Geomagnetic secular variation and secular acceleration in the Red Sea area

Summary. Estimates of the secular variation in the Red Sea over the period 1959 to 1972 have been obtained from an analysis of marine magnetic data. A total of 318 crossings of ships' tracks were used to determine the mean secular variation for the intervals 1959–72, 1959–65 and 1965–72. The mean secular variation 1959–72 shows a marked northward increase from approximately -10 nT/yr at 13°N to +27 nT/yr at 24°N. North of this, the data suggest a small decrease to + 25 nT/yr at 27° N. These values are consistent with the secular variation recorded at the nearby geomagnetic observatory at Helwan, Egypt, but less than those predicted by the 1965 IGRF for the same period.
Comparison of the mean secular variations for 1959–65 and 1965–72 yields a rough estimate of the secular acceleration of - 1.5 nT yr⁻². Analysis of the cross-over information, corrected for the latitude dependence of the secular variation, shows a regular decrease in the secular change over the period 1959–72 at all latitudes of about -1 nTyr⁻². This secular acceleration makes a substantial contribution to the overall secular change in the Red Sea and as such must be included in the correction of magnetic data covering more than a few years.     

Estimability analysis of geodetic, astrometric and geodynamical quantities in very long baseline interferometry

Summary. Within the framework of Newtonian kinematics VLBI observations are analysed with respect to estimability of geodetic and astrometric quantities. An Earth model of either rigid or deformable type is designed; instrumental clock offsets and clock drifts are included. Observational patterns are studied in all detail reviewed in seven tables. Appendix A is an introduction to the set-up of the observational model for a deformable Earth both in terms of coordinate-free and coordinate-related geometry. Appendix B is a study of the invariance characteristics of VLBI observations. Interrelations of three fundamental quantities, length unit, time unit and velocity of light are discussed. An overall result of an Earth model of deformable type is the need of simultaneous observations to more than one source; VLBI time delay observations cannot distinguish between secular changes of network size (expansion or shrinking) and a common secular drift (deceleration or acceleration) of clocks used.     

The secular acceleration of the Earth's spin

Summary. The power spectrum of the Earth's spin has important components with periods ranging from a few days to at least a few thousand years, and probably to the age of the Earth. The secular acceleration, as the term is used here, refers to the components with periods longer than three centuries. In the year 600, the secular acceleration was —19.9 ± 0.8 parts in 10⁹ per century, while the value at the present time is less than half this size. The spin acceleration has important contributions from tidal friction and from an effect that is proportional to the square of the magnetic dipole moment. When these contributions are subtracted from the observed acceleration, we are left with a contribution that amounts to +41 parts in 10⁹ per century. This amount probably results from an unknown combination of changes in the size of the core, in the amount of glaciation, and in the size of the gravitational constant.     

Monopoly

Summary. A model for the geomagnetic secular variation field is given, consisting of a series of magnetic monopoles at the surface of the Earth's core. These are distributed according to the density of the data to allow more detailed representation in areas where the density of observations is high, without introducing spurious detail where data are sparse. A monopole model is calculated from observatory secular change data for the epoch 1957.5–1962.5 and its usefulness assessed.     

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.     

Secular variation of the poloidal magnetic field at the core–mantle boundary

A region of enhanced conductivity at the base of the mantle is modelled by an infinitesimally thin sheet of uniform effective conductance adjacent to the core–mantle boundary. Currents induced in this sheet by the temporally varying magnetic field produced by the geodynamo give rise to a discontinuity in the horizontal components of the poloidal magnetic field on crossing the sheet, while the radial component is continuous across the sheet. Treating the rest of the mantle as an insulator, the horizontal components of the poloidal magnetic field and their secular variation at the top of the core are determined from geomagnetic field, secular variation and secular acceleration models. It is seen that for an assumed effective conductance of the sheet of 10⁸  S, which may be not unrealistic, the changes produced in the horizontal components of the poloidal field at the top of the core are usually ≤10 per cent, but corrections to the secular variation in these components at the top of the core are typically 40 per cent, which is greater than the differences that exist between different secular variation models for the same epoch. Given the assumption that all the conductivity of the mantle is concentrated into a thin shell, the present method is not restricted to a weakly conducting mantle. Results obtained are compared with perturbation solutions.     

