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1.
The Antarctic magnetic anomaly map compiled marine and airborne surveys collected south of 60°S through 1999 and used Magsat data to help fill in the regional gaps between the surveys. Ørsted and CHAMP satellite magnetic observations with greatly improved measurement accuracies and temporal and spatial coverage of the Antarctic, have now supplanted the Magsat data. We combined the new satellite observations with the near-surface survey data for an improved magnetic anomaly map of the Antarctic lithosphere. Specifically, we separated the crustal from the core and external field components in the satellite data using crustal thickness variations estimated from the terrain and the satellite-derived free-air gravity observations. Regional gaps in the near-surface surveys were then filled with predictions from crustal magnetization models that jointly satisfied the near-surface and satellite crustal anomalies. Comparisons in some of the regional gaps that also considered newly acquired aeromagnetic data demonstrated the enhanced anomaly estimation capabilities of the predictions over those from conventional minimum curvature and spherical harmonic geomagnetic field models. We also noted that the growing number of regional and world magnetic survey compilations involve coverage gaps where these procedures can contribute effective near-surface crustal anomaly estimates.  相似文献   

2.
The geomagnetic power spectrum   总被引：1，自引：0，他引：1  
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.  相似文献   

3.
Summary. Price's thin sheet analysis for electromagnetic fields has been extended in order to model the effects of crustal resistivity and conductivity variations on magnetotelluric fields. These extensions allow for a general layered medium below the crust and also account for the vertical resistance of the crust as well as its horizontal conductance. An important parameter emerges from the analysis which determines the distance it takes for the crustal current levels to readjust to changes in the crustal conductance. This adjustment distance is given by the square root of the conductivity thickness product multiplied by the resistivity thickness product. Approximate analytical solutions were developed for two-dimensional geometries in order to demonstrate these effects as well as the modifications produced by finite source wavelengths.  相似文献   

4.
Spherical Slepian functions and the polar gap in geodesy   总被引：4，自引：0，他引：4  
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. We show that this potential-field estimation problem has deep-seated connections to Slepian's spatiospectral localization problem which seeks bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures such as bias, variance and mean squared error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of our method make the use of spherical Slepian functions in earth and planetary geodesy practical.  相似文献   

5.
We describe a new technique for implementing the constraints on magnetic fields arising from two hypotheses about the fluid core of the Earth, namely the frozen-flux hypothesis and the hypothesis that the core is in magnetostrophic force balance with negligible leakage of current into the mantle. These hypotheses lead to time-independence of the integrated flux through certain 'null-flux patches' on the core surface, and to time-independence of their radial vorticity. Although the frozen-flux hypothesis has received attention before, constraining the radial vorticity has not previously been attempted. We describe a parametrization and an algorithm for preserving topology of radial magnetic fields at the core surface while allowing morphological changes. The parametrization is a spherical triangle tesselation of the core surface. Topology with respect to a reference model (based on data from the Oersted satellite) is preserved as models at different epochs are perturbed to optimize the fit to the data; the topology preservation is achieved by the imposition of inequality constraints on the model, and the optimization at each iteration is cast as a bounded value least-squares problem. For epochs 2000, 1980, 1945, 1915 and 1882 we are able to produce models of the core field which are consistent with flux and radial vorticity conservation, thus providing no observational evidence for the failure of the underlying assumptions. These models are a step towards the production of models which are optimal for the retrieval of frozen-flux velocity fields at the core surface.  相似文献   

6.
Summary. In terms of lateral variations in conductivity structure, the southern Southern Uplands and Northumberland Basin are characterized by a region of attenuated vertical magnetic fields with small spatial gradients reflecting the presence of a substantial conducting zone. Five magnetotelluric data sets from the region have been analysed to provide accurate and unbiased estimates of the impedance tensor. The response data are used to investigate the deep geoelectric crustal structure of the region. Three appropriate sets of response data have been subjected to two construction algorithms for 1-D inversion. The geoelectric profiles recovered identify a deep crustal conducting zone underlying the Northumberland Basin. The zone, modelled as a layered structure, dips steeply from mid-crustal depths underneath the Northumberland Basin to lower crustal depths to the NW. The structure thus correlates, in location and geometry, with a deep crustal reflecting wedge detected offshore by a deep seismic reflection profile.  相似文献   

7.
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.  相似文献   

8.
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9.
Surface integral formulae are derived expressing any one of certain field quantities, namely current functions, magnetic potentials and normal components of magnetic fields, in terms of any one other, for current systems flowing in concentric spherical surfaces. In all, 36 such formulae are obtained, which should prove useful in many geomagnetic studies, especially in geomagnetic induction problems.  相似文献   

