traces are expressions of incipient "cones of shear" with apices at the centre of the offset core. It will be shown below how these cones can be used to predict intrusive and tectonic events.

The planar stress planes have been termed "incipient planes of shear" in order to emphasise that the planes are not active faults. At the Earth’s surface the planes appear to be broad zones capable of distortion, may be quiescent or exhibit tectonic activity along restricted parts, but are never active along their full lengths. Some planes are presently more active than others. For example, the b-plane appears to be marked by a shallow depression from the NMP to about the Mexican Gulf, is marked by a low drainage divide across Western Australia (and a very broad zone of faulting in the Southern Ocean), is closely paralleled by major north-south faulting in the Philippines, and is closely paralleled by the Chile Trench south from latitude 18°S. Obvious movement along any of these planes is uncommon. Rather, it appears that the plane behaves the same as the material on either side of it until a tensile stress acts at right angles to it. Such a stress results in a broad, sheet-like zone on or closely related to the plane becoming plastic and, if the stress is sufficient, "streaks" of fluid form. This fluid probably normally passes up the "plane" (e.g. ocean ridges) but if other stresses are present movement may be modified; a trench on or adjacent to the plane may form.

The "conical" planes of shear behave quite differently. Although there are theoretically eight surface traces it can be seen on Figure 2 and by constructing the circles on an Earth globe that only four presently show more than nominal activity. The best developed are the 32½°bW and the 30°aA. Real movement takes place along these planes. Figure 3, which can easily be correlated with Figure 2, shows the known Earth-surface lateral movements across the planes in the Pacific region.

If these planes really are cones then it would seem that there is a spiral movement upwards of mantle material from at least the core-mantle boundary to the Earth" surface. Where movement is taking place along a part of a cone cutting oceanic crust it is marked by a trench or an ocean ridge. Where it is covered by a continental plate it may be marked by a low drainage divide, possibly due to the entrapment by the plate of upwelling magma. Where the cone plane trace parallels a continental edge volcanicity is common. Figure 3 shows that some half of the 32½°bE and 32½°bW cone surface traces are also marked by earthquake epicentres. Not so obvious is the 60° of arc of the 30°aA cone from the Gulf of Hormuz to the Bosphorus, which is marked by an almost continuous zone of right lateral faulting.

There is one cone of stress which does not have its centre of radius at a principal pole of the stress field. This is the Aleutian cone of shear and it was studied separately. The author concluded that it was distantly related to the previous seventeen curves. It is provisionally suggested that the cone was initiated by the collision of the Asian and North American continents. The point latitude 71°N, longitude 175°W was assumed the point of impact and this gives a circle radius of 20° measured due south to the Aleutian trench. It was found after construction of the surface trace of the cone(?) that the Aleutian Trench is very closely circular. Also, the curve passes practically through the aP68° - f2-plane and aP68° - a-plane intersections. The curve was not constructed to do this. It is possible that the Aleutian tectonic zone was initiated by continental collision but that the radius of the cone was controlled by planes and cones of the Earth’s stress field; that the aP68° cone forces followed an easier path between the triple points noted, a path which normally would have been temporary but for its being able to fit in so neatly with the primary structures.

The 20°Al cone surface trace is not confined to the Aleutian Trench. It passes within 2° west of the NMP and very nearly forms a triple intersection with the b- and f2- planes intersections, suggesting that a near-perfect fit of a curve to the four triple intersections could be constructed. The cone may structurally control the lower half of the Lena River in Russia (it runs along the western edge of the Verkhoyanskiy Mountains immediately to the east of the river) and closely coincides with a weakly formed ocean ridge that joins Asia with the North Pole and on to North America. It thus encloses the main part of the Arctic Basin.

The 20°Al cone of stress is the only curve that cannot be simply explained by the hypothesis.

USE OF THE HYPOTHESIS IN TECTONICS

A brief description of the western part of the Pacific "Ring of Fire" will now be sketched in terms of the planes of incipient shear developed from the hypothesis to show how the hypothesis can, in a broad way, explain the tectonics, intrusions, and mineralisation of the fiery zone.