The geomagnetic field over the past 5 million years

The modern geomagnetic field is usually expressed as a spherical harmonic expansion. Although the palaeomagnetic record is very incomplete in both space and time, sufficient data are available from a span of ages to generate time-averaged spherical harmonic field models with many degrees of freedom. Here three data sets are considered: directional measurements from lavas, inclination measurements from ocean sediments, and intensity measurements from lavas. Individual data are analysed, as well as site-averages, using the same methods that have been developed for the modern field, to give models for the past 5 Myr. The normal-polarity field model has an axial-dipole intensity similar to that of the modern-day field, whilst the equatorial-dipole component is very much smaller. The field is not axisymmetric, but shows flux concentrations at the core's surface under Canada and Siberia similar to those observed in the field over historical timescales. Tests on synthetic data show that it is unlikely that these similarities result from the overprinting of the palaeomagnetic field due to inadequate cleaning of the samples. The reverse-polarity field model does not show such obvious features, but this may be due to the sparsity of the data.
The patterns observed in the normal-polarity field, with persistent features in the northern hemisphere and a smooth southern hemisphere, could be explained if the present pattern of secular variation is typical of the past several million years. This would reveal itself as large variations over time in the direction of the magnetic vector in regions of high secular variation, with relatively little change over quieter regions. However, we have been unable to find any evidence for a geographical pattern of secular variation in the data.     

Geomagnetic evidence for fluid upwelling at the core-mantle boundary

Summary. Previous studies, both geomagnetic and seismic, have been unable to show conclusively whether or not there is fluid upwelling at the core-mantle boundary. Here a new method is developed, in which an attempt is made to invert geomagnetic secular variation data measured at the Earth's surface for a frozen-flux purely toroidal core-mantle boundary (CMB) velocity field, under the assumption that the mantle is electrically insulating and flux is frozen in at the CMB. These data have previously been inverted for the core-mantle boundary radial secular variation, from which the appropriate fit between model and data is known. Two different main field models were used to assess the effect of uncertainty in its radial component at the CMB. The conclusions were the same in both cases: frozen-flux purely toroidal motions provide a poor fit. A statistical test allows very firm rejection of the hypothesis that the residuals are not significantly larger, whereas there is no statistical difference between the residuals of inversions for radial secular variation and frozen-flux velocity fields at the CMB if upwelling and down-welling is included. The inherent non-uniqueness in the velocity field obtained is not of concern, since only their statistical properties are utilized and no physical significance is attached to the flows obtained.     

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.     

On Rates and Acceleration Trends of Global Glacier Mass Changes

Worldwide glacier mass changes are considered to represent natural key variables within global climate-related monitoring programmes, especially with respect to strategies concerning early detection of enhanced greenhouse effects on climate. This is due to the fact that glacier mass changes provide important quantitative information on rates of change, acceleration tendencies and pre-industrial variability relating to energy exchange at the earth/athmosphere interface. During the coming decades, excess radiation income and sensible heat (a few watts per square metre) as calculated with numerical climate models are both estimated to increase by a factor of about two to four as compared to the mean of the 20th century. The rate of average annual mass loss (a few decimetres per year) measured today on mountain glaciers in various parts of the world now appears to accelerate accordingly, even though detailed interpretation of the complex processes involved remains difficult. Within the framework of secular glacier retreat and Holocene glacier fluctuations, similar rates of change and acceleration must have taken place before, i.e. during times of weak anthropogenic forcing. However, the anthropogenic influences on the atmosphere could now and for the first time represent a major contributing factor to the observed glacier shrinkage at a global scale. Problems with such assessments mainly concern aspects of statistical averaging, regional climate variability, strong differences in glacier sensitivity and relations between mass balance and cumulative glacier length change over decadal to secular time scales. Considerable progress has recently been achieved in these fields of research.     

A definitive model of the geomagnetic field and its secular variation for 1965 — I. Derivation of model and comparison with the IGRF

Summary. Using a very large body of post-1955 data, a spherical harmonic model of the geomagnetic field and its secular variation is derived for 1965.0. This model is compared with the original International Geomagnetic Reference Field (IGRF) and with individual models used, or proposed for use, in producing the IGRF. Positions of the dip-poles, the geomagnetic poles and the eccentric dipole are derived from the model, together with their rates of change, and comparisons are made with other estimates of these positions.     

Daily Variation and Secular Variation of the Geomagnetic Field from Shipboard Observations in the Gulf of Aden

Summary The problems of reducing geomagnetic observations from ships at sea in areas influenced by the effect of the equatorial electrojet are discussed. In particular, observations within the Gulf of Aden have been corrected for daily variation and secular variation for the purposes of constructing a contoured magnetic anomaly chart.
An empirical formula is given with which the range of daily variation at different latitudes within the Gulf was estimated for the purpose of correcting the data for daily variation. The observed secular variation, which was used to correct the data, is—11 γ/yr. which differs from the secular variation of +19 γ/yr. in the Gulf of Aden given by the recently adopted International Geomagnetic Reference Field (Zmuda 1969).     

