What is the significance of polar wandering curves

In this study, we have chosen Central Africa to be the reference continent. In order to rotate palaeopoles from all the other continents into the African reference frame, an accurate and detailed global plate tectonic model plate circuit is required. The LIPs data set is a modified version of the digital compilation available via anonymous ftp from the University of Texas Institute for Geophysics, at. Most of the elements of oceanic crust were extracted from the latest release version 1.

In this paper we focus on a selected subset of the continental blocks whose relative motions are well constrained by marine magnetic anomalies and fracture zones, or by structural features on land. Only palaeopoles associated with these continental blocks were used. Outlines of these 16 blocks and plates are shown in Fig. The total finite rotations Euler poles describing the motions between these plates are given in Table 1.

Plate identifiers and outlines of blocks that contribute with palaeopoles to the synthesis of APW paths in the present study. This map also shows the global set of isochrons associated with the rotation model. Ages are in Ma. Our kinematic solution for the plates bordering the Indian Ocean is slightly different from the solution proposed by Royer We also use a different set of rotation parameters to describe the early stages of breakup of Gondwana, in particular the relative motion of India and Madagascar prior to the initiation of seafloor spreading in the Mascarene Basin.

In particular, the steepest horizontal gradient of gravity anomalies Blakely was used to identify the boundaries of unstretched pre-rift COBs. All reconstructions and palaeomagnetic analyses were made using PCME, an interactive software tool for plate tectonic modelling designed by Schettino Any accurate reconstruction of the Jurassic and Cretaceous palaeo-continental positions must take into account deformation within Central Africa.

Because Africa is the topmost node in the plate circuit, relatively small motions between the African blocks may have large effects on the positions of other continents and may affect the transfer of palaeopoles into African coordinates. This is an especially worrisome problem for any reconstruction of the Tethyan realm and Mediterranean region, which rely on long plate circuit paths to link the eastern continents of Gondwana Australia, India and East Antarctica to Eurasia.

This seaway resulted from a long period of Early Cretaceous extension, which was pre-dated by Late Jurassic magmatic activity in northeast Brazil and in the Benue Trough. In the Benue Trough, graben formation began in the Aptian ca. Extension in this region probably ceased in the Santonian ca. As we discuss later, the beginning and ending of rifting approximately coincided with two successive cusps on the African APW path see Fig. This implies that the Cretaceous deformation between the Northwest African Block and the Central African Craton may have been driven by plate tectonic events at global scale.

Smoothed apparent polar wander path of Central Africa since the Early Jurassic. During the Early-Mid Cretaceous, strike-slip and extension between four major African blocks resulted into deformation across the northern and central regions of this plate. We now address the problem of the fit of the continents that made up eastern Gondwana prior to the initiation of seafloor spreading approximately Middle Jurassic in the Mozambique-Riisen-Larsen and Somali basins.

We will also discuss the mechanism of separation of India from Madagascar at the Albian-Cenomanian boundary. Since , several studies have described the tectonic history of the breakup of Gondwana. Scotese presented nine reconstructions from anomaly M17 to anomaly A2 , based on the global isochron map of Larson As pointed out by these authors, the plate tectonic reconstructions showed large overlaps or gaps in the Somali, Mozambique and Antarctic basins at M0 and M17 times.

Powell estimated the amount of continental extension that took place between Antarctica and Australia prior to the onset of seafloor spreading Middle Jurassic, Ma, to the Middle Cretaceous, 96 Ma. Royer published a global isochron chart, which was consistent with plate motions and eliminated most of the inconsistencies from the map of Larson Finally, Roeser presented a detailed, though qualitative, description of the early stages of breakup of the central part of Gondwana based on the analysis of magnetic anomalies in the Mozambique-Riisen-Larsen basins, and these authors suggested that strike-slip motions may have played an important role during the early breakup of Gondwana.

Regarding the breakup of East Gondwana, an important concern is the amount and direction of strike-slip motion between Madagascar and India prior to the start of seafloor spreading ca.

Both Roeser and Royer suggest that a component of transcurrent motion took place along the long, linear coastlines of eastern Madagascar and western India. The model of Roeser requires about km of left-lateral strike-slip motion between chrons M10 and M0. This strike-slip movement links rifting between India and Antarctica with seafloor spreading in the Somali Basin. In contrast, the model of Royer implies km of right-lateral strike-slip movement or transtension between and Ma.

