Geological Implications of an Expanding Earth (part 2)

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Cox & Doell (1961a) further considered that, if contemporaneous palaeomagnetic data from two localities on the same stable continental block have different inclinationsI₁ and I₂(Figure 52) so that the two localities are on different circles of geomagnetic latitude, and if the ancient geomagnetic field was dipolar, then the ancient Earth radius R_a may be found from:

Cox & Doell (1961a) used this method to evaluate the Earth's radius during the Permian, from data analysed from palaeomagnetic studies of 16 sample sites from western Europe and 5 sample sites from Siberia (Figure 53). The European and Siberian data being chosen specifically because they were the only data available at the time located supposedly on, or approximately on, the same palaeomeridian.

Figure 53 Permian virtual geomagnetic pole positions used by Cox & Doell (1961) to determine the palaeoradius of the Earth. Palaeomagnetic data are from sampling sites located at (1) Siberia and (2) Western Europe, represented by virtual geomagnetic pole positions at (3) Siberia and (4) Western Europe. (From Cox & Doell, 1961)

The method of calculation adopted by Cox & Doell (1961a, 1961b) was to pair each of the inclinations from Western Europe with those from Siberia giving a total of 80 determinations of R_a. The average of the 80 values calculated for the Earth's radius during the Permian was found to be:

Compared with the present Earth radius of 6371 kilometres Cox & Doell (1961a) therefore concluded that the Permian magnetic field, as seen from the two sampling areas almost 5000 kilometres apart on the European land-mass, was consistent with a Permian Earth radius equal to the present.

The palaeomeridian method of determining palaeoradius from site data located along the same palaeomeridian is mathematically sound only if the primary assumptions are correct. That is, assuming that the continental lithosphere between the sample sites has remained spatially static and site separation has remained essentially constant. For the excessive site separation chosen, and continental area involved however, Earth expansion must involve some adjustment for relief of surface curvature.

This point was considered by Carey (1958, 1975, 1976, 1986) and appreciated in principle by most palaeomagneticians considering palaeoradius (eg. Cox & Doell, 1961, 1961b; Ward, 1963; van Hilten, 1963, 1965, 1968; van Andel & Hospers, 1968a, 1968b; McElhinny & Brock, 1975; Schmidt & Clark, 1980) however was largely ignored.

Palaeomagnetic sample sites used by Cox & Doell (1961a) are shown in Figure 53 located in Western Europe (France and England) and Siberia, with a site separation of almost 5000 kilometres on the present radius Earth. This may be compared to the Arctic Ocean small Earth sequential spreading history (Figure 24) detailed previously. As can be seen in this small Earth figure, modeling indicates that the northern European continent has undergone a considerable amount of crustal extension, from the Early Jurassic to the present, in sympathy with opening of the Arctic Ocean. This extension occurred throughout the region, in particular the West Siberian Basin (Ob sphenochasm of Carey (1976)), the Baltic Sea and North Sea regions. The sample sites, when relocated on the Early Jurassic small Earth model also suggest that the actual site separation at that time, and throughout much of the Mesozoic, crossed the North Atlantic spreading axis, as it extended into the Arctic Ocean region.

Figure 54 Suggested radial dispersal of continental fragments and development of Tertiary intracratonic sedimentary basins for Western Europe and Siberia during the Phanerozoic. In this model geocentric angles p 1 , p 2 , and p 3 do not decrease as assumed by Cox & Doell (1961) hence site separation increases, resulting in a palaeopole position and R a /R ratios which mistakenly suggest that the Earth has not expanded.

Figure 54 is a schematic representation of the northern European region used by Cox & Doell (1961a) demonstrating the effect of radial expansion, crustal thinning, fragmentation and formation of Tertiary intracontinental sedimentary basins. In this model the geocentric angles between sites do not decrease as assumed by Cox & Doell (1961a), palaeocolatitudes accord with the conventional dipole equation and site separation increases with time, resulting in Ra/R ratios approaching unity, mistakenly considered by Cox & Doell (1961a) to imply a constant Earth palaeoradius.