10.
Summary. A problem in modelling electromagnetic fields used in exploration geophysics is treated mathematically. Analytical expressions are obtained for the electric field due to a harmonic current in a horizontal loop on or above a conducting ground in which is buried a conductive and permeable sphere (ore body). The loop is coaxial with the sphere. For a general time-varying current in the loop, the analysis is carried to the stage where a Fourier inversion can be used to obtain readily the electric field in the time-domain. A new relationship between spherical and cylindrical wave functions is obtained as a transformation of local elements.
Solution of this problem has not been presented before in this form. Lee's solution of 1975 which uses an integral-equation formulation treats a similar problem without taking account of differences in magnetic permeability. The effects of magnetic permeability may have important and useful implications for geophysical explorations.  相似文献   

11.
Magnetic fields originating from magnetized crustal rocks dominate the geomagnetic spectrum at wavelengths of 0.1–100 km. It is not known whether the magnetization is predominantly induced or remanent, and static surveys cannot discriminate between the two. Long‐running magnetic observatories offer a chance, in principle, of separating the two sources because secular variation leads to a change in the main inducing field, which in turn causes a change in the induced part of the short‐wavelength crustal field. We first argue that the induced crustal field, b I( t ), is linearly related to the local core field, B ( t ), through a symmetric, trace‐free matrix A : b I( t )= A B ( t ). We then subtract a core field model from the observatory annual means and invert the residuals for three components of the remanent field, b R( t ), and the five independent elements of A . Applying the method to 20 European observatories, all of which have recorded for more than 50 years, shows that the most difficult task is to distinguish b R from the steady part of b I. However, for nine observatories a time‐dependent induced field fits the data better than a steady remanent field at the 99 per cent confidence level, suggesting the presence of a significant induced component to the magnetization.  相似文献   

12.
Summary. A solution is found for the seismic radiation from an arbitrarily growing spherical source in an inhomogeneously prestressed elastic medium. The general problem of the growing seismic source in a prestressed medium is formulated as a boundary value problem. For the special case of the growing spherical source, an expansion in vector spherical harmonics reduces the problem to a set of one-dimensional Volterra integral equations. The equations can be easily formed through the use of Bessel function recursion relations. The integral equations for a growing spherical cavity are solved numerically. Waveforms are then computed for homogeneous and inhomogeneous stress fields for several growth histories. The resulting waveforms are similar to the waveforms of the corresponding instantaneous problem, but stretched out in time and reduced in amplitude. The effects of diffraction and the overshoot of equilibrium are reduced with a reduction in growth rate. The effects caused by inhomogeneity of the stress field are quite strong for the growing as well as for the instantaneous seismic source.  相似文献   

13.
Telluric distortion occurs when electric charges accumulate along near-surface inhomogeneities. At low frequencies, the electric currents associated with these charges can be neglected compared to currents induced deeper in the Earth. At higher frequencies, the magnetic fields associated with these currents may be significant. Some parameters describing the distortion magnetic fields can be estimated from measured magneto-telluric impedance matrices. For regional magnetic fields aligned with regional strike directions, parameters associated with the distortion magnetic field component parallel to the regional magnetic field are undeterminable, whereas parameters associated with the distortion magnetic field component perpendicular to the regional magnetic field can be estimated. Optimal estimates are straightforward even for the realistic case of measurement errors that are correlated between elements of a measured impedance matrix. In a simple example of a 1-D anisotropic model with anisotropy direction varying with depth, the modelling of distortion magnetic fields results in regional impedance estimates corresponding more closely to the responses of uncoupled isotropic models, allowing sensible interpretation of an additional one and a half decades of data.  相似文献   

14.
It is well known that the vector fields derived from spherical harmonics are orthogonal over the sphere. It is now shown that the vector fields derived from spherical cap harmonics are orthogonal over the cap, to the same extent as the cap potentials are, and expressions are given for their mean squares.  相似文献   

15.
b
Spherical harmonics are orthonormalized using the Gram-Schmidt process in a function space. The problem of linear dependence of spherical harmonics over the oceans is studied using the Gram matrices and consequently three sets of orthonormal (ON) functions have been constructed. For the process an efficient formula for computing inner products of spherical harmonics has been developed. Important spectral properties of the ON functions are addressed. The ON functions may be used for representing the sea surface topography (SST) in the analysis of satellite altimeter data. The geoid error can be transformed to a representation by the ON functions and hence the comparison of powers of the geoid error and the SST signal only over the oceans is possible, leading to a better way of determining the cut-off frequency of the SST in the simultaneous solution using satellite altimeter data. As a case study, the modified Levitus SST is expanded into the ON functions. The results show that 99.90 per cent of that signal's energy is contained within degree 24 of the orthonormal functions. Such expansions also render better spectral behaviour of oceanic signals as compared to that from spherical harmonic expansions. The study shows that these generalized Fourier functions are suitable for spectral analyses of oceanic signals and they can be applied to future altimetric mission where the geoid and the SST are to be recovered.  相似文献   