This km offset was estimated by back-tracking northeast-directed fracture zone flowlines in the Mascarene Basin e. If we start from a fit of the isochrons at anomaly A34 time and move India back along the trend of these fracture zones until India fits against Madagascar, then the southern tip of India will be offset by about km southwards of the southern margin of Madagascar.

The straight continental margins of eastern Madagascar and western India certainly suggest that strike-slip motion might have occurred prior to rifting. However, to date, there is no geological evidence confirming the existence of strike-slip faults anastomosed arrays of fault zones, flower structures, pull-apart basins, etc. Consequently, we minimize the amount of strike-slip motion between India and Madagascar, and suggest that, at most, km of left-lateral displacement may have taken place during the Early and Middle Jurassic before the start of active seafloor spreading.

This is the minimal amount of displacement required to prevent compression between India and East Antarctica during the early stages of breakup. With respect to the pre-breakup configuration, our model suggests there was little strike-slip motion between India and Madagascar before the initiation of seafloor spreading in the Mascarene Basin.

This in turn implies that the initial stage of separation of India from Madagascar Ma to anomaly 34, The main differences between the model presented in this paper and the mechanism proposed by Royer are summarized in Table 2. These differences are expressed in terms of direction and magnitude of the relative velocity field, tectonic regime and total displacement for each stage. Rotation parameters for the fit of India and Madagascar, as well as the other Gondwana continents, are listed in Table 1 and are in substantial agreement with the recent palaeomagnetic-based reconstruction of Torsvik Model for the early stages of separation between India , Madagascar , Australia and East Antarctica Arrows represent predicted amplitudes and directions of expansion at the spreading centres.

This reconstruction refers to chron 34 Comparison between two models for the opening history of the Mascarene Basin. It is also necessary to briefly discuss the criteria that were used to constrain the fit of the continents on the west side of Africa North and South Atlantic Oceans.

Regarding the South Atlantic, a tight fit of Patagonia and the Falkland plateau around south-central Africa was obtained by using a new definition of the COB. To the north we adopted the fit of Martin between the Brazilian craton and Central Africa, because, when used in conjunction with the fit between Patagonia and southern Africa, it predicts a consistent pattern of deformation in South America.

How best to construct an APW path has been debated by palaeomagnetists for more than two decades. Two very different approaches have been developed that produce smoothed APW curves from large sets of dispersed palaeopoles. Each mean pole is calculated using Fisherian statistics, along with the associated precision parameter K and cone of confidence A Though the general trend of the APW path is correctly determined using this method, rapid changes in the global plate motions and other important details can be obscured by the averaging procedure.

In fact, the minimum duration of each time interval is limited by the local density of available data and by uncertainties in the age of the palaeopoles. The curves produced using this method assume a segmented character that may misrepresent the gradual changes that are implicit in the plate tectonic process.

A second technique constructs APW paths by best-fitting smoothed curves through swaths of palaeomagnetic data APW regression analysis. Finally, Musgrave applied a modified version of the weighted least-squares regression method to a study of Cretaceous and Cenozoic Australian palaeomagnetic data. In our opinion any regression method, independently of the characteristic of being based on simple or sophisticated statistical techniques, must adequately take into account the physical meaning of palaeomagnetic poles.

Consider a compilation of palaeopoles for an arbitrary reference continent A. These data could have been sampled at different sites on the reference plate only or even on different plates. This new representation has several advantages, because it allows us to separate two distinct pieces of information that are included in each palaeopole position relative to S. In this example three palaeopoles having comparable values of declination relative to a reference site S contribute for time 1, but the third of them has a bad colatitude component.

This causes a shift toward the northeast of the mean palaeopole at time 1. Similarly, four palaeopoles having compatible values of the colatitude component contribute to the formation of a mean palaeopole for time 3.

However, a bad declination value of the fourth of them determines a shift towards the southeast of the mean at time 3. As shown in Fig. In the first two cases information associated with individual components can be excluded from the data processing while preserving the remaining piece of information included in the palaeopoles. In fact, in contrast to the classic Fisherian statistics of palaeomagnetic data that have been sampled at a single site, it is now possible that the vector average of unit vectors that come from different sites will be strongly affected by the time uncertainty of individual components, localized intraplate deformation processes and unknown errors in the rotation model.

This is illustrated in Fig. In this instance, the deformation process would have a small influence on the palaeolatitude component but a significant impact on the estimated declination at site S.

