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.     

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.     

Geomagnetic lunar analysis—the estimation of errors

Summary. It has recently been proposed that a reliable estimate of the errors of tidal harmonics present in geomagnetic data can be obtained by the following method: (1) randomly assign each observation to one of 10 subsets, (2) determine the tidal harmonics separately for each subset, and (3) calculate the standard deviation of the mean from the scatter among the 10 determinations. This method is valid if the subsets are statistically independent, but will lead to an underestimate of the errors if they are not. Here we show that, for real geomagnetic data, the assumption of statistical independence is valid.     

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).     

The pole-tide signal in the geomagnetic field at a low-latitude station

summary . The equilibrium pole-tide's signal is identified at a period around 14.22 month (427 day) in geomagnetic elements H and Z at a low-latitude coastal station, Alibag, in the Indian region. The signal however, could not be detected clearly in the element D . Consistent amplitudes and phases, over the hours, of this tide in H spectra of both'all days'and'IQ days'indicate that the origin of the tide in the geomagnetic field cannot be due to modulation of an external current system. It is suggested that the probable source of excitation may be the'ocean dynamo'.     

On the anomalous features of the geomagnetic quiet-day field variations at Nagpur, India

The quiet-day geomagnetic field variation data from the recently commissioned Nagpur geomagnetic observatory, which has augmented the currently active latitudinal chain of Indian magnetic observatories, are analysed for the year 1993- The variations for diurnal frequencies (Sq) recorded at Nagpur do not follow the expected trend with latitude. This is most conspicuous in the northward horizontal ( X ) component. The anomalous behaviour at Nagpur is also seen in the diurnal harmonic amplitudes when compared with those of the neighbouring stations Alibag (south of Nagpur) and Ujjain (north of Nagpur). This behaviour is attributed to the presence of electrically conducting anomalous sources in the vicinity of Nagpur. The anomalous internal source is inferred to be located at relatively shallower depths and is highly localized.     

A comparison of time and frequency domain geomagnetic sounding

Summary. A three-site geomagnetic data set from the Borders region of southern Scotland is used to examine the empirical relationships established by differential geomagnetic sounding experiments. A time domain analysis of such relationships reveals time domain transfer functions which appear to be almost independent of time. A frequency domain analysis is then used to illustrate both a significant phase rotation and a significant dependence on period of the equivalent frequency domain response functions. The formalism of conventional geomagnetic sounding is re-examined. It is found that difference fields are not required to establish the appropriate horizontal field relationships.     

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS-related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system and light detection and ranging have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.     

Geomagnetic induction in a heterogeneous sphere: fully three-dimensional test computations and the response of a realistic distribution of oceans and continents

Long-period geomagnetic data can resolve large-scale 3-D mantle electrical conductivity heterogeneities which are indicators of physiochemical variations found in the Earth's dynamic mantle. A prerequisite for mapping such heterogeneity is the ability to model accurately electromagnetic induction in a heterogeneous sphere. A previously developed finite element method solution to the geomagnetic induction problem is validated against an analytic solution for a fully 3-D geometry: an off-axis spherical inclusion embedded in a uniform sphere. Geomagnetic induction is then modelled in a uniform spherical mantle overlain by a realistic distribution of oceanic and continental conductances. Our results indicate that the contrast in electrical conductivity between oceans and continents is not primarily responsible for the observed geographic variability of long-period geomagnetic data. In the absence of persistent high-wavenumber magnetospheric disturbances, this argues strongly for the existence of large-scale, high-contrast electrical conductivity heterogeneities in the mid-mantle. Lastly, for several periods the geomagnetic anomaly associated with a mid-mantle spherical inclusion is calculated. A high-contrast inclusion can be readily detected beneath the outer shell of oceans and continents. A comparison between observed and computed c responses suggests that the mid-mantle contains more than one order of magnitude of lateral variability in electrical conductivity, while the upper mantle contains at least two orders of magnitude of lateral variability in electrical conductivity.     

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.     

A geomagnetic scattering theory for evaluation of earth structure

Summary. Structural features of the Earth's lower crust and upper mantle can be mapped by the analysis of temporal geomagnetic fluctuations using the electromagnetic scattering theory developed in this paper. Decomposing geomagnetic field fluctuations at the Earth's surface into an excitation part and a scattered part forms the basis of a power series development. The vertical field component is interpreted as a scattering of the excitation field. The horizontal gradient and geomagnetic depth sounding methods are special cases of the theory developed. The horizontal gradient sounding method has a tensorial aspect which has not been recognized before; it should be included to obtain correct penetration depth parameter evaluations from field data.     