In contrast, by adopting the present day site separation of approximately 5000 kilometres, and assuming that the European continent has undergone a radial expansion of its continental lithosphere to the present, marked by opening of the Ob sphenochasm for instance, then during the Early Jurassic the site separation calculates as approximately 2650 kilometres. This equates with the actual separation of the same sites located on the Early Jurassic small Earth model (Figure 24).

Van Hilten's triangulation method

The method, developed by van Hilten (1963) and modified by van Hilten (1968), utilises palaeomagnetic data not located on the same palaeomeridian. The method uses spherical trigonometry to determine a pole position from the intersection point of great circles passing through the sample localities, in the direction given by the declination.

Figure 55 Van Hilton's (1963, 1968) triangulation method of determining palaeoradius of the Earth from palaeomagnetic site data not on the same palaeomeridian. Right figure shows Carboniferous and Triassic palaeomagnetic site and VGP data from North America and, left figure shows Permian palaeomagnetic data from Siberia, Russia and Western Europe. (From van Hilten, 1963)

Van Hilten (1963) used five sets of palaeomagnetic data of various ages from North America and Western Europe and initially concluded that the palaeomagnetic evidence seemed to indicate a noteworthy increase in the Earth's radius since the Carboniferous, the rate of which roughly agreed with the hypotheses of Carey (1958) and Heezen (1959). Van Hilten (1968) later modified his calculation methods to calculate the palaeomagnetic positions for different radii of the Earth, in order to determine the Earth's radius for which the coeval poles of one continent show the least scatter. The method was modified to make allowance for crustal deformation, although he concluded that the consistency of area of the continents during expansion or contraction seemed justified in first approximation.

In his revised estimates of palaeoradius for the Permian of Europe van Hilten (1968) maintained that there was an inconsistency in the data which may be explained by tectonic events. His remaining calculations for North America however failed to produce evidence for either a change in the Earth's radius or a constant one.

The triangulation method used by van Hilten (1963, 1968) acknowledges some degree of crustal deformation, however the method assumes that the angular relationships of the spherical triangles used on the present Earth's radius are consistent with those of the ancient palaeoradius. As Carey (1988) pointed out however, surfaces cannot be transferred between spherical surfaces of different radii without distortion of area, angle or shape.

The triangulation method of van Hilten is in effect demonstrated in hypothetical example (3) (Figures 50 and 51). Depending on the clustering and inclination of site data used in the investigation, the VGP positions will triangulate as a palaeomagnetic pole position. Ra/R ratios calculated from the PPs will vary from the correct ratio, derived from site data containing polar located site inclinations, to ratios approaching unity for site data containing equatorially located site inclinations. Because of the statistics used in reducing the scattered pole positions to a mean pole position, Ra/R values will always be higher than the true value, and figures of 0.73 to 0.97 calculated in the hypothetical example (Figure 51) are consistent with published values (eg. van Hilten, 1963, 1968).

Ward's method of minimum scatter of VGPs

The method of minimum scatter, developed by Ward (1963), was applied to Devonian, Permian and Triassic data from Europe and Siberia. The method was again based on the assumption that, during any change in the Earth's radius, the size of each continent remained constant, and during a particular geological age being studied, the position of the pole did not changed markedly.

Figure 56 Ward's (1963) graphical representation of the dispersion of Triassic, Permian and Devonian palaeomagnetic data from Europe and Siberia. A pole precision parameter k is represented as a function of the hypothetical Earth's radius R a , where R a =1 for the Present Earth radius. Small arrows indicate the point on each graph where k is at a maximum, the point at which palaeomagnetic poles had minimum dispersion. (From Ward, 1963)

The method of minimum scatter of VGPs established the Earth's palaeoradius by generalizing from pairs to sets of site data, using the criterion that the most probable palaeoradius was the radius derived from a set of palaeomagnetic pole positions which had minimal dispersion (Ward 1963). The analysis of dispersion on a sphere was performed by Fisher's (1953) statistical method whereby the pole positions were assumed to be distributed about a true mean. The Fisher (1953) method involved determination of the dispersion of a population of directions, referred to as the precision parameter k, where the most probable ancient Earth radius was considered to be where k was maximum (Ward 1963).

