Extraction of the M2 ocean tide from SEASAT altimeter data

Summary. Three complementary methods for the extraction of the M2 ocean tide using SEASAT altimetry are presented and compared. The first method (that developed by Cartwright & Alcock), which provides 'point measurements'of the tide at the crossovers of the SEASAT repeat orbit ground track, has been applied to a study of the tide in tropical ocean areas. The other two methods involve spatial expansions of M2 in terms of either surface spherical harmonics (in the case of the method developed by Mazzega) or Platzman normal modes of the world ocean. The results obtained by each method from only one month of SEASAT data reproduce many features of the tide represented in recent tidal models, and promise well for satellite altimetry as a future source of tidal knowledge.     

Distribution analysis of errors due to relocation of geomagnetic data using the 'Conversion via Pole' (CVP) method: implications on archaeomagnetic data

Secular variation 'master' curves are built up using geomagnetic historical observations or archaeomagnetic data from a limited area and their use is usually restricted to regions of around 1000 km radius. Relocation of data within this distance is a common practice to enable comparison of data, although the errors due to such process are rarely taken into account. A detailed analysis of the distribution of relocating geomagnetic data has been done using three popular sets of geomagnetic models (IGRF-9, GUFM and CALS7K-2). This study improves the error analysis of relocating geomagnetic directions made up to date and expands it to geomagnetic intensities. Maximum errors correlate with the non-dipole to dipole field ratio. Archaeomagnetists could use this analysis to valuate the error introduced by reducing data.     

On the construction of geomagnetic timescales from non-prejudicial treatment of magnetic anomaly data from multiple ridges

When marine magnetic-anomaly data are used to construct geomagnetic polarity timescales, the usual assumption of a smooth spreading-rate function at one seafloor spreading ridge forces much more erratic rate functions at other ridges. To eliminate this problem, we propose a formalism for the timescale problem that penalizes non-smooth spreading behaviour equally for all ridges. Specifically, we establish a non-linear Lagrange multiplier optimization problem for finding the timescale that (1) agrees with known chron ages and with anomaly-interval distance data from multiple ridges and (2) allows the rate functions for each ridge to be as nearly constant as possible, according to a cumulative penalty function. The method is applied to a synthetic data set reconstructed from the timescale and rate functions for seven ridges, derived by Cande & Kent (1992) under the assumption of smooth spreading in the South Atlantic. We find that only modest changes in the timescale (less than 5 per cent for each reversal) are needed if no one ridge is singled out for the preferential assumption of smoothness. Future implementation of this non-prejudicial treatment of spreading-rate data from multiple ridges to large anomaly-distance data sets should lead to the next incremental improvement to the pre-Quaternary geomagnetic polarity timescale, as well as allow a more accurate assessment of global and local changes in seafloor spreading rates over time.     

南极长城站冬季地磁S_q变化特征

本文利用南极长城站1987年4月至9月的地磁资料,分析了长城站地区冬季地磁S_q变化特征。分析结果表明:(1)南极长城站在初冬(4月)与冬末(9月)月份的S_q变化形态与北半球中纬度的北京地磁台的S_q变化形态基本相似,这可能是由中纬度电离层中的发电机电流所控制的。在仲冬月份(6月与7月),由于太阳紫外辐射效应减少,高纬度的地磁扰动占主导地位,反映出S_q变幅很小和以8小时以下的较短周期谐波起主要作用,(2)在初冬与冬末月份的S_q等效电流矢量,白天比黑夜大约5倍;其矢量方向在白天(08—15时)为顺时针,黑夜为反时针。在仲冬月由于电离层中电流的影响相对减弱,S_q等效电流矢量很小,白天与黑夜基本一样;其矢量分布方向与初冬和冬末的矢量方向不同,这可能是极区的电离层电流或场向电流的影响造成的。     

CHARACTERISTICS OF Sq VARIATION OF GEOMAGNETIC FIELD AT THE GREAT WALL STATION, ANTARCTICA IN WINTER

In this paper the characteristics of Sq variation of geomagnetic field in the region of the Chinese Great Wall Station (CGWS), Antarctica, in winter are analyzed from geomagnetic data obtained at the Geomagnetic Observatory of CGWS. The result enables us to reveal the following aspects: (1) The pattern of Sq variation at CGWS in early (Apr.) and Late winter (Sep.) is similar to that at Beijing Geomagnetic Observatory (BJO) at the middle latitude in the Northern Hemisphere. It may be controlled by the midlatitudinal ionospheric dynamo current. Amplitude of Sq variation is very small, and the harmonics in 8 hours or shorter periods in midwinter (June and July) is predominant because of the decreased effect of solar ultraviolet radiation and the dominant geomagnetic disturbance at high latitudes. (2) The vectors of Sq-equivalent current in the daytime are about five times more than that in the night. The direction of the vectors is clockwise in the daytime (08-15h) and counterclockwise in the night in earl     