Rotated palaeomagnetic poles (Beck, 1980), major transcurrent faults (McKenzie, 1972), and even borehole stress test measurements near cone faces (Hillis, 1991) show that mantle rock is moving anticlockwise within the 68°aP, 32½°bE, and 20°Al cones. Figure 3 illustrates in sketch form the relationship of the three cones to one another and to relevant parts of the principal and shear planes. It shows cone intersections, directions of movement of underlying mantle at the cone faces, and lines of earthquake epicentres clearly related to cone circle traces and stress planes. The collated information clearly shows that upper mantle mass movement is taking place around the edge of the Pacific Basin.

The rim of the 68°aP cone passes under the North American continent. If mantle material in the cone at this location is moving, as the rotation of palaeomagnetic poles indicates, then the material is moving northwesterly. The mantle material, on reaching the 20°Al cone intersection situated under the Gulf of Alaska, is opposed by mantle material moving northeastwards within the 20°Al cone. A build-up of mass should occur. The crossed square just west of the intersection and shown on Figure 3 indicates where a gravity high has been measured. Similarly, a concentration of mass should also occur in the area between the 68°aP, 32½°bE, and 20°Al cones – at about the Sea of Okhotsk – and does as is shown by a measured gravity high. Again, concentration of mass certainly occurs at the southern intersection of the 68°aP and 32½°bE cones above western New Guinea because, if the Mariana-Izu-Japan Trench defines the warped edge of the strongest moving circumferential cone flow at the locality, movement within the 68°aP cone must be the more powerful. An exceptionally high gravity anomaly exists just west of this southern intersection and within the 32½°bE cone (Bostram et al, 1983). It can thus be confidently stated that an upper mantle mass movement is taking place within the rim of the 68°aP cone.

Following the mantle mass movement from the Gulf of Alaska, the mantle mass, which at this location is moving from east to west, is deflected around the 20°Al cone across the northern part of the Pacific Ocean to where the cone is intersected by the 32½°bE cone at about 40°N,154°E. This flow is probably augmented by a weak westerly Coreolis force. Thus at the intersection it could be expected that the 68°aP cone mass would develop a circumferential bulge into the 32½°bE cone and some of the mass would leak into the smaller cone to become part of that system. Leakage is suggested by the westerly deflected rim of the 68°aP curve south of the cones’ intersection to about 22°N latitude as shown by the Japan, Izu, and Mariana Trenches.

It can be deduced from cone mass movements shown in Figure 3 that a part of the leakage from the 68°aP cone at the Sea of Okhotsk intersection has activated the incipient g1-plane, which forms a triple intersection with the two cones at this point. This part is passing southwestwards along the g1-plane, and to a limited extent under Japan, to as far as the bE pole of the principal axis just east of Taiwan. Here, it possibly turns southwards along the b-pane through the Philippines to finally merge with the southern west-to-east circumferential mantle mass flow of the 32½°bE cone.

Most of the augmented mass in the 32½°bE cone at the Sea of Okhotsk intersection should flow anticlockwise within this smaller cone under the eastern part of Asia, where a low drainage divide marks the edge, until it curves eastwards then northwards before coming to its southern intersection with the 68°aP cone. Here, not only are the cones’ mass movements opposed, with the 68°aP cone movement the stronger, but at this altitude, at the equator, the westerly Coreolis force is at its greatest. This means a large resistance to the augmented 32½°bE cone mass flow, resulting in a large build-up of mass within the 32½°bE cone north of New Guinea. This explains the very large positive gravity anomaly known to exist there and shown by the four crossed squares on Figure 3.

The southern intersection of the two cones almost forms a triple intersection with the g2-plane, which plane bears approximately northwest-southeast and lies just northeast of the coast of Papua-New Guinea and parallel to it. As has been discussed earlier in the paper the g2-plane is an incipient plane of weakness. Should any part of it come under sufficient stress then tectonic activity will result along that part. The build-up of moving mantle material at the triple intersection as indicated by the very large gravity high there indicates the g2-plane is under high stress. Relief of the stress can be argued as occurring by deflection of some of the moving mantle material southeasterly along the southern face of the g2-plane to at least the s1-, g2-, f2- triple intersection. Should shearing occur along this plane the strike slip should be sinistral, which Figure 3 shows to be the case.

