Calculating palaeomagnetic poles for oceanic plates

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The information available for determining palaeopoles for oceanic plates includes data of four types: (1) palaeomagnetic measurements of inclinations but not declinations from core samples; (2) palaeopoles determined from magnetic anomalies over seamounts; (3) phase shifts of linear magnetic anomalies; and (4) palaeoequators determined from geological analysis of sediment cores. A method is presented which combines these different kinds of data and their respective confidence limits to yield a best fit pole, a confidence ellipse, estimates of the data importances and goodness of fit parameters. Using this method we calculate the Campanian pole position for the Pacific plate which is shown by a chi-squared test to be a reasonable fit to the data. We conclude that the method should be a useful tool for calculating pole paths for oceanic plates such as the Pacific and Indian plates.     

Deglaciation effects on the rotation of the Earth

Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)10²³ poise (P) and 10⁴ (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 10²³ P with upper and lower limits of 1.1 × 10²³ and 2.8 × 10²³ P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 10²³ P.     

Comments on'The palaeomagnetism of the Central Zone of the Lewisian foreland, north-west Scotland'by J. D. A. Piper

Summary. Piper suggested that the Lewisian has rotated 30° anticlockwise since magnetization, whereas the opposite appears more likely. The main magnetization in the Lewisian recognized by Piper and Beckmann was imposed upon cooling after the Laxfordian metamorphism at about 1750 (± 50) Ma. The palaeomagnetic pole corresponding to this magnetization is at 37.6° N, 273.2° E ( dp = 3.7°, dm = 5.2°).
In Greenland, palaeomagnetic poles similar to each other, with a mean pole at 21.6° N, 280.1° E ( K = 52, A ₉₅= 9.4°), have been determined from five widely separated regions in central West Greenland and from Angmags-salik in East Greenland. The magnetization observed in all these regions was established upon cooling after the Nagssugtoqidian metamorphism, again at about 1750 (± 50) Ma.
The Laxfordian and Nagssugtoqidian metamorphisms were equivalent. It is therefore assumed that the two palaeomagnetic poles quoted above were originally identical. Their present difference can be explained by clockwise rotation of north-west Scotland about a local rotation pole since the Lewisian became magnetized, in addition to opening of the Atlantic assuming conventional reconstructions:
(1) assuming the reconstruction of Bullard, Everett & Smith, the local rotation proposed is 39.5° (± 18.1°) about a pole of rotation at 60.3° N, 354.5° E, or
(2) assuming the reconstruction of Le Pichon, Sibuet & Francheteau, the local rotation is 28.0° (±17.7°) about a pole of rotation at 54.1° N, 354.6° E.
These proposals of local clockwise rotation of north-west Scotland accord with that of Storetvedt based on palaeomagnetic results from Devonian rocks on the north-west side of the Great Glen Fault.     

Palaeomagnetism of the Fongen-Hyllingen gabbro complex, southern Scandinavian Caledonides; plate rotation or polar shift?

Summary. Palaeomagnetic results are presented from the c . 160 km² Caledonian synorogenic layered Fongen-Hyllingen gabbro complex (of probable late Silurian age) located about 75 km SE of Trondheim, Norway, in the allochthonous Seve-Kdli Nappe Complex. A total of 80 oriented samples from eight sites in the northern part of the gabbro were investigated. After detailed af demagnetization two stable high coercivity components emerge: one with a well defined NW direction with D =325°, I =−21° (α₉₅=8°, N =8), and another, less well defined, probably younger, SW direction with D = 237°, I = 6° (α₉₅= 9°, N = 8). Correction for dip of these two directions gives D = 329°, I =−7° (α₉₅= 10°) and D = 238°, I =−11° (α₉₅= 12°), respectively. The corresponding pole positions are P ₁ : 19° N, 225° E and P ₂: 19° S, 308° E, respectively. The reversed pole -P ₂ of the SW direction lies close to other NW European palaeomagnetic poles of Caledonian, Upper Silurian-Lower Devonian age. However, the dominant pole PI is far away from these, and could be due to a late Caledonian geomagnetic excursion of considerable duration; or it could record a c . 90° rotation around a vertical axis of a crustal block within the Scandinavian Caledonides. Block rotation could have been related to nappe translation, although geological observations do not at present appear to support the occurrence of such an event.     

Pleistocene deglaciation and the Earth's rotation: implications for mantle viscosity

Summary. Recent results from the analysis of postglacial rebound data suggest that the viscosity of the Earth's mantle increases through the transition region. Models which fit both relative sea-level and free air gravity data have viscosities which increase from a value near 10²² poise in the upper mantle beneath the lithosphere to a value of about 10²³ poise in the lower mantle. In this paper we analyse the effect of deglaciation upon the Earth's rotation and thereby show that the observed secular trend (polar wander) evident in the ILS—IPMS pole path, and measurements of the non-tidal acceleration of the length of day, are both consistent with the viscosity profile deduced from postglacial rebound. The two analyses are therefore mutually reinforcing.     