The results of deep geomagnetic soundings in the West Carpathians

Summary. The results of geomagnetic soundings in the West Carpathians are presented. The number of observation sites in this region was approximately 90. The data treatment included the calculation of single-station transfer functions and the separation of the fields into external and internal parts on some profiles. The interpretation was based on the construction of two-dimensional models explaining the observed features. The observed distribution of geomagnetic induction vectors is very regular and the axis of the anomaly runs in the contact region between the outer and inner Carpathians. The thickness of the well-conducting rock complex exceeds 10 km. The well-conducting rocks seem to be the sediments which accumulated in the contact region of the platform. The asymmetry in the distribution of induction vector amplitudes on some profiles can be accounted for by asymmetrical geometry, which is characteristic of the underthrusting of rocks.     

Palaeomagnetic record in Late Pleistocene and Holocene dry lake deposits at Tlapacoya, Mexico

Summary. A palaeomagnetic investigation of Carbon-14-dated marsh and near-shore lacustrine sediments deposited between about 25000–5000 yr bp at Tlapacoya, Mexico, reveals normal polarity of the geomagnetic field in all samples measured. At one site, anomalous palaeomagnetic directions in a mud unit dated about 14500 yr bp raised the possibility of a geomagnetic excursion, but subsequent work at six additional sites in the unit revealed no abnormal directions. Thus the anomalous directions are most likely not a true reflection of geomagnetic field behaviour, although no specific alternative explanation is entirely convincing. The preliminary Tlapacoya data of anomalous directions have been cited by others as positive evidence for an excursion. We strongly recommend it no longer be considered as such.     

Uplift by thermal expansion of the lithosphere

Summary. If one can measure the anomalous horizontal magnetic field associated with a (locally bounded) two-dimensional conductivity anomaly, the transfer function which results from correlating the vertical with the anomalous horizontal magnetic field directly indicates the depth to an equivalent line-current. A. numerical model can be used to illustrate this. If three-dimensional effects (including current channelling) produce the current anomaly, interpretation in terms of conductive structure would be less clear. It has been claimed (Babour & Mosnier etc.) that such three-dimensional effects are experimentally observed in the highly coherent transfer functions determined from differential geomagnetic sounding experiments. These effects are, specifically, the 'linear polarization' of the anomalous fields, and the invariance of the phase of the measured anomalous field across the anomaly. It is suggested in this present paper that both these effects can be explained in terms of simple local induction models.
If the embedded two-dimensional anomaly is sufficiently close to the Earth's surface, the transfer function (between the vertical and the total horizontal field) contains more information than is usually interpreted. With this in mind, the magnetovariational data collected by Rooney & Hutton in the Kenyan Rift is re-examined.     

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.     

Late Mesozoic and Cenozoic palaeomagnetism of Australia – III. Bias-corrected pole paths for Australia, Antarctica and India

Summary. Palaeomagnetic results from Part I of this study and their analysis in Part II are combined to eliminate bias from the Cenozoic apparent polar wander path for Australia – a bias due to non-dipole components in past geomagnetic fields or, for poles calculated from hot-spot data, due to the motion of hot spots relative to the Earth's rotational axis. This path is extended in approximately bias-free form to the late Mesozoic, and indicates a significant change in the drift direction of the continent between 26 and about 60 Ma.
The bias-corrected Australian path is used, first, with seafloor spreading data for the Southern Ocean to derive a corresponding late Mesozoic–Cenozoic pole path for Antarctica. The latter shows that the Antarctic drift direction reversed in the early Tertiary. It is suggested that the early Tertiary directional changes of both Australia and Antarctica are part of a global reorganization of plates during the Eocene, postulated by Rona & Richardson, Cande & Mutter and Patriat & Achache.
Next, the Australian path is compared with hot-spot data from the African and Australian plates, indicating a movement of the hot spots relative the Earth's rotational axis during the Cenozoic. The direction of this movement is found to be consistent with previous results from other parts of the world.
Finally, the Australian path is used together with non-dipole components in the geomagnetic field to explain a prominent westward displacement of the mid- and late Cenozoic poles of India relative to those of Australia.
Because of uncertainties in the original poles and in the analysis, the present results are likely to contain appreciable errors. Nevertheless, their consistency with independent findings supports the dipole-quadrupole model of Part II for mid- and late Cenozoic geomagnetic fields.     