The large gravity high at the cone of intersection suggests a buildup of matter at the base of the lithosphere due to opposition of the mantle flows in the cones. This in turn suggests a zone of stagnation at the cone intersection, even though the unequal mantle flows indicate that the cone flows have not ceased but been deflected. Such a zone of stagnation, and relief of pressure by faulting, would be conducive to at least partial melting of the material there, resulting in some differentiation of the material into different magma types. That part of the magma which is moving along the g2-plane will be further modified as the magma stopes upwards through crustal rocks in this zone of pressure relief.

The hypothesis thus permits an explanation to be developed for the presence of the broad seismically and volcanically active northwest-southeast zone along the northeastern part of New Guinea and of the Solomon Islands; and allows a prediction to be made of the types of mineralisation within that zone. A similar interpretation can be made for the volcanic activity and mineralisation in the Philippines, southern Japan, the Kuril Islands, and the Aleutian Arc.

 

PART B

CONTINENTAL PLATE PATH PLOTTING

As given above, the use of planes and cones of stress to explain tectonic activity is of limited value, as predictions can only be made for the Present. What is needed is a method of determining the positions and orientations of continental plates throughout past time. Then it would be possible to determine the relationship of any plate of interest to planes of stress for some particular age and so allow determination of the most likely part of the plate to carry mineralisation. And this even though the containing rocks may be covered by later beds.

It is a point in favour of the hypothesis given in Part A of this paper that it permits the mathematical location and orientation of a plate throughout time if a sequence of palaeomagnetic poles is available for that plate. The method is as follows:

Draw the traces of the four "vertical" stress planes a, b, s1, and s2 described at the beginning of Part A of this paper onto a globe of the Earth.

Assume that palaeomagnetic poles as given in the literature are ancient spin poles (accepted in the literature; see McElhinny, 1979) and that these ancient spin poles had associated magnetic poles, here termed palaeocore poles, at the same relative positions as have the present spin poles.

Then if the palaeocore poles of two not too widely time-spaced palaeomagnetic poles of a continental plate are plotted on the globe of the Earth and both poles moved equally so that one coincides with a present magnetic pole, it will be observed that the second pole always falls on or very near the surface trace of one of the four a, b, s1, and s2 planes. Figure 4A gives an example of this observation and Figure 4B shows how it is applied to plate path plotting.

If the reader does not like the idea of ancient spin poles having magnetic poles then he can modify the assumption to "take a point distant from each ancient spin pole the same in length and orientation as that of the present magnetic pole from its respective spin pole" and then continue in the same way. An assumption then disappears.

Experience has shown the author that where this condition is not met, the palaeomagnetic poles are too widely time-spaced; that the continental plate changed its direction of movement during the time interval used. When the author has been able to obtain an intermediate palaeomagnetic pole the condition has always been met.

The above allows the relative direction and distance of a plate to be estimated but there is still doubt as to its absolute location and its rotation. For these another assumption is needed, one which must be proved by trial and error testing. It is: Continental plates move only as dictated by the above statement. In other words, plates do not rotate about their own centres nor are their movements controlled by other plates.

Applying the above assumptions and construction method it will be found by testing that it is possible to plot back in time from the Present the path of a continental plate using only palaeomagnetic pole data. An outline of how a plate path is determined and of how a plate is moved backwards in time is given by Lee in Gondwana 8 (1993), but see Figure 4. The following Rule encapsulates the mathematical method.

The movement of any continental plate throughout at least Phanerozoic time has been such that it has always and only been parallel to one of the four "vertical" planes of the hypothesis at any one time.

It must be emphasised that the term continental plate means just that. The plate does not incorporate or have attached oceanic crust.

The Rule has been tested by plotting the paths of all major continental plates and several smaller plates, singly and in groups, back in time from the Present. Some plots have only been to the Permian, several to the Cambrian, and one into the Proterozoic. It has been found that:

  1. no overlapping of plate paths or plates occurs over any given time;

  2. where plates are unequivocally known to have separated or joined, the plotting gives separation or joining, and at the known age if it is known (see Figure 5); and

  3. where the latitude and approximate orientation of a plate has been closely determined using current methods of determination a similar position but including longitude is given by plate path plotting (see Figure 6).