16.
Summary. Exact spherical harmonic expansions are given for calculating the gravitational and magnetic fields associated with certain uniform solids of revolution. The figures are those made by rotating a conic section about one of its principal axes. The coefficients in the expansions can be computed accurately and efficiently and this approach leads to a very satisfactory method for calculating the fields of geological bodies with approximate circular symmetry about a vertical axis. A complete theory of convergence is given for the expansions. Somewhat unexpectedly, the sphere of convergence is determined by the location of a number of equivalent point or line sources that lie within the body or on its edges.  相似文献   

17.
Summary. The transient fields resulting from an abrupt current switch-off in a vertically oriented finite loop and a magnetic dipole above a permeable and conducting half-space have been investigated by Fourier methods, utilizing an appropriate Green's function. Two partial fields are identified, one 'radiative' and evanescent and one 'diffusive'. Asymptotic formulae for the diffusive field above the interface, applicable for late times, are developed, and from these the effects of height of the transmitting source and the permeability contrast are calculated. It is shown that for 'late enough' times and at sufficient distances the dipole formulae provide adequate approximations to the field due to a finite loop.  相似文献   

18.
For studying the auroral electrojet and for examining the effects it can produce in power systems on the ground, it is useful to be able to calculate the magnetic and electric fields that the electrojet produces at the surface of the Earth. Including the effects of currents induced in the Earth leads to a set of integral expressions, the numerical computation of which is complicated and demanding of computer resources. An approximate solution can be achieved by representing the induced currents by an image current at a complex depth. We present a simple derivation of the complex-image expressions and use them to calculate the fields produced by the auroral electrojet at the surface of an earth represented by layered conductivity models. Comparison of these results with ones obtained using the exact integral solution show that the errors introduced are insignificant compared to the uncertainties in the parameters used. The complex-image method thus provides a simple, fast and accurate means of calculating the magnetic and electric fields.  相似文献   

19.
Summary. Attention is drawn to a direct analytic method of calculating the quadrupole parameters of a planetary main magnetic field. Following a brief survey of the general theory of magnetic multipoles, an explicit algorithm is derived for calculating the quadrupole moment and the directions of the two quadrupole axes, given the five spherical harmonic coefficients of the second degree. It is shown that the direct analytic method of calculating the quadrupole parameters yield results for the geomagnetic quadrupole that are in exact agreement with those obtained by the more usual iterative procedure. Moreover, the direct analytic method has the distinct advantage that it does not require approximate values of the quadrupole parameters to be specified in advance. The direct analytic method of solution is used to calculate the quadrupole parameters for three different models of the main field of the Earth at epoch 1975; these computations provide some indication of the current uncertainties in the geomagnetic quadrupole parameters. It is also pointed out that a pseudo-quadrupole moment, which has been used to compare the quadrupole strengths of different planetary magnetic fields, is not strictly consistent with Maxwell's classical definition of a quadrupole moment. A precise physical definition of this pseudo-quadrupole moment is propounded.  相似文献   

20.
Abstract Rifted margin architecture along part of the southern Gabonese margin is interpreted from four deep-penetration, multichannel seismic reflection (MCS) profiles. A series of synthetically faulted crustal blocks are identified, separated by dominantly seaward-dipping fault zones formed during Cretaceous rifting between Africa and South America. Extensional strain ratios are ≅ 1.5. These faults appear either to transect the entire crustal section or are interrupted by discontinuous zones of midcrustal reflections which may represent detachments.
Outer acoustic basement highs are situated just seaward of the continental slope. On the combined basis of seismic geometry, an associated positive magnetic anomaly and an increase in free-air gravity, these outer highs are interpreted to mark faulted transitions from rifted continental crust to 'proto-oceanic crust', presumably composed of mafic volcanic rocks and possibly slivers of attenuated continental crustal blocks. The outer edge of Aptian salt lies °165 km south-west of the edge of the continental shelf. The salt forms an° 1.5-km-thick horizon overlying the outer highs, and it may be autochthonous there, suggesting salt was deposited contemporaneously with emplacement of proto-oceanic crust.
Differential subsidence and tilting between continental rift-blocks during post-rift margin subsidence has resulted in a sympathetic terrace-ramp geometry in overlying Aptian salt. Salt terraces form above tops of crustal blocks, where salt tends to rise vertically, creating pillows and diapirs. Ramps connecting terraces tend to form above seaward-facing fault zones; salt flowage there has been both lateral and vertical, creating triangular diapirs along the footwalls of growth faults. Most of these growth-faults sole within the salt base, but a few continue into the interpreted synrift succession.  相似文献   

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