The results of Wards determinations were presented as graphs of pole precision k as a function of the hypothetical Earth's radius, where radius equals 1 for the present radius (Figure 56). From these Ward (1963) concluded that the results for Europe and Siberia could not be considered to indicate any variation of the Earth's radius during the Devonian, Permian or Triassic periods from the present radius.

Irrespective of the lack of acknowledgment of any crustal distortion within the European continent, or the possibility of radial crustal expansion, the primary flaw in this method of palaeoradius determination is the assumption that the most likely palaeoradius is that at which the precision parameter k is maximum, hence VGP scatter is at a minimum.

Hypothetical examples (1) (Figure 48) and (2) (Figure 49) demonstrate two important features not considered by Ward (1963):

1. during Earth expansion ancient pole positions disperse along a small circle arc determined by the age of the rock formation, and;
2. pole positions, using conventional pole equations, actually reach a maximum dispersion when Ra = Ra and a minimum dispersion only when Ra approaches unity R, on an Earth of the present radius.

Ward's method of minimum scatter of VGPs was used by McElhinny & Brock (1975) for twenty six pole positions from Triassic and Cretaceous sample sites at widely separated parts of Africa (Figure 57). The mean poles determined by McElhinny & Brock, 1975, from northwest and southern Africa, form a cluster whose distribution was considered to be typical of poles sampled from regions of continental extent. This led McElhinny & Brock, 1975, to conclude that the palaeopole position, with respect to Africa, remained in essentially the same position throughout the whole of the Mesozoic.The method of minimal dispersion of VGPs set out by Ward (1963) was applied to the African Triassic and Cretaceous groups of data separately to determine the mean pole position, and a close approximation to the palaeoradius determined using the palaeomeridian method of Egyed (1960) where:

R_a = present angular separation of the sites/past angular separation of the sites

The data of McElhinny & Brock (1975) differ from the European data of Egyed (1960) and Cox & Doell (1961a) in that, the sample sites from Africa straddle the palaeoequator. As such, the latitudes calculated from site-data were added together rather than subtracted as in the European case.

The value of R_a determined by McElhinny & Brock (1975) amounted to 1.11 ± 0.20 for the Triassic, 1.06 ± 0.24 for the Cretacious, and 1.12 ± 0.17 for all of the Mesozoic values combined. These may be compared to values of 1.08 for the Triassic and 1.03 for the Cretacious determined by McElhinny & Brock (1975), using Fisher statistics to determine the palaeoradius from a pole precision (k) maxima plot. The values of R_a determined demonstrated to McElhinny & Brock (1975) that hypotheses of Earth expansion "are very difficult to sustain".

Figure 57 McElhinny & Brock's (1975) African Mesozoic site locations (lower figure) and palaeomagnetic pole positions (upper figure) used to determine palaeoradius of the Earth. Full circles represent Triassic, and full squares represent Cretaceous site locations and pole positions in both figures. (From McElhinny & Brock, 1975)

At first glance McElhinny & Brock's (1975) determination of palaeoradius appears conclusive. Africa is generally considered geologically stable therefore site separation may be deemed constant, pole positions form a relatively neat cluster and the R_a/R ratios determined from two independent methods consistently indicated nil expansion. Like Egyed (1960), Cox & Doell (1961a, 1961b), van Hilten (1963, 1968) and Ward (1963) the primary assumption in determining palaeoradius was the constancy of continental surface area. As previously demonstrated the conventional palaeomeridian method is insensitive to crustal extension, and the method of minimal dispersion assumes that the most probable palaeoradius is determined from the point of minimal dispersion of poles. In addition it must be noted that the fundamental dipole equation determines latitude/colatitude only from site mean inclination data. The dipole equation cannot determine longitude, hence any rotation of either or both of the site locations relative to each other cannot be detected using the palaeomeridian method.

Rotation of the site locations will however decrease the meridional angular separation, while still retaining a constant angular separation and constant pole position. Intracontinental deformation of Africa was documented independently by Unternehr et al(1988), which complements observations from empirical small Earth modeling (Figure 25) suggesting the possibility of intracratonic plate rotation for Africa.This rotation allowed for a better reconstruction for South America and Africa along the South Atlantic spreading axis in both conventional and small Earth reconstructions.