 

It is necessary to emphasise that the Rule is an empirical rule based on the plotting of many poles. The only exception to the Rule so far found has been the Italian plate before the Upper Cretaceous. But plotting shows that Italy was struck glancingly by the African plate in the Upper Cretaceous. Correct for this glancing blow by rotating the Italian plate 45° clockwise in the Upper Cretaceous and the Rule is followed to the cessation of plotting in the Upper Permian.

Two examples are given here to show the advantages of using plate path plotting when investigating the relationship of two continental plates.

  1. The Separation of Madagascar from Africa.

    2. It has been argued for many years that Madagascar was once a part of the African plate. Exactly where it fitted against Africa is still in dispute, as is when it separated. Separation is still commonly argued as being in the Late Triassic or Jurassic despite good field data suggesting an Upper Permian age. See for example Wopfner (1991). Figure 7 shows the plate path plotted positions of Africa and Madagascar in the Upper Permian. Plotting shows attachment of the plates in the Upper Carboniferous and separation in the Triassic, so supporting a separation beginning in the Upper Permian.

  2. The Relationship of Australia and North America in the Cambrian.

Dalziel (1991) and others have argued by computer comparisons of geological data that Eastern Australia abutted the North American continent in the Early Cambrian. There is argument as to the exact relative position and the exact time of separation but the broad relationship is now generally accepted. Plate path plotting of the Australian and North American plates back to the Middle Cambrian (500 My?) has shown that the two plates were indeed adjacent to one another but for only a brief time (Figure 8). Palaeomagnetic poles for Australia in the Early Palaeozoic were few and far between when this study was carried out so that the relationship of the two plates as determined by plate path plotting is approximate. None-the-less it can be stated with confidence that the plotting supports the plates’ relationship in the Cambrian as claimed by other authors. However, plotting shows that the two plates were only briefly in contact. Australia from the top of the Proterozoic to the Middle Cambrian moved rapidly northwards from the Southern Hemisphere, struck North America, and rebounded at a lesser speed southwards

Although plate path plotting has not been used to determine plate positions back into the Proterozoic, it is not because it cannot be applied. Plotting has not been carried out because the palaeomagnetic poles available are relatively few and tend to be clustered in very widely time-spaced groups. The author has developed an approximate method of plate path plotting which can be used to determine approximate paths back to the Middle Proterozoic but has turned his attention to other, to him, more interesting problems. He can say with confidence, however, on the basis of his other studies, that the Rule will apply back to at least the beginning of the Proterozoic and probably much further.

Plate path plotting also permits the measurement of the rotation of a continental plate over time and thus the relative rotations of two plates. It also permits simple computation of a plate’s speed over time. The author has done this for the Indian plate from the Upper Cretaceous to the Present and obtained average speeds closely similar to other workers (Lee, 1996).

 

PART C

THE USE OF PLATE PATH PLOTTING WITH EARTH PLANES OF WEAKNESS

Plate path plotting is a non-subjective, mathematical plotting method. While it gives many similar relative positions between plates as those determined by the highly subjective, presently accepted plate theory there are a number of instances where it does not. The position of South America relative to Africa other than between the Silurian and Middle Carboniferous, and the time of break-up of Gondwana are two major differences. Yet there is ample palaeontological, palaeobotanical, and at least some stratigraphic evidence supporting the locations of plates as given by plate path plotting, and against that determined by current theory. It is impossible in this short paper to argue the case and to show why present plate theory breaks down under certain conditions. This will have to be left to another paper (But see Lee, 1992). Instead, three increasingly complicated examples of plate movements will be given here to show how size, location, direction of movement, and rotation of a continental plate are all important factors in predicting igneous intrusives, the types of intrusives, and whether mineralisation may be present.

Example 1.

Figure 9 shows the location of the Indian plate during the extrusion of the Deccan Basalts. This great eruption of basalts has been dated at between 65 and 69 My and the complete outpouring could have taken place in less than 1 My (Duncan and Pyle, 1988; Cortillot et al, 1988). The figure shows that at 70 My the plate lay over a plane triple junction, was virtually centrally located over the g1-plane, and was moving rapidly at right angles to that plane. After this time the g1-plane would have had a tensile force acting across it and at a triple junction there would have been an easy path for magma from depth. Is it any wonder such an outpouring of lava took place? At 60 My the plate was largely off the g1-plane and so the plane would have closed and extrusion ended. Extrusion of lava accordingly must have begun after 70 My and ended before 60 My and such is known to have been the case.