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.     

A continuous deployment-based approach for the collaborative creation,maintenance, testing and deployment of CityGML models

Georeferenced 3D models are an increasingly common choice to store and display urban data in many application areas. CityGML is an open and standardized data model, and exchange format that provides common semantics for 3D city entities and their relations and one of the most common options for this kind of information. Currently, creating and maintaining CityGML models is costly and difficult. This is in part because both the creation of the geometries and the semantic annotation can be complex processes that require at least some manual work. In fact, many publicly available CityGML models have errors. This paper proposes a method to facilitate the regular maintenance of correct city models in CityGML. This method is based on the continuous deployment strategy and tools used in software development, but adapted to the problem of creating, maintaining and deploying CityGML models, even when several people are working on them at the same time. The method requires designing and implementing CityGML deployment pipelines. These pipelines are automatic implementations of the process of building, testing and deploying CityGML models. These pipelines must be run by the maintainers of the models when they make changes that are intended to be shared with others. The pipelines execute increasingly complex automatic tests in order to detect errors as soon as possible, and can even automate the deployment step, where the CityGML models are made available to their end users. In order to demonstrate the feasibility of this method, and as an example of its application, a CityGML deployment pipeline has been developed for an example scenario where three actors maintain the same city model. This scenario is representative of the kind of problems that this method intends to solve, and it is based on real work in progress. The main benefits of this method are the automation of model testing, every change to the model is tested in a repeatable way; the automation of the model deployment, every change to the model can reach its end users as fast as possible; the systematic approach to integrating changes made by different people working together on the models, including the possibility of keeping parallel versions with a common core; an automatic record of every change made to the models (who did what and when) and the possibility of undoing some of those changes at any time.     

Reconstructing air temperature at eleven remote alpine and arctic lakes in Europe from 1781 to 1997 AD

Pristine and sensitive environments, such as remote alpine and arctic lakes, are particularly susceptible to the effects of climate change. However, these remote environments do not have sufficiently long instrumental climate records to support studies on contemporary climate change. The issue of the scarcity of instrumental climate data at remote regions is addressed by reconstructing monthly mean air temperatures from 1781 to 1997 AD at eleven remote alpine and arctic lakes in Europe, as part of the MOuntain LAke Research (MOLAR) project. Stepwise multiple regression is applied to establish linear transfer functions of temperatures between each of eleven upland records and twenty homogenised long lowland records. Twelve monthly transfer functions are obtained for each lake. The skill of these transfer functions is found to range typically between 60 and 99%. The lower skill values generally correspond to winter months. The temperature reconstructions obtained using the transfer functions need to be corrected with vertical temperature gradients. Air-temperature lapse rates were obtained for each lake region by spatial interpolation of radiosonde air-temperature data (1990–1997). The resulting reconstructions at each lake were checked using air-temperature data (1996–1997) from automatic weather stations installed at the lakes during the MOLAR project. We estimate the typical reconstruction errors to be about 1.3 °C for low-sun months and about 0.98 °C for high-sun months. Trend analyses on the reconstructed annual mean air temperatures at the lakes show two distinct types of trends for the 19th and 20th centuries. During the period 1801–1900, the western European lakes show no significant trend whereas annual mean air temperatures at the eastern European lakes decrease significantly. The period 1901–1997 presents a warming trend at all but the Fennoscandian lakes. Our results are in good agreement with previous studies on the spatial distribution and magnitude of temperature change in Europe. Principal component analysis performed on the reconstructed annual mean air temperature reveals two different regimes of trends for the past two centuries. It also allows a regional clustering of the inter-annual variability of air temperature at the lakes to be identified.     

INCORPORATING INHERENT MAP ERROR INTO FLOOD-HAZARD ANALYSIS

Maps are an important source of data for planning and land use analysis of flood-prone areas. Map users with inadequate training are not aware that map errors can lead to ineffective decisions. Although inherent errors introduced by transformation, map construction, and symbolization are never identified on maps, they limit the effectiveness of maps as sources of data. Additional vertical and horizontal errors can be introduced during map use. Knowledge of the sources and amounts of such errors should result in more effective decisions regarding flood hazards.