This implies that the best APW path does not necessarily coincide with the curve on the sphere that approximates at best in the least-squares sense the sequence of palaeopole positions through time.

In summary, we feel that the extension of Fisherian statistics that is, the vector average of palaeomagnetic directions, or regression methods that are based on palaeopole statistics to groups of palaeopoles that have been sampled on different sites of the same plate, or even on different plates, does not necessarily produce the best results in the construction of APW paths and therefore it could not give the best representation of the tectonic history of a continent.

Sketch illustrating the effect of intraplate deformation on the calculation of mean palaeopoles. In fact, once we have chosen a reference site on this continent any motion on the sphere can be resolved into three elementary rotations:. A pure north-south component, described by an equatorial Euler pole and associated with variations of latitude of the reference site. A pure rotation about the vertical axis at the reference site, which is responsible for changes in declination.

A rotation about the spin axis z axis , which only changes the site longitude. We also note that the order in which these three elementary rotations are performed does not affect the final result. Finally, though the longitudinal component of the plate motion cannot be resolved through standard palaeomagnetic analysis, this problem does not affect plate tectonic reconstructions.

In fact, the palaeomagnetic frame of reference adopted here is built in such a way the z -axis coincides with the spin axis, whereas the choice of x - and y -axes in the equatorial plane is arbitrary. This means that two reference frames, related to one another by a rotation about the z -axis, are equivalent from the point of view of plate tectonics. Decomposition of Euler rotations.

Given an arbitrary rotation about an Euler pole a , a reference site S will be subject to a variation of latitude, a variation of declination, and a change of longitude. In this paper we propose a new technique for the construction of smoothed APW paths that is not based on the statistics of palaeomagnetic directions.

In fact, our approach requires:. Step 2: A preliminary regression analysis of these series and the detection of outliers on each curve. Step 3: An iterative process for the removal of outliers from the corresponding curves. During this stage a component palaeopole p i t could be filtered in the process of construction of the smoothed palaeolatitude curve but it may still participate in the formation of the declination plot, or vice versa. Therefore, two different series of mean palaeopoles were built at the end of this step;.

Step 4: The compilation of an unsmoothed series of mean palaeopoles. In general these two palaeopoles will not coincide, because the filtering process performed during step 3 removed some if not all of the components that were present in the original palaeopole compilation. Then, a smoothed series of synthetic palaeopoles, that is, a smoothed APW path was calculated from the resulting smoothed curves of palaeolatitude and declination.

They do not contain the same number of elements, because of the application of independent filtering procedures. The two series are physically independent, because they describe independent components of the plate motion. The two regression curves should be characterized by oscillations about the general trend that are compatible with the mean time uncertainty and large-scale periodicity of changes as recorded by the geological history.

It can be shown that smoothing spline estimators are natural splines, that is, piecewise polynomials subject to a maximum number of continuity constraints. The segmented nature of these functions gives them more flexibility than polynomials and allows a better adaptation to the local characteristics of the data.

In general, any palaeopole may be used to calculate palaeolatitude and declination at an arbitrary site on the same plate or even on another plate when the relative positions of the two continents are known. Our method is a spline-based regression analysis that fits smoothed curves through plots of declination and palaeolatitude.

This version has been recently updated using the latest stratigraphic chart published by the International Commission on Stratigraphy Gradstein Each palaeopole in the modified version of the GPMDB is given an additional attribute, a tectonic element number, that identifies the continent, terrane or fault-bounded block where the palaeomagnetic data were sampled. Palaeopoles were assigned to tectonic elements according to the sampling site using a spherical point-in-polygon algorithm developed by Schettino Superseded palaeopoles and data already included in other results were excluded from subsequent calculations.

We believe that these filtering parameters eliminated the most unreliable palaeomagnetic results, while leaving a sufficient number of palaeopoles to calculate meaningful estimates of error.

The palaeopoles that passed the selection criteria are listed in Table 3 available in the online version of this article. In the next step, all palaeopoles were rotated in turn to North American, South American Brazilian Craton , Eurasian, Indian, Central African, Australian and Antarctic coordinates, according to the global plate tectonic rotation model Table 1.

At this stage, palaeopoles having the same mean magnetization age were averaged to obtain mean poles for each 1 Myr time interval. We used these mean palaeopoles to construct preliminary palaeolatitude and declination plots for each of the seven continents.