Long-term features of drifting and standing non-dipole fields as determined from Holocene palaeomagnetic secular variations

Geomagnetic field motions of Holocene secular variations are investigated using a separation method. The palaeomagnetic secular variations from Britain, North America and Australia have been subjected to maximum-entropy method analyses. Based on the results of spectral analyses, the secular variations are separated by band-pass filters into low-frequency components, generally including the period band 1800-3600 yr, and high-frequency components, generally including the period band 1000-1200 yr. There is an interval, from 4200 to 1700 yr BP, which shows clockwise rotational motions in the low-frequency components of all three sites. Westward drifting of geomagnetic fields may be globally dominant. Swinging or elliptical looping motions constrained to a certain direction were observed in the low-frequency components of the British data. The time duration for the persistence of the swinging motion constrained to a certain direction was 3500 years or so, which could be the lifetime of an oscillating stationary field. The duration of the transitional motion was 1000-1300 years, which may indicate the recurrence time of a stationary field.     

Long-period geomagnetic variations and mantle conductivity: an inversion using Bailey's method

Summary. We have implemented an algorithm which is based on Bailey's solution of the inverse problem of electromagnetic induction in the Earth. The study was motivated by recent determinations of very long period data and also benefited from recent redeterminations of high frequency data. The algorithm has been successfully tested to provide reliable estimates of conductivity down to a depth of 2000 km, using synthetic data in the period range from 4 days to 11 years. Smooth data sets, which are required for the inversion, were constructed from various sources. At a given depth, the range of inverted models is less than one order of magnitude. Due to the lack of high frequency data, the conductivity of the upper 600 km of the mantle, which is found to be of the order of 10⁻¹Ω⁻¹ m⁻¹, may be overestimated. The algorithm performs well in the middle mantle, where conductivity rises steadily from 1 to 50 Ω⁻¹ m⁻¹. The lack of very low frequency data and limitations of the algorithm prevent one from obtaining meaningful estimates in the lower mantle. However, the study of the propagation of the late 1960s secular variation acceleration provides an estimate of the mean conductivity of the whole mantle. Thus, a complete mantle profile can be constructed. It is found that deep mantle conductivity probability does not exceed a few hundred Ω⁻¹ m⁻¹.     

Centennial to millennial geomagnetic secular variation

A time-varying spherical harmonic model of the palaeomagnetic field for 0–7 ka is used to investigate large-scale global geomagnetic secular variation on centennial to millennial scales. We study dipole moment evolution over the past 7 kyr, and estimate its rate of change using the Gauss coefficients of degree 1 (dipole coefficients) from the CALS7K.2 field model and by two alternative methods that confirm the robustness of the predicted variations. All methods show substantial dipole moment variation on timescales ranging from centennial to millennial. The dipole moment from CALS7K.2 has the best resolution and is able to resolve the general decrease in dipole moment seen in historical observations since about 1830. The currently observed rate of dipole decay is underestimated by CALS7K.2, but is still not extraordinarily strong in comparison to the rates of change shown by the model over the whole 7 kyr interval. Truly continuous phases of dipole decrease or increase are decadal to centennial in length rather than longer-term features. The general large-scale secular variation shows substantial changes in power in higher spherical harmonic degrees on similar timescales to the dipole. Comparisons are made between statistical variations calculated directly from CALS7K.2 and longer-term palaeosecular variation models: CALS7K.2 has lower overall variance in the dipole and quadrupole terms, but exhibits an imbalance between dispersion in   g ¹₂  and   h ¹₂  , suggestive of long-term non-zonal structure in the secular variations.     

典型红壤丘陵区土地利用空间优化配置

选择具有红壤丘陵区典型特征的江西省泰和县千烟洲为研究区域,在分析当前土地利用结构并进行土地适宜性评价的基础上,依据2000年千烟洲试验站研究数据及农户调查资料,将GIS技术与线性规划模型有效地耦合起来,探讨实现典型红壤丘陵区各种具有特定数量、质量的农用土地资源在空间上最优配置的方法与技术。结果表明,优化方案从现状中牧业短缺的粮、果、林结构转化为较为完善的粮、果、牧、林结构,耕地资源利用结构也由重水轻旱、粮作为主、经作为辅的传统生产模式,转变为粮-经-饲并举的三元优化配置结构;同时,由果业和畜牧业共同支撑的优化方案的经济效益明显优于现状,在经济上更具稳定性和可持续性。     