Example 2.

Dawson (1980), Table 2, pp.14 and 15, gives the ages of almost forty Mesozoic diamondiferous pipes in southern Africa. These ages range from 150 My to a little less than 60My. In detail, there is a small group with an age of about 140-150 My – say upper Middle Jurassic to Upper Jurassic – a slightly larger group between about 115-125 My – upper Lower Cretaceous to Middle Cretaceous – and a large group between 70-100 My – Upper Cretaceous – with the maximum number in the Upper Cretaceous. This latter group tapers out in the Eocene.

Plate path plotting shows that the plate rotated clockwise some 13° from the Middle Jurassic to the Lower Cretaceous and then anticlockwise approximately 35° from the Lower Cretaceous to the Eocene, when the large rotational movement ceased.

Comparing the time distribution of the intrusions of Dawson’s table with the plate movements calculated by plate path plotting shows that diamondiferous kimberlite intrusion began a little after the commencement of clockwise rotation in the Middle Jurassic and (almost?) ceased in the Upper Jurassic, a little before rotation was reversed. There was a new burst of intrusive activity in the upper Lower Cretaceous after anticlockwise rotation commenced, followed by a short lull in the upper Middle Cretaceous before the main intrusive activity in the Upper Cretaceous. Intrusive activity then decreased, and ceased in the Eocene when the large rotational movement, begun in the Lower Cretaceous, ended.

Figure 10 permits an understanding of why intrusion occurred and why it occurred in pulses; Figure 10B shows the fracture pattern which must have developed during plate rotation. From Middle Jurassic to Eocene the centre of the African plate lay about 6° of arc from the African pole of the b-plane, which itself lay about 6° of arc from pole aA. Further, the southern part of the plate lay over the f1-plane. As a result, when the plate rotated a near vertical stress developed across the face of the f1-plane.

While the "leading" (western) side of the plate was less than the "trailing" side the f1-plane was in compression. Compression decreased until, the leading side exceeding the trailing, the stress became tensile. Assuming constant plate speed the change from compression to tension would have occurred in the Upper Jurassic. Tension would have resulted in plasticising of material in the plane zone and almost certainly along the intersecting 30°aA plane and so have allowed intrusion of mantle material into the plate. Dawson gives fault strikes of E-W, N-S, WNW-ESE, and NE-SW in present day orientations. Adjusting these to fit the Lower Cretaceous final plate position gives a distribution as shown in Figure 10B. This is a good approximation of a fracture pattern for a tensile stress at right angles to the f1-plane.

When rotation ceased in the Lower Cretaceous the plate fractures would have closed, though the f1-plane might have remained "open", depending on how quickly the plate stopped and reversed direction.

On rotation reversing, the fractures in the plate would have opened and if the f1-plane zone had not yet "frozen" some material could have been extruded from the mantle into the plate. This would probably have been minor in amount as the plate would have begun to exert compression once more on the f1-plane and have closed it. Intrusion would have ceased until the leading side of the plate (now the eastern side) was farther from the f1-plane than the trailing side. Once again a tensile stress would have developed and extrusion from the mantle up into the plate could have once more taken place.

As the "trailing" edge of the plate receded from the f1-plane, friction between the base of the plate and the mantle (and plasticity in the mantle) would have begun decreasing the tensile force on the plane and ultimately the plane would have become quiescent. This would have been some time in the (Early?) Eocene.

Figure 10 therefore allows a simple explanation of why the Mesozoic was so important for kimberlite intrusions in South Africa and why the intrusions came in bursts. More importantly, it shows a mechanism (one of several?) to look for in an office study for kimberlite deposits on other plates.

Example 3.

This is of the Peruvian Andes. Figure 11A shows the plotted positions of the Peruvian part of the South American plate for Middle Triassic, Middle Jurassic, Lower Cretaceous and Lower Tertiary/Upper Cretaceous. The figure also gives the positions of the b, c, g1, and g2 stress planes. Movement of the plate during this period was north but with varying clockwise rotation to give an effect on the plate edge of equal northerly and northeasterly movement. Movement from Middle Triassic to Middle Jurassic was moderate, from Middle Jurassic to Lower Cretaceous was slight, and from Lower Cretaceous to Lower Tertiary/Upper Cretaceous was rapid.