Rotation of the geomagnetic field about an optimum pole

Since 1693, when Halley proposed that secular change was the result of the westward drift of the main field, his simple model has undergone many refinements. These include different drift rates for dipole and non-dipole parts; separation into drifting and standing parts; latitudinal dependence of drift rate; northward drift of the dipole; and non-longitudinal rotations of the individual harmonics of the geomagnetic field. Here we re-examine the model of Malin and Saunders, in which the main field is rotated about an optimum pole which does not necessarily coincide with the geographical pole. The optimum pole and rotation angle are those that bring the main field for epoch T ₁ closest to that for T ₂ , as indicated by the coefficients of correlation between the spherical harmonic coefficients for the two epochs, after rotation. Malin and Saunders examined the pole positions and rates of rotation using data from 1910 to 1965, and noticed a number of trends. We show that these trends are confirmed by recent IGRF models, spanning the interval 1900–2000 and to degree and order 10. We also show that the effect of the level of truncation is small.     

Secular trend of the Earth's rotation pole: consideration of motion of the latitude observatories

Secular polar motion has been recorded in ILS data over the past 75 years, an amount greater by a factor of ten than the 'true polar wandering' deduced from paleomagnetic data. In this work, the possibility that the secular trend is an observational artifact of the continental drift of the ILS stations is directly examined by consideration of several absolute plate velocity models earlier proposed by Minster et al. (1974), Kaula (1975), and Solomon, Sleep & Richardson (1975). The assumptions underlying those models are discussed; in general, the absolute velocity models are more likely to be valid when geologically short timescales are considered.
The corrections to the ILS data due to the stations' motion fail by an order of magnitude to explain the ILS trend; even by taking into account possible plate hyperactivity and non-rigidity, the corrections could explain no more than 30 per cent of the trend. The corrections are small because the absolute plate velocities of North America and Eurasia are small and primarily east—west. Consequently, the rotation pole is undergoing significant motion of its own relative to the surface of the Earth.
The Kimura z term found by the ILS observations provides an independent means of estimating the relative motion between Eurasia and North America. It also contains other geophysical information; the 7.5-yr periodicity discovered by Naito & Ishii (1974) may be widespread.
Lastly, tectonically induced changes in the zenith direction, such as at Mizusawa, are probably too small to be detected, contrary to earlier proposals.     

基于空间信息的烤烟种植适宜性 评价与轮作规划

基于遥感计算的气温和土壤水分及DEM计算的太阳辐射等地表参数代替站点观测数据,采用100m×100m栅格和适宜性评价指数对泸西县的烤烟种植适宜性进行评价,分析其空间分布规律。在此基础上,进行了烤烟的烟田轮作规划与核查监督。研究表明,泸西县的烤烟种植最适宜区的耕地利用率偏低,仅为28.1%,尚有2165ha的最适宜耕地有待开发利用。烤烟轮作率虽然逐年增长,最高也仅为63.7%,离95%的目标轮作率仍存在较大差距。适宜性评价时,利用遥感和DEM计算的地表参数代替观测站点的插值数据,能获得可靠的数据支持,弥补因观测站点缺失而导致的数据失真。基于空间信息的轮作规划与核查监督,可有效改善烤烟轮作率,提高烤烟的质量和产量。     

Simplified algorithms for calculating double-couple rotation

We derive new, simplified formulae for evaluating the 3-D angle of earthquake double-couple (DC) rotation. The complexity of the derived equations depends on both accuracy requirements for angle evaluation and the completeness of desired solutions. The solutions are simpler than my previously proposed algorithm based on the quaternion representation designed in 1991. We discuss advantages and disadvantages of both approaches. These new expressions can be written in a few lines of computer code and used to compare both DC solutions obtained by different methods and variations of earthquake focal mechanisms in space and time.     

中国中西部发展中城市的增长极作用

为了分析增长极在中部崛起和西部开发中可能发挥的作用,对我国中西部地域相连、经济水平接近的山西、河南、安徽、湖北、湖南、江西、广西、四川、重庆、陕西10个省(直辖市、自治区)的942个市县2000~2007年非农业GDP和就业增长的空间溢出效应进行了检验。模型估计表明,中西部地区各市县非农业经济增长的主要决定因素是自身的投入,同时,中心城市也存在明显的扩散和回流效应。地级市的非农业GDP增长对县级市有扩散效应,意味着城市间经济有一体化趋势,但是地级市的就业增长对县级市有抑制作用;地级城市对相对更不发达的县镇的GDP和就业增长同时具有带动作用;相邻的县级市相互间有较强的促进作用,但是对邻近县镇却有抑制倾向。     