The location of these reference sites are listed in Table 4. A preliminary smoothed curve was fitted through the declination and palaeolatitude plots using non-parametric spline regression analysis. Parameters used in regression analysis and resulting standard regressions errors. A post-filtering process was then employed that removed those outliers that caused the observed deviations. This analysis was performed independently for each continent and for each curve palaeolatitude or declination.

As explained in the previous section, we did not completely remove palaeopoles from the data set, unless they caused deviations in all 14 plots.

In other words, a single component could contribute to palaeolatitude or declination curves for one continent but could be excluded from similar computations for other continents. The reason for this is that even a high-quality palaeopole, when transferred from one plate to another, might be unusable due to systematic errors in declination or colatitude.

In general, the applicability of the palaeopole transfer method via the global plate tectonic rotation model depends on the relative positions of the plates at the time of the reconstruction and the nature of the palaeolatitude and declination errors.

Application of was necessary for consistency with the geocentric axial dipole GAD hypothesis e. Butler along the whole time interval from Ma up to the present. This means that the results presented in this paper are valid within the limits of the GAD approximation. An estimation of the magnitude of this approximation can be given, in terms of Gauss expansion coefficients, by the ratios of the zonal coefficients g 0 2 quadrupole and g 0 3 octupole with respect to the dipolar term g 0 1 , granted that the non-zonal coefficients of the time-averaged palaeomagnetic field can be considered as negligible.

In a more recent study, performed on marine magnetic anomalies, Acton estimated that the quadrupole component was about 6 per cent of the size of the dipole component during the Brunhes normal polarity chron 0. In summary, a geocentric axial dipolar palaeomagnetic field is assumed for the considered time range Ma. Consequently even for the top of this interval the recent past we assume that the time-averaged palaeomagnetic field can be modelled according to the GAD hypothesis.

Therefore, site palaeolatitudes must tend to coincide with the present-day latitudes, and declinations must tend to be zero. In other words, no far-sided Wilson or right-handed effects Wilson must be included in the resulting APW paths because these features are related to higher-order coefficients of the spherical harmonic expansion.

We note that calculations performed without the boundary condition led to the far-sided effect for the recent past. The previous analysis was successful for all continents. Table 4 reports the parameters that were adopted in the post-filtering process and the non-parametric spline regression analysis of palaeolatitude and declination temporal series. Palaeomagnetic data were equally weighted, because a rigorous application of weighting criteria would have to take into account time uncertainty—a problem that cannot be addressed within the scope of this study.

One palaeopole, result , was considered to have reversed polarity and the corresponding coordinates appear to be inverted in Table 3. The resulting statistics of residuals for each continent are shown in Figs Figs can be seen in the online version of this article only. We note that in most cases the distribution of residuals is not Gaussian, though all curves have a low skewness. In fact, these quantities could be chosen automatically by an algorithm that searched for the best match between the effective distribution of the residuals and the theoretical normal distribution having the same mean and standard deviation.

We did not apply automatic selection of smoothing parameters for the reasons explained above. The declination and palaeolatitude of a reference site are kinematic quantities that represent the plate motion.

Hence, the general trend of the corresponding curves must match both physical and geological constraints. Physical constraints are represented by the request that the expected values of velocity and acceleration at any time be compatible with plate dynamics, whereas geological constraints are given by the stratigraphic record on a global scale. Finally, the regression curves must not be characterized by oscillations about the general trend having frequency comparable with the mean time uncertainty of the palaeomagnetic data.

The corresponding uncertainties are estimated using and. Figs show the palaeolatitude and declination curves that result from the regression and post-filtering analysis described in the previous section. Figs are synthetic APW paths that were constructed using the declination and palaeolatitude values from the smoothed regression curves.

These APW paths were calculated using palaeolatitudes and declinations estimated from the smoothed regression plots Figs Tables list present-day coordinates latitude, longitude of the palaeopoles that make up each APW path.

Circles: model-predicted palaeolatitudes A and declinations B. Smoothed apparent polar wander path of North America since the Early Jurassic. Smoothed apparent polar wander path of South America since the early Jurassic. Smoothed apparent polar wander path of Eurasia since the Early Jurassic. Smoothed apparent polar wander path of India since the Early Jurassic. Smoothed apparent polar wander path of Australia since the Early Jurassic.

Smoothed apparent polar wander path of East Antarctica since the Early Jurassic. In this section we discuss the results of the analysis, paying particular attention to the shapes of the regression curves and their implications with regard to plate motion and times of global plate reorganization.