The geomagnetic power spectrum

Combining CHAMP satellite magnetic measurements with aeromagnetic and marine magnetic data, the global geomagnetic field has now been modelled to spherical harmonic degree 720. An important tool in field modelling is the geomagnetic power spectrum. It allows the comparison of field models estimated from different data sets and can be used to identify noise levels and systematic errors. A correctly defined geomagnetic power spectrum is flat (white) for an uncorrelated field, such as the Earth's crustal magnetic field at long wavelengths. It can be inferred from global spherical harmonic models as well as from regional grids. Marine and aeromagnetic grids usually represent the anomaly of the total intensity of the magnetic field. Appropriate corrections have to be applied in estimating the geomagnetic power spectrum from such data. The comparison of global and regional spectra using a consistently defined azimuthally averaged geomagnetic power spectrum facilitates quality control in field modelling and should provide new insights in magnetic anomaly interpretation.     

Stacking gravity tide observations in central Europe for the retrieval of the complex eigenfrequency of the nearly diurnal free-wobble

We have used tidal gravity measurements from six stations in central Europe to investigate the resonance in the diurnal tidal band, caused by inertial coupling between the mantle and outer core of the Earth. By the use of stacking it was possible to determine the eigenfrequency and quality factor of this eigenmode, commonly called the 'nearly diurnal free-wobble'. We assessed the effect of systematic errors from the ocean correction to the tidal measurements employing a Monte-Carlo method. The observed eigenfrequency is 1 + 1/(434 ± 7) cycles per sidereal day, and is significantly higher than predicted by theories. The observed quality factor is (2.8 ± 0.5) × 10³.     

A microgravimetric network for secular gravity studies in Scotland

Summary. Tests with the LaCoste and Romberg gravity meter G-275 show that random reading errors generate a standard deviation of less than 0.02 gu (2 μgal) under typical microseismic conditions. Reproducible, systematic errors are commonly an order of magnitude larger, due mainly to residual tidal effects and drift induced by clamping. The latter, possibly related to thermal gradients in the oven, can be eliminated by observing along-enough section of the drift curve at each field station so that equilibrium is reached there. A measurement of the gravity difference between the NGRN (73) sites at Edinburgh and Linlithgow, giving 5.565⁵± 0.018 (se) gu, is described as an example of the method.
A loop of eight gravity stations associated with Ordnance Survey Fundamental Bench Marks, east—west between Dunbar and Bowling (Dumbartons) and northwards to Crubenmore (Inverness) is being measured as the basis of a secular gravity study by a calibrated small-difference method. The uses of such a network are discussed.     

Robust estimation of geomagnetic transfer functions

Summary. We show, through an examination of residuals, that all of the statistical assumptions usually used in estimating transfer functions for geomagnetic induction data fail at periods from 5 min to several hours at geomagnetic mid-latitudes. This failure can be traced to the finite spatial scale of many sources. In the past, workers have tried to deal with this problem by hand selecting data segments thought to be free of source effects. We propose an automatic robust analysis scheme which accounts for the systematic increase of errors with increasing power and which automatically downweights source contaminated outliers. We demonstrate that, in contrast to ordinary least squares, this automatic procedure consistently yields reliable transfer function estimates with realistic errors.     

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.     