Palaeomagnetism of the Macaronesian Insular Region: The Cape Verde Islands

Palaeomagnetic pole positions have been determined for a collection of igneous rocks, comprising nearly five hundred samples, from the Cape Verde Islands of Santa Antao, Sao Vicente, Sao Nicolao and Sao Tiago. Limited data from the islands of Sal, Maio and Fogo are also presented. Stratigraphic control suggusts that the lavas are overwhelmingly Miocene in age on Sao Tiago and Sao Nicolao. Similarity in the palaeomagnetic pole positions indicates that Miocene lavas are also dominant on Santa Antao and Sao Vicente.
Substantial areas within two of the islands are of reversed polarity only, suggesting either a rapid extrusion rate, or the existence of a long reversed polarity epoch during the Miocene period. The palaeomagnetic pole positions for each island are close to the present geographic pole, excluding the possibility of Post-Miocene differential crustal spreading (or rotation about a vertical axis) in this part of the Atlantic. The palaeomagnetic pole position for the entire survey is consistent with the Miocene geographic pole being removed from, but close to, the present geographic pole; and is in harmony with the European polar wandering curve.     

Modelling the pole tide and its effect on the Earth's rotation

Summary. The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, we construct both analytical and numerical models for the pole tide. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of the non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.     

Contribution of domain rotation to the magnetic susceptibility of spherical two-domain particles of magnetite

Summary. Starting with a simplified picture of the presumed magnetization configuration in a two-domain sphere of magnetite, the initial susceptibility due to rotation of the magnetization in the domains has been calculated. In particles between 100 and 300 nm in diameter the calculated susceptibility for randomly oriented particles drops rapidly from about 6 to a little over 3, which is the value to be expected for large multidomain particles. The results agree well with the available experimental results and imply that in magnetite particles in this size range the low field susceptibility is dominated by the domain rotation and that wall motion is effectively inhibited.     

Studies of partial rotational remanent magnetization and rotational remanent magnetization at slow speeds of rotation

Summary. Rotational remanent magnetizations and partial rotational remanent magnetizations have been induced in four specimens using alternating magnetic fields of 55 mT maximum peak strength and 128 Hz, and speeds of rotation between 0.0016 and 0.4 rev s⁻¹. Each partial rotational remanent magnetization ( PRRM ), was produced by rotating the specimen only at the maximum setting of the alternating field. The variation of PRRM with (a) speed of rotation, ω, and (b) total angle of rotation, θ, was investigated. In (a), PRRM fell slowly but steadily as ω increased; for (b) it rose sharply as θ increased up to 60° and reached a maximum for θ between 90° and 120°. Alternating field demagnetizations of PRRMs were performed with the specimen (a) at rest, and (b) rotating about an axis perpendicular to the field. Rotation significantly enhanced the demagnetization process. Variation of the time T , taken to remove the inducing alternating field produced no detectable effect in the case of PRRM , but affected the value of ω at which a given feature of the RRM —ω curve appeared, and the product θ_F(=ω T ) appears to be more important than either ω or T separately. Current theories on RRM can be used to explain some of the new experimental data on PRRM .     

Geomagnetic variations recorded in Older (≫ 23 000 B.P.) and Younger Yoldia Clay (∼ 14 000 B.P.) at Nørre Lyngby, Denmark

Summary. Detailed palaeomagnetic results from a rapidly deposited 12.5-m Younger Yoldia Clay sequence of age around 14 000 B.P. at the coast cliff at Nørre Lyngby (northern Jutland, Denmark) and a 2-m Older Yoldia Clay sequence of age somewhere between 23 000 and 40 000 B.P. are presented and discussed. The Younger Yoldia Clay spans some 1000–1500 yr and shows swings in inclination and declination of about that period, and also more rapid oscillations which are particularly marked in inclination, showing that rapid secular variations as have occurred during historic times were indeed also present back in time. There exist easterly declinations of 80° to 90° in the upper half of the Younger Yoldia Clay which cause the virtual geomagnetic pole to migrate clockwise to around 50° away from the rotation pole. This we name the 'Nørre Lyngby declination excursion'.
In the Older Yoldia Clay, as well as secular variations in both declination and inclination, significant low inclination values are found, confirming the existence of the recently named 'Rubjerg low inclination excursion', with the virtual geomagnetic pole moving first in a clockwise then in an anticlockwise sense at 40° to 60° away from the rotation pole.
It is therefore inferred that models for the Earth's geomagnetic field should involve at least local rapid eastward as well as westward 'drift' of the non-dipole field components at various times in the past.     