Geomagnetic field analysis - I. Stochastic inversion

Summary. Most of the Earth's magnetic field and its secular change originate in the core. Provided the mantle can be treated as an electrical insulator, stochastic inversion enables surface observations to be analysed for the core field. A priori information about the variation of the field at the core boundary leads to very stringent conditions at the Earth's surface. The field models are identical with those derived from the method of harmonic splines (Shure, Parker & Backus) provided the a priori information is specified appropriately.
The method is applied to secular variation data from 106 magnetic observatories. Model predictions for fields at the Earth's surface have error estimates associated with them that appear realistic. For plausible choices of a priori information the error of the field at the core is unbounded, but integrals over patches of the core surface can have finite errors. The hypothesis that magnetic fields are frozen to the core fluid implies that certain integrals of the secular variation vanish. This idea is tested by computing the integrals and their standard and maximum errors. Most of the integrals are within one standard deviation of zero, but those over the large patches to the north and south of the magnetic equator are many times their standard error, because of the dominating influence of the decaying dipole. All integrals are well within their maximum error, indicating that it will be possible to construct core fields, consistent with frozen flux, that satisfy the observations.     

An improved geomagnetic data selection algorithm for global geomagnetic field modelling

A spherical harmonic degrees 60, global internal field model is described (called BGS/G/L/0706). This model includes a degree 15 core and piecewise-linear secular variation model and is derived from quiet-time Ørsted and Champ satellite data sampled between 2001.0 and 2005.0. For the satellite data selection, a wide range of geomagnetic index and other data selection filters have been used to best isolate suitably quiet magnetospheric and ionospheric conditions. Only a relatively simple, degree one spherical harmonic, external field model is then required. It is found that a new 'Vector Magnetic Disturbance' index ( VMD ), the existing longitude sector A indices, the auroral zone index IE , and the polar cap index PC are better than Kp and Dst at rejecting rapidly varying external field signals at low, middle, auroral and polar latitudes. The model quality is further enhanced by filling spatial and temporal gaps in the quiet data selection with a second selection containing slightly more disturbed data. It is shown that VMD provides a better parametrization than Dst of the large-scale, rapidly changing, external field. The lithospheric field model between degrees 16 and 50 is robust and displays good coherence with other recently published models for this epoch. BGS/G/L/0706 also shows crustal anomalies consistent with other studies, although agreement is poorer in the southern polar cap. Intermodel coherency reduces above about degree 40, most likely due to incompletely filtered signals from polar ionospheric currents and auroral field aligned currents. The absence of the PC index for the southern hemisphere for 2003 onwards is a particular concern.     

Electromagnetic core–mantle coupling—I. Explaining decadal changes in the length of day

Measured changes in the Earth's length of day on a decadal timescale are usually attributed to the exchange of angular momentum between the solid mantle and fluid core. One of several possible mechanisms for this exchange is electromagnetic coupling between the core and a weakly conducting mantle. This mechanism is included in recent numerical models of the geodynamo. The 'advective torque', associated with the mantle toroidal field produced by flux rearrangement at the core–mantle boundary (CMB), is likely to be an important part of the torque for matching variations in length of day. This can be calculated from a model of the fluid flow at the top of the outer core; however, results have generally shown little correspondence between the observed and calculated torques. There is a formal non-uniqueness in the determination of the flow from measurements of magnetic secular variation, and unfortunately the part of the flow contributing to the torque is precisely that which is not constrained by the data. Thus, the forward modelling approach is unlikely to be useful. Instead, we solve an inverse problem: assuming that mantle conductivity is concentrated in a thin layer at the CMB (perhaps D"), we seek flows that both explain the observed secular variation and generate the observed changes in length of day. We obtain flows that satisfy both constraints and are also almost steady and almost geostrophic, and therefore assert that electromagnetic coupling is capable of explaining the observed changes in length of day.     

A Late Holocene geomagnetic secular variation record from Erhai Lake, southwest China

A secular variation record of the geomagnetic field direction for the last 6.5  kyr has been obtained from the magnetization of sediment cores from Erhai Lake, southwest China. In order to make a comparison with this record, secular variation in east-central China was investigated by combining available magnetic field data from historical records and archaeomagnetic measurements since about 350 bc . The secular variation in Erhai Lake shows features consistent with the combined record, except for the oldest three observed declination swings in Sian from 720 to 900 ad . Many features of declination and inclination in China also occur in Japan. From 500 to 1000 ad , declination was westerly ranging from about −20° to −5° in Erhai Lake, east-central China, and Japan.