Geomagnetic disturbance fields: an analysis of observatory monthly means

SUMMARY
This work quantifies the extent to which disturbance phenomena contribute to the observed geomagnetic field on the time-scale of months to years. A deterministic approach was adopted in which geomagnetic monthly means were analysed in the time domain. By presupposing the time dependence of the external and induced field variations, which we assume to vary as the aa geomagnetic index, we arrived at an estimate of the relative amplitude of the disturbance to each component of the field at a number of observatories. In all some 58 000 geomagnetic monthly means from 59 observatories operating this century were analysed. Special attention was paid to the selection and validation of the data as otherwise the numerical computations would have been unduly compromised.
The results consist of 177 estimates of the relative amplitude of disturbance, one for each of three orthogonal components north ( X ), east ( Y ) and vertically down ( Z ) at each observatory. The disturbance to the X component was found to be consistently negative over the whole of the Earth's surface with an intensification in auroral regions. The disturbances to the Z component were found to be smaller than that for X except in high latitudes. Mean disturbances to the Y component were smaller still. Results were in general consistent with the dipole field of the magnetospheric ring current, aligned with, though of opposite polarity to, the Earth's main field. Typical amplitudes of the mean disturbance field from month to month were of the order 10 nT.
The results can be used to estimate the variation of the disturbance field. Subtracting this from both monthly and annual means yields an improved estimate of the field originating in the core and its secular variation. Some examples are presented.     

STANDARD ERRORS IN THE EIGENVALUES OF A CROSS-PRODUCT MATRIX:THEORY AND APPLICATIONS

New expressions are derived for the standard errors in the eigenvalues of a cross-product matrix by themethod of error propagation.Cross-product matrices frequently arise in multivariate data analysis,especially in principal component analysis (PCA).The derived standard errors account for the variabilityin the data as a result of measurement noise and are therefore essentially different from the standarderrors developed in multivariate statistics.Those standard errors were derived in order to account for thefinite number of observations on a fixed number of variables,the so-called sampling error.They can beused for making inferences about the population eigenvalues.Making inferences about the populationeigenvalues is often not the purposes of PCA in physical sciences,This is particularly true if themeasurements are performed on an analytical instrument that produces two-dimensional arrays for onechemical sample:the rows and columns of such a data matrix cannot be identified with observations onvariables at all.However,PCA can still be used as a general data reduction technique,but now the effectof measurement noise on the standard errors in the eigenvalues has to be considered.The consequencesfor significance testing of the eigenvalues as well as the usefulness for error estimates for scores andloadings of PCA,multiple linear regression (MLR) and the generalized rank annihilation method(GRAM) are discussed.The adequacy of the derived expressions is tested by Monte Carlo simulations.     

Spectral analysis of Pennocarboniferous geomagnetic variation data from glacial rhythmites

Summary. Palaeomagnetic results for a sequence of Permocarboniferous rhythmites presented in the previous paper have been submitted to maximum entropy spectral analysis to test whether these palaeomagnetic data could supply information on geomagnetic variations. There is a good correlation between the thickness of the rhythmites and sunspot spectra, suggesting that these sediments are really seasonal. The palaeomagnetic spectra are compared with those of observatory records. Periods of approximately 24.4, 12.4, 8.6, 6.7 and 5.5 found for palaeomagnetic data have corresponding values in the geomagnetic spectrum. Most of these periods, however, are the same as those found in the thickness data, implying that magnetization can be influenced by the sedimentation process as suggested by other investigators. On the other hand, both geomagnetic and climatic (thickness) variations seem to be related to solar activity. Therefore, at least indirectly, palaeomagnetic data may reflect geomagnetic variations.     

Palaeosecular variation over the past 5 Myr based on a new generalized database

A generalized database of global palaeomagnetic data from 3719 lava flows and thin dykes of age 0–5 Ma has been constructed for use with a relational database management system. The database includes all data whose virtual geomagnetic poles (VGP) lie within 45 of the spin axis and can be used for studies of palaeosecular variation and for geomagnetic field modelling. Because many of these data were collected and processed more than 15–20 years ago, each result has been characterized according to the demagnetization procedures carried out. Analysis of these data in terms of the latitude variation of the angular dispersion of VGPs (palaeosecular variation from lavas) strongly suggests that careful data selection is required and that many of the older studies may need to be redone using more modern methods. Differences between the angular dispersions for separate normal- and reverse-polarity data sets confirm that many older studies have not been adequately cleaned magnetically. Therefore, the use of the database for geomagnetic field modelling should be carried out with some caution. Using a VGP cut-off angle that varies with latitude, the best data set consists of 2636 results that show a smooth increase of VGP angular dispersion with latitude. Model G for palaeosecular variation, which is based on modelling of the antisymmetric (dipole) and symmetric (quadrupole) dynamo families, provides a good fit to these results.     

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.     