The coupled rotation of the inner core

The rotation of the inner core (IC) is influenced by the rest of the Earth through a number of coupling mechanisms. Among four possible coupling mechanisms, gravitational, pressure, viscous and electromagnetic, the first two torques are dominant. Numerous existing IC gravitational torque estimates have been shown to agree very well with one another Xu & Szeto 1996 ). It is shown in this paper that different estimates of the IC pressure torque are also in good agreement.
The coupled rotation of the IC has been investigated in the frequency domain by several research groups (Mathews et al. 1991a,b; De Vries & Wahr 1991 ; Dehant et al. 1993; Jiang 1993 ). Not all of these efforts obtained two IC-related rotational modes, the inner-core wobble (ICW) and the free-inner-core nutation (FICN). We investigate this problem in the time domain and confirm the existence of the two modes. The periods of ICW and FICN are in good agreement with those obtained by other researchers. In studying the effects of coupling torques on the IC rotational modes we have found that depending on whether the IC net torque is 'restoring' or otherwise, an increased torque magnitude will respectively shorten or lengthen the ICW period. We have also found that the sense of FICN is determined by the orientation of the net coupling torque on the IC.     

The Passive Influence of the Oceans upon the Rotation of the Earth

A general theory is developed which allows the exact numerical computation of the static equilibrium response of a non-rotating spherically symmetric Earth model covered by thin oceans with geometrically irregular coastlines to the action of an imposed static tidal or centrifugal potential. The theory is self-consistent, and takes into account the gravitational self-attraction of the oceans and the elastic-gravitational response of the Earth model to both the applied potential and the equilibrium oceanic tidal load on the surface. The results are used to determine the influence of an equilibrium pole tide on the free period and the associated rotational eigenfunction of the Chandler wobble. If the pole is globally well represented by this equilibrium approximation, its effect is to increase the Chandler wobble period by 27·6 days. It is shown that a fully self-consistent theory of the rotation of an Earth model with oceans predicts that changes in spin and wobble will be coupled, and that the Chandler wobble should, as a result, be accompanied by an associated periodic change in the length of day. The consequences of spin-wobble coupling are explored quantitatively, and found to be slight.     

New seismological constraints on differential rotation of the inner core from Novaya Zemlya events recorded at DRV, Antarctica

Novaya Zemlya nuclear test records at the seismic station DRV, Antarctica, are analysed in order to obtain further constraints on a possible differential rotation of the inner core with respect to the mantle. These data allow the sampling of the inner core along a nearly polar path in very stable conditions over more than two decades, from 1966 to 1990. The PKP (BC)– PKP (DF) traveltime residuals, which reflect the inner-core anisotropy and/or heterogeneities sampled along the path, exhibit a great stability through time. A computation of the residuals that are expected for various differential rotation rates and the same rotation axis as the mantle has been performed using the worldwide residual catalogue of Engdahl et al . (1997) for summary rays that include the time as an additional parameter in data stacking. Comparison of data and predictions shows that an eastward differential rotation with a rate as large as 3°  yr⁻¹, as suggested by some authors, is not possible, but an eastward rotation at 1°  yr⁻¹ or lower cannot be rejected.     

Palaeomagnetism of dykes and tuffs from the Mesudiye region and rotation of Turkey

Summary. The pole positions obtained from Upper Cretaceous and Eocene tuffs and dykes of the Mesudiye region, which is located between the north of the North Anatolian Fault Zone and eastern Black Sea coast, are at 75.3° N, 275.4° E and 41.7° N, 138.6° E respectively. These results, taken together with the results of previous studies of Turkish rocks, suggest that rotational movements of Turkey have been 45–50° counterclockwise to Europe since the Upper Cretaceous.     

Palaeomagnetism and magnetic fabric in the Freetown Complex, Sierra Leone

About six separately orientated cores were collected at each of 14 sites distributed throughout the arcuate, west-dipping, 6  km thick, Freetown layered igneous complex. Alternating field and thermal demagnetization both isolate a stable component of remanent magnetism which corresponds to a palaeomagnetic south pole from 13 sites (nine reverse, four normal polarity) at 82.9°S, +32.7°E ( α ₉₅ = 5.6°). This is indistinguishable from that reported in 1971 based on alternating field demagnetization of cores from 10 orientated hand samples.
  The difference between the Freetown pole (age: 193 ± 3  Ma) and other mid-Jurassic poles from West Africa could be due to its greater age. The difference between the whole West African Jurassic pole group and the Karoo pole from southern Africa, however, suggests moderate (∼10°) differential rotation of West Africa relative to the Kaapvaal craton.
  A prevalent magnetic foliation fabric coincides generally with the petrological layering, as might be expected, but a ubiquitous magnetic lineation is predominantly down-dip. This is compatible with a down-dip pyroxene lineation reported to be present in some field outcrops, and interpreted in terms of late-stage deformation during the slow crystallization and cooling of the large igneous body. However, a fold test shows that the igneous layering had already achieved its present attitude before the Complex cooled to ∼570 °C (the maximum blocking temperature of the characteristic remanence).