The results of McElhinny & Brock (1975) therefore cannot be considered conclusive of zero Earth expansion with time, and in fact can be equally shown to be evidence for expansion.

Discussion

The geological implications of an expanding Earth, as can be appreciated, is a topic which requires as much geological input and research as has plate tectonics to do it justice. The subject is further discussed in Carey (1975, 1988, 1994) (see David Ford's web site "The EXPANDING EARTH"), covering a broad range of topics not included in this paper. The brief discussions on relief of surface curvature, orogenesis, atmospheric and hydrospheric accumulation, and palaeomagnetics were addressed as the major perceived problems confronting the general acceptance of Earth expansion as a viable alternative to plate tectonics.

During Earth expansion, when dealing with relief of surface curvature, it was considered important to recognize the broad tectonic distribution of cratons, orogens, and sedimentary basins,each with their own definitional tectonic framework, which differ fundamentally from the modern ocean basin setting. Small Earth modeling demonstrated that each of these tectonic regimes react differently during Earth expansion, from fragmentation of Precambrian cratons, such as the Canadian Arctic Islands and Greenland, to large scale continental extension marked by intracratonic sedimentary basins, such as the West Siberian Basin in central Russia.

Orogenesis was considered intimately related to asymmetric expansion of the Earth resulting in intracratonic interaction during relief of surface curvature. This asymmetric expansion process was attributted to the hemihedral and antipodal distribution of the present day continents and oceans. The radial and tangential vector components of this asymmetric expansion process giving rise to a continuum of orogenic models varying from compressional to translational and torsional.

Similarly, during Earth expansion, it was suggested that the whole column of atmosphere, hydrosphere, oceanic lithosphere and underlying mantle has been added at an accelerating rate through geological time, which Carey (1983c) considered to have been accreted primarily at the growing ridges and rift zones. As the ocean waters and ocean floors both have the same origin it is to be expected that they would be produced pari passu, with the generation of ocean water and atmosphere keeping pace with the growth of oceanic lithosphere (Carey, 1983c).

Palaeomagnetics has long been considered the cornerstone of plate tectonics yet fundamental premises regarding the constancy of continental surface area, used to determine palaeoradius, stem from the early 1960s, prior to the development of modern global tectonic concepts or completion of the oceanic crustal database. Mathematical equations were developed by palaeomagneticians from conclusions that insist that continental surface areas have remained essentially constant, hence any variation in palaeoradius was concluded to have been negligible with time. Since these equations were first derived, modern plate tectonic concepts have demonstrated that the Earth's crust is not a passive adjunct of lithospheric plates, but a dynamic, interactive layer of the Earth (Grant, 1992).

The modified palaeomagnetic equations developed in this web site for the determination of palaeopole positions since the Early Jurassic prompts a need for a more thorough overhaul of the concepts of palaeomagnetics, in particular the conclusions drawn from the interpretations of pole positions, apparent polar wander paths, and displaced terranes.

Summary and Conclusions

The many geophysical and geological paradoxes that have accumulated during the past two or three decades are apparently the consequences of forcing observational data into an inadequate tectonic model (Storetvedt 1992).

Carey (1958) demonstrated, on a globe representing the Earth's modern dimensions, that if the continents were reassembled into the Pangaean configuration the fit was reasonably precise at the centre of the reassembly, and along the common margins of northwest Africa and the United States east coast embayment, however became progressively imperfect away from these areas. Carey concluded from this research that the fit of the Pangaean reassembly could be made much more precise in these areas if the diameter of the Earth were assumed to have been smaller at the time of Pangaea.Early model makers such as Hilgenberg (1933), Barnett (1962, 1969), and Vogel (1983, 1984, 1990) in particular, demonstrated empirically, through use of small Earth models, that the Pangaean continental reassemblage could be fitted together at a reduced Earth radius of between 55 to 60% of the present radius, to form a closed crust. Vogel (1983) concluded that, the Earth has therefore expanded exponentially with time from this early Pangaean configuration to the present, with continental separation caused by a "radial expansion" of the Earth.