应用卫星影像系列海图叠合法分析沙洲动态变化——以江苏东沙为例

利用1973~2000年9个时相的卫片、海图,提出了卫星影像系列——海图叠合分析法来分析辐射沙洲中大沙洲的动态变化,并将之运用到东沙的动态趋势分析中。研究结果表明:(1)通过卫星影像系列——海图叠合分析法,可避开了不同时相卫片的潮位校正难点,揭示了沙洲的冲蚀淤长变化。(2)东沙北缘向南移动;沙洲东缘向东移动;在沙洲西部遭受侵蚀,边缘东移,但幅度不大。     

苏北平原龙冈LG孔晚第四纪地层与环境演化记录

通过研究已经获得的苏北平原龙冈LG孔岩芯野外描述、照片、粒度、¹⁴C测年、有孔虫、孢粉、重矿物等原始测试分析数据,并参考邻区发表成果和该区新近补充的资料数据,再分析和讨论了LG孔的地层层序、年代框架和环境演化记录等内容。结果表明：① LG孔34.8 m岩芯保存了MIS 4以来沉积环境演化记录,先后经历了河漫滩、河湖相洪泛平原（第二硬黏土层）、较开放潮滩的潮间带和潮下带、较开放潮滩的潮下带、较开放潮滩的潮间带和潮上带下部、河湖相洪泛平原（第一硬黏土层）、潮上带滨海沼泽和海岸沙堤等一系列环境演化过程,其中潮滩环境的MIS 3海侵层发育;② 西冈贝壳沙堤龙冈段的全新统厚度很薄,一般在10 m以内,由于LG孔可见两个硬黏土层,应位于古河间地而非下切古河谷区,且以其第一硬黏土层顶面作为全新统底界更为合理,故原报道该孔全新统厚达25 m难以成立;③ 老于末次冰盛期的常规和加速器¹⁴C测年数据皆存在着不同程度的误差和不确定性,加之淤泥和钙质结核等测年材料易受污染等,故LG孔第二硬黏土层中的2个¹⁴C测年数据明显偏年轻,皆不宜用于解释地层年代。     

Fractal analysis of tidal channels in the Bahía Blanca Estuary (Argentina)

The fractal dimension (D) was estimated for nine tidal channels depicted in thematic mapper (TM) Landsat-5 imagery to derive information about the degree of geomorphological control on a tidal channel network characteristic of the Bahía Blanca Estuary (Argentina). Two methods, box counting and contiguity, were used to estimate fractal dimensions for each tidal channel. All channels produced D values close to 1, meaning that they are self-affine fractal features. However, these fractal dimensions do not represent the meandering pattern complexity characteristic of the tidal channels analysed. Although both methods allowed for estimation of D, the contiguity method showed that three of the channels actually are not fractal but have sinusoidal characteristics, a condition that was not detected by the former method.     

The lunar and solar daily geomagnetic variations at Sabhawala and Hyderabad

Summary . The first four harmonics of the lunar, L, and the solar, S, daily geomagnetic variations in the H, D and Z elements are determined for the observatories at Sabhawala and Hyderabad. Also included are similar results for Alibag with the main lunar terms separated into parts of oceanic and ionospheric origin. The data used are the alternate hourly mean values of H, D and Z for locally selected quiet days during the IQSY period, 1964–66. The predominances of the first lunar harmonic of H at Sabhawala and Alibag, and of the second solar harmonic at Sabhawala, are pointed out and discussed. The ratios of the seasonal ranges of both L and S to the respective annual mean ranges are found relatively enhanced in two of the seasons, in comparison with. the average global values for these latitudes for the IGY/C (sunspot maximum) period. This would indicate an inverse relationship of these ratios with solar activity.     

A six-parameter statistical model of the Earth's magnetic field

A six-parameter statistical model of the non-dipole geomagnetic field is fitted to 2597 harmonic coefficients determined by Cain, Holter & Sandee (1990) from MAGSAT data. The model includes sources in the core, sources in the crust, and instrument errors. External fields are included with instrument errors. The core and instrument statistics are invariant under rotation about the centre of the Earth, and one of the six parameters describes the deviation of the crustal statistics from rotational invariance. The model treats the harmonic coefficients as independent random samples drawn from a Gaussian distribution. The statistical model of the core field has a correlation length of about 500 km at the core-mantle boundary, too long to be attributed to a white noise source just below the boundary layers at the top of the core. The estimate of instrument errors obtained from the statistical model is in good agreement with an independent estimate based on tests of the instruments (Langel, Ousley & Berbert 1982).