Electromagnetic induction fields in the deep ocean north-east of Hawaii: implications for mantle conductivity and source fields

Summary. We have analysed a thirty-six day recording of the natural electric and magnetic field variations obtained on the deep ocean floor north-east of Hawaii. The electromagnetic fields are dominated by tides which have an appreciable oceanic component, especially in the east electric and north magnetic components. The techniques of data analysis included singular value decomposition (SVD) to remove uncorrelated noise. There are three degrees of freedom in the data set for periods longer than five hours, indicating a correlation of the vertical magnetic field and the horizontal components, suggesting source field inhomogeneity. Tensor response functions were calculated using spectral band averaging with both SVD and least squares techniques and rotated to the principal direction. One diagonal component, determined mainly by the north electric and east magnetic fields, is not interpretable as a one-dimensional induction phenomenon. The other diagonal term of the response function indicates a rapid rise in conductivity to 0.05 mho m⁻¹ near 160 km. No decrease in conductivity below this depth is resolvable. Polarization analysis of the magnetic field indicates moving source fields with a wavelength near 5000 km. Model studies suggest that the two dimensionality in the response function may be caused by motion in the ionospheric current system.     

Multiscale tomography of buried magnetic structures: its use in the localization and characterization of archaeological structures

We have previously developed a method for characterizing and localizing 'homogeneous' buried sources, from the measure of potential anomalies at a fixed height above ground (magnetic, electric and gravity). This method is based on potential theory and uses the properties of the Poisson kernel (real by definition) and the continuous wavelet theory. Here, we relax the assumption on sources and introduce a method that we call the 'multiscale tomography'. Our approach is based on the harmonic extension of the observed magnetic field to produce a complex source by use of a complex Poisson kernel solution of the Laplace equation for complex potential field. A phase and modulus are defined. We show that the phase provides additional information on the total magnetic inclination and the structure of sources, while the modulus allows us to characterize its spatial location, depth and 'effective degree'. This method is compared to the 'complex dipolar tomography', extension of the Patella method that we previously developed. We applied both methods and a classical electrical resistivity tomography to detect and localize buried archaeological structures like antique ovens from magnetic measurements on the Fox-Amphoux site (France). The estimates are then compared with the results of excavations.     

Application of Global Particle Swarm Optimization for Inversion of Residual Gravity Anomalies Over Geological Bodies with Idealized Geometries

A global particle swarm optimization (GPSO) technique is developed and applied to the inversion of residual gravity anomalies caused by buried bodies with simple geometry (spheres, horizontal, and vertical cylinders). Inversion parameters, such as density contrast of geometries, radius of body, depth of body, location of anomaly, and shape factor, were optimized. The GPSO algorithm was tested on noise-free synthetic data, synthetic data with 10% Gaussian noise, and five field examples from different parts of the world. The present study shows that the GPSO method is able to determine all the model parameters accurately even when shape factor is allowed to change in the optimization problem. However, the shape was fixed a priori in order to obtain the most consistent appraisal of various model parameters. For synthetic data without noise or with 10% Gaussian noise, estimates of different parameters were very close to the actual model parameters. For the field examples, the inversion results showed excellent agreement with results from previous studies that used other inverse techniques. The computation time for the GPSO procedure is very short (less than 1 s) for a swarm size of less than 50. The advantage of the GPSO method is that it is extremely fast and does not require assumptions about the shape of the source of the residual gravity anomaly.     

Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements

Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency–time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.     

A new method to compensate for bias in magnetotellurics

Error estimates from statistical regression analysis are often obviously too small, leading to doubts about the given equations, the statistical method itself and finally, with resignation, to the conclusion that mathematical equations and reality never agree. However, for magnetotelluric data we have found an almost perfect fit between observed scattering and predicted confidence limits of regression coefficients after accounting for a systematic error—the bias.
Different methods to compensate for bias in magnetotelluric impedance estimation have been described using additional data from a reference station. However, sufficiently accurate reference data are often not available. A new method has been developed that enables bias compensation without additional data. For the new method we derive a linear relationship between the effect of bias and an expression depending on the data fit. From this we extrapolate the solution for the unbiased impedance. The new method assumes a special model of uncorrelated noise as well as an approximation for the structure of the impedance tensor. From each pair of components of the unrotated impedance tensor corresponding to the same output channel, one of the pair can be compensated if its magnitude is large compared to that of the other.
The method has been successfully applied in many cases. We claim that the solution is closer to the true impedance than any solution based on the selection of events. It gives a measure of the partitioning of noise between the electric and magnetic channels.
We applied the method to measurements from the North Anatolian Fault Zone (Turkey) and from the Merapi volcano (Central Java) in the period range 10–2500 s. Different instrumentation was used for the two sets of measurements, but in both cases we used fluxgate magnetometers to measure the magnetic variations.     

The magnetic structure of convection-driven numerical dynamos

The generation of a magnetic field in numerical simulations of the geodynamo is an intrinsically 3-D and time-dependent phenomenon. The concept of magnetic field lines and the frozen-flux approximation can provide insight into such systems, but a suitable visualization method is required. This paper presents results obtained using the Dynamical Magnetic Field line Imaging (DMFI) technique, which is a representation of magnetic field lines accounting for their local magnetic energy, together with an algorithm for the time evolution of their anchor points. The DMFI illustrations are consistent with previously published dynamo mechanisms, and allow further investigation of spatially and temporally complex systems. We highlight three types of magnetic structures: (i) magnetic cyclones and (ii) magnetic anticyclones are expelled by, but corotate with axial flow vortices; (iii) magnetic upwellings are amplified by stretching and advection within flow upwellings, and show structural similarity with helical plumes found in rotating hydrodynamic experiments. While magnetic anticyclones are responsible for the regeneration of a stable axial dipole, here we show that excursions and reversals of the dipole axis are caused by the emergence of magnetic upwellings, which amplify and transport a generally multipolar magnetic field from the inner to the outer boundary of the models. Geomagnetic observations suggest the presence of magnetic structures similar to those found in our models; thus, we discuss how our results may pertain to Earth's core dynamo processes. In order to make DMFI a standard tool for numerical dynamo studies, a public software package is available upon request to the authors (supplementary material is available at: http://www.ipgp.jussieu.fr/~aubert/DMFI.