Initially the plate edge was approximately 1000 km from and parallel to the g1-plane, which lay under the plate. By the Middle Jurassic the distance between plate edge and plane was halved. The distance was approximately halved again on average (movement was chiefly rotational) by the Lower Cretaceous, and the plate edge would have passed over the plane in about the Middle Cretaceous. The position and the movement of the plate relative to the g1-plane over this time would be expected to cause gradually increasing tension across the plane and so open it, greatly in the northern part of the plate and by a slightly decreasing amount southeastwards.

Using a similar interpretation it would be expected that planes b, c, and g2 would be chiefly under compression and that there would possibly be some dextral force along g2 and b.

Figure 11B shows the three plate positions for the Lower Tertiary/Upper Cretaceous, Pliocene/Upper Tertiary, and Present as determined by plate path plotting. This shows that plate movement reversed at the beginning of the Tertiary. Movement from Lower Tertiary/Upper Cretaceous to Pliocene/Upper Tertiary was southerly and with a slight anticlockwise rotation resulting in a resultant movement somewhat west of south. Such a movement would close the g1-plane as the southerly moving plate would have exerted compression on the plane. There would have been little change in stress size on the b- and c- planes but the stress would have been reversed. In the case of the g2-plane there would be little change at first but an increasing oblique stress with time, as the plate centre moved, would have resulted in activation along the southwestern part to form a trench or, if the stress caused deep fracture, a ridge of volcanicity.

Total movement of the plate from Lower Tertiary/Upper Cretaceous to Pliocene/ Upper Tertiary was as great as that between Middle Jurassic and Lower Tertiary/Upper Cretaceous. If plate movement is by sliding over or through mantle then it would be expected during this time that the plate slid under the fringing, edge-blanketing deposits laid down from the Middle Triassic to the Upper Cretaceous. Northwest-trending folds and faults should have formed.

Finally, the plate movement again approximately reversed in the Pliocene/Upper Tertiary and movement from then to the Present was northerly, with a continuing slight anticlockwise rotation. As Figure 11B shows, movement over this time span was relatively small. Movement at the Equador border was almost nil, but the anticlockwise rotational component resulted in a progressive increase with distance to the southeast. Thus there was increasing tension across the g1-plane southeastwards to at least, and possibly a little beyond, the bW pole (the intersection of the planes).

It is possible to use the above plate movements and stress variations to predict the stratigraphic and tectonic development of the Peru coastal areas of the South American plate during the Mesozoic and Cainozoic. In summary it is:

  1. Moderate maritime sedimentation with perhaps some acidic volcanism from Middle Triassic to Middle Jurassic.

  2. A decrease in sedimentation and that possibly of shallower water origin, with perhaps increased volcanism (andesitic?) from south to north from Middle Jurassic to Lower Cretaceous.

  3. Extensive sedimentation from Lower Cretaceous to Lower Tertiary/Upper Cretaceous. Sedimentation should have changed from marine at the coast to terrestrial inland to the northeast and volcanism (and/or plutonism) should have been extensive at the coast; with volcanism at the coast dominant from about Middle Cretaceous onwards. This should have become increasingly basic with time.

  4. Sedimentation and volcanism should have ended at the end of the Cretaceous, and northwest-striking folding should have formed. The folding should have developed into thrust folding and/or large thrusts.

  5. Some time at about the beginning of the Pliocene, perhaps earlier, thrusting should have ended and partial isostatic balance may have been reached. This should have been followed by renewal of volcanism on the plate, near its edge; volcanism being greater towards the Chilean end of the coast. Minor sedimentation should be taking place.

A comparison of the actual stratigraphic-tectonic development of Peru given by Megard et al (1984), and briefly described by Atherton et al (1983), with the development predicted using plate path plotting show close similarity of process and timing.. It is true that the compression began at the base of the Upper Cretaceous while plotting gives it at the top but then, no poles between Lower Cretaceous and Lower Tertiary/Upper Cretaceous were available for the study to check this discrepancy. The difference is probably only due to lack of detail. Again, it appears from Megard's’description that there was a (brief?) reversal of direction of the plate some time near 40 My ago. This event cannot be shown by the hypothetical development as, again, no palaeomagnetic poles were available around this date. (The study was made some few years ago and new poles are now probably available.) The hypothetical development is also in good agreement with the geological description given by Zeil (1979). In particular, the age of the coastal batholith mass accords well with the hypothetical, and the maximum development of volcanoes at about the Peru-Chile border is what should be expected.