The palaeolatitude of north-central North America remained approximately constant between Ma and the present. However, three additional rotations are observed in the declination plot: counter-clockwise between and Ma, clockwise between and 73 Ma and strongly counter-clockwise between 73 Ma and the present day. Four phases are also evident in the corresponding APW path Fig. The Ma transition is marked by a change of direction and slowing down of polar wandering. The Ma phase boundary is associated with the apex of a narrow hairpin that characterizes the period between and 80 Ma.

Finally, the 73 Ma transition is visible as a cusp in the APW curve and the starting point of the accelerated wandering path that encompasses the Late Cretaceous and the Cenozoic. Conversely, the curve illustrated in Fig. Figs 16 a and b illustrates the changing palaeolatitude and rotation of the Brazilian Craton during the last Myr. Finally, during the last phase 48 Ma-present day , South America was subject to 7. The portion of the APW path between and Ma is represented by a narrow loop having the apex at Ma.

Similarly, the portion between Ma and the present day is represented by a prominent U-shaped bend. These curves can be divided into three distinct phases. The next period from to 72 Ma was characterized by little or no systematic change in palaeolatitude or declination.

The Jurassic and the Cenozoic tracts of this path make a right-angle bend emerging from the Cretaceous standstill. Only two phases of movement and rotation are easily identified, on the basis of events that occurred between and Ma. At Ma Central India ceased its slow clockwise rotation and started to rotate counter-clockwise.

This rotation continued for the whole Cretaceous and Cenozoic. Regarding the palaeolatitude of the reference site, we observe that a transition occurred some time later, at Ma, when India started its rapid northward motion. At about 40 Ma, both the rate of northward motion and the rate of rotation slowed. Again, only two segments tracks are easily identified: Ma and Ma to the present day. However, APW rates show that a relevant change occurred at about 40 Ma.

Three phases of movement and rotation are clearly distinguishable. However, the palaeolatitude of this reference point did not change significantly. This APW path is especially interesting because the path appears to double-back on itself at the Ma cusp.

The APW path clearly shows all three motion phases. Finally, during the third phase of movement 70 Ma to the present , Australia appears to have accelerated slightly northwards, and reversed its direction of rotation counter-clockwise to clockwise.

The last continent we will consider is Antarctica Figs 21a and b. The next phase of motion, from 73 to 34 Ma, was characterized by slow counter-clockwise rotation and increasing palaeolatitudes of the reference point. Note that at the end of the Cretaceous the palaeopole position practically coincides with the present day geographical north. Table 12 summarizes the times at which plate motions changed. In summary, we recognize three major phases of global plate motion since the Early Jurassic.

In order to define the single, best, palaeomagnetic reference frame, we rotated all of the mean palaeopoles that make up the synthetic APW paths Figs into African coordinates Fig.

This operation was also performed to test the self-consistency of the model and robustness of the procedure explained above. Finally, we calculated a representative best-fit APW path to be used for the assignment of finite reconstruction poles to Central Africa, by vector averaging the seven synthetic palaeopoles associated with each continent. Read our guide on Where to take your learning next for more information. Not ready for formal University study?

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Course content Course content. Plate Tectonics Start this free course now. Free course Plate Tectonics. The study of the Earth's magnetic field as recorded in the rock record was an important key in reconstructing the history of plate motions. We have already seen how the recording of magnetic reversals led to the confirmation of the seafloor spreading hypothesis.

The concept of apparent polar wander paths was helpful in determining the speed, direction, and rotation of continents. To illustrate the idea of polar wander, imagine you have a composite volcano on a continent like the one in the sketch below.

I assure you that the sketch will be better understood if you also watch the screencast in which I talk while I draw it. The magnetic field lines are going like that. It looks like this. A composite volcano spews out lava and it gradually builds up the mountainside with its lava flows like this.

We have a magnetometer and so we can try to figure out which way all these lava flows thought north was when they formed and cooled. The green one was formed during the field like it is today so its north is like that. There are two possible explanations for how this could have occurred. Explanation 1 is that the poles moved around and the continent stayed in the same place. When the most recent lava formed, this green stuff, the pole was right up here, where it is today. But back when this volcano was making the yellow lava, the pole was in a slightly different place.

It was more like over here. The oldest lava flow is recording a pole that was more like in that direction.