In order to accurately quantify any variation in the Earth's palaeoradius, and constrain plate configuration with time it was argued that, it is necessary to take into account the area and pattern of oceanic lithospheric generation as portrayed in maps such as Larson et al (1985) and CGMW & UNESCO (1990). By using the method of least squares to calculate gradients of curves of best fit from the cumulative empirical oceanic and continental surface area data, it was concluded that the goodness of fit is best described by an exponential curve of best fit. Palaeoradius was then determined and an equation for the exponential increase in palaeoradius of the Earth from the Archaean to the Present was therefore established as:

This equation, assuming the assumptions used to derive the equation are correct, was considered to be the "fundamental equation" for Global Expansion Tectonics, enabling the kinematics of an Earth undergoing an exponential expansion, from the Archaean to the Present, to be readily determined. Modeling the kinematics of Earth expansion suggested that the controlling influence on Earth expansion may not be a result of a secular increase in mass with time, as suggested by Carey (1983a). The cause of Earth expansion was considered however to being intimately related to a cosmological expansion of the Universe.

Very low rates of expansion during the pre-Early Jurassic were demonstrated to agree well with Glikson's (1980) conclusions of a prolonged period of widespread tensional taphrogenesis during the Archaean and Proterozoic, with intense thermal and ductile activity during the Proterozoic mobile belt phase, prior to onset of intrasialic rifting, crustal thinning and development of modern oceans and "geosynclinal" sedimentation during the Palaeozoic.

To test Global Expansion Tectonics and, in particular, the mathematical parameters developed from the empirical sea floor magnetic isochron data, spherical small Earth models were constructed. These models indicated that, if the Earth has expanded exponentially since the at least the Early Jurassic, in accordance with the derived mathematical expression for exponential palaeoradius, then small Earth reconstructions coincide fully with the spreading and geological fit data.

This coincidence applied not only to the passive margin oceans, where conventional reconstructions agree in principle, but also to the Pacific Ocean whereby the necessity for subduction of all or part of, the oceanic lithosphere generated at spreading ridges was refuted.

Relief of curvature and orogenesis on an exponentially expanding Earth, although thoroughly covered by Rickard (1969), Carey (1975, 1976, 1983a, 1986) and Glikson (1979), is still very much in its infancy, compared to the voluminous coverage of plate tectonics Earth dynamic processes. The onset of orogenesis became marked during the Early to Mid Phanerozoic as continental lithosphere fragmented and dispersed under the action of accelerating increase in surface area and isostatic crustal equilibration to the changing surface curvature. Both Rickard (1969) and Carey (1975, 1976, 1983a, 1986) put forward models for orogenesis and geosynclinal development, under conditions of surface curvature readjustment, and demonstrated that continental collision may not be required to promote orogenesis as is required in conventional plate tectonics.

The magnitude of horizontal foreshortening during isostatic equilibration of the surface curvature however, effectively demonstrated the potential for tangentially directed compression acting within a continental plate during exponential expansion of the Earth. This suggested a prime mechanism for orogenesis during Earth expansion.

The nature of mantle fluids, and mantle metasomatism, although briefly touched on, indicated, within the limitations of experimental constraints, that mantle devolatilization of the volatile species in the system C-O-H-S can exist in the Earth's mantle. It was suggested that retention of these species within the mantle was made possible by the high P-T-g conditions prevailing during the Precambrian, due to the much reduced Earth radius, and that devolatilization to form the hydrosphere and atmosphere was a progressive and possibly accelerating process of outgassing of the mantle with time, as a direct consequence of the reduction of P-T-g conditions. The implications of the application of the modified dipole equations to palaeomagnetism was such that every palaeopole position determined to date, using the existing conventional dipole equation is potentially wrong, and conclusions drawn from the interpretations of these pole positions, such as apparent polar wander paths, are therefore misleading.

It is concluded that, Global Expansion Tectonics provides the necessary "motor and mechanism" for Earth expansion, which enables the dynamic principles behind all major geologic phenomena to be resolved and readily explained.

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