The close similarity between Megard’s and Atherton’s descriptions of the Peruvian Andes and the hypothetical development using the hypothesis supports the contention that the method of interpretation is correct. It suggests that the Andes did NOT develop by underthrusting of the Pacific plate but by the overriding of the South American plate over oceanic, lower elevation rock. It also shows how plate path plotting allows one to predict in certain instances the presence and type of igneous intrusions and the type of mineralisation which may be associated with them.

CONTINENTAL LINEAMENTS

A continental plate is in effect a thin plate lying draped over a three-dimensional body, the Earth. The upper surface of the plate material is brittle but becomes ductile with depth. Because the Earth is three-dimensional, when a continent moves over its surface the continent moves about a rotation point on the Earth’s surface. This means that the leading edge of the plate experiences a couple acting on it. A couple is force times radius. In the case of creep of the continental plate, if resistance per unit length and angular velocity of the plate are constant then the couple will increase with distance from the rotation point.

Should the plate move slowly or movement be small it is possible that the varying couple along the leading edge of the plate will not reach a size where failure will occur. But for a large plate moving other than very slowly, a couple value will be reached at some point (or points) along the leading edge of the plate where failure will take place. A line of shearing or distortion will develop at this point parallel to the plate movement and steeply dipping down into the plate. At the surface of the plate the plane of failure may occur as faulting but at depth it will be distortion in a narrow, ductile sheet. Put another way, a continental lineament will develop.

The same phenomenon will develop whether movement is due to creep of the plate over the Earth or drag by "mantle currents", the only difference being that relative movement along the fracture zone will be opposite for the two cases. For a similar argument on global lineaments see McElhinny (1979), pp.173-5.

For the hypothesis given in this paper to be correct some or all major continental plates must exhibit continental lineaments which can be shown to be parallel or near parallel to past movements of the plate. The qualification "near parallel" is required because if a lineament has resulted from a plate movement and a new movement occurs not quite parallel to the older, failure of the plate during the new movement will probably utilise the existing, near parallel, lineament zone because it is a zone of weakness.

When a continental plate lies consistently a considerable distance from the centres of successive rotations the paths taken by the plate are only slightly curved and a particular style of path grouping develops. Plotting reveals that if, for example, the plate moves about the aP pole, and after rotations about other poles, again rotates about the aP pole then the second aP path will very nearly parallel the former path. Thus if lineaments had formed at the first aP movement, failure during the second would probably utilise the old zones of weakness. The result, taking into account all the movements of the plate, is that a limited number of lineament orientations develop and these will be related to a limited number of clusters of plate paths. If such a relationship can be shown not to develop then the hypothesis as given in this paper is incorrect.

Australia has been mostly distant from rotation points for much of the Phanerozoic. It has occasionally approached a rotation point and so there should be a splay of paths about average directions. The plate will be used to show that continental lineaments do parallel plate paths.

Lee (1989) calculated the plate paths of the Australian plate for the period Cambrian to Recent. The paths from the Cambrian to the Cretaceous are shown on Figure 12, on which figure are also shown the gravity anomaly lineaments numbers 1 to 10 of O’Driscoll (1981). The lineament numbers have been moved to align with those paths nearest to parallel with the lineament, the orientation of the lineament being the critical factor and location being of no importance. The diagram clearly illustrates that continental lineament and plate path orientations coincide as required by the hypothesis and theoretically described above. It can thus be claimed that continental lineaments are produced by movement of a continental plate over the three-dimensional surface of the Earth.

The above discussion has been on continental plates; oceanic crust has not been considered. It may well be that the megafracturing of oceanic crust was produced by torsional stress associated with planetary spin, a currently popular idea in some geological circles. And if the fracturing is termed "global crustal lineaments" this author has no present objections. But continental lineaments cannot be produced by torsional stress associated with planetary spin. Nor can they be due to Earth expansion. The proof of this latter statement is simple, the other a little more involved and cannot be argued in this short paper.

Earth expansion in any form proposed in the geological literature can be dismissed by the following argument. Fuller and more rigidly correct arguments have been developed by the author but are too extensive to give here.

Compare the ratios of the radii of the planets Neptune (RN), Uranus (RU), Earth (RE), and Venus (RrV); i.e.,

RU/RN = 26150/24750 = 1.05657 (0.33% from 1.23¼)

RE/RV = 6378/6050 = 1.05421 (0.10% from 1.23¼)

RU/RE = 26150/6378 = 4.10003 (1.96% from 1.198)

RN/RV = 24750/6050 = 4.09091 (1.73% from 1.198)

The ratio 1.23 is by far the most common ratio in Universe calculations and 1.19 is probably the second most common (Kokus, 1994, remembering that 2.3 and 2 are closely powers of 1.23 and 1.19 respectively). The numbers certainly repeatedly occur in Solar System calculations.

If Earth is or has been expanding or contracting, the above set of ratios and their relationships to the Universe ratios 1.23 and 1.19 would have to be accidental. Just now, in this instant in time, the radius of the Earth must be what it is. At any other time the set of ratios, which relate Earth to the other three planets and to 1.23 and 1.19, would not exist. This condition appears highly unlikely; the odds against it must be enormous. Much more likely is that (i) all the planets are expanding or contracting proportionately to retain the ratios or (ii) none of the planets are expanding. Without arguing why, it is here stated that the case (ii) is by far the most likely condition. That is, there has been no expansion as argued by proponents of Earth expansion. Also note that the inclinations of the spin axes of Uranus and Earth, measured in the positive direction, have a ratio of (180°-2.083°) divided by 23.450° = 4.17557 or 1.84% different to the ratio of the planets’ radii; while if we take the tilt of Venus as 180° plus 2.67° rather than 180° minus 2.67°, then Tilt N + 720° divided by 182.67° gives 4.09920 or 0.02% different to the ratio of the planets’ radii. This suggests an even more restricted physical condition for Earth.

It has been shown in this paper that time-adjacent palaeomagnetic poles of any continental plate can be used to illustrate that continental plates move; and permit determination of the direction and distance a plate moves, together with its rotation relative to a north-south line, for the time-span considered. Plotting of the plate paths has shown that all the plates move and rotate such that it is impossible for a torsional stress due to Earth spin to produce over geological time the various continental lineaments that exist. It may assist on occasion but torsional stress cannot produce the lineaments. Even if one assumes the lithosphere of the Earth slips over the main body of the Earth, or the Earth’s spin axis changes position, torsional stress still cannot account for continental lineaments. But continental plate path plotting CAN explain why continental lineaments are present and it does so simply. There is no doubt in the author’s mind that the solution developed from plate path plotting is correct.

CONCLUSIONS

A simple and credible hypothesis has been presented, namely that the Earth’s inner core is offset from the Earth’s figure centre and is exerting an outward radial pressure. The core centre is argued as being at the intersection of the straight line joining the magnetic poles and the 6°N latitudinal plane.

The hypothesis allows the development of simple theoretical explanations for various physical phenomena of the Earth. In particular it gives an explanation of the locations and causes of major lineal tectonic and physiographic features on the Earth’s surface, and permits a simple formula to be developed to PLOT the past positions and paths of continental plates using only palaeomagnetic poles of the individual plates.

It is possible to use the above developments to explain why various geological processes have taken place and to predict where on a continental plate and when in geological time such processes occurred. Examples have been given to show how this knowledge can be applied, e.g. Explanations for the Deccan Traps of India, the locations and timing of the Mesozoic kimberlite intrusions of southern Africa, and the development of the Peruvian Andes Mesozoic-Cainozoic stratigraphy. Also given has been an explanation of the cause of continental lineaments, structures which are becoming increasingly accepted as important in regional mineral exploration.

The simplicity of the hypothesis, the few assumptions used with it, and the positive testing in a number of branches of geology and geophysics leads the author to believe that the hypothesis is based on fact, allows valid predictions to be made in tectonics, and is a geological model which cannot be validly ignored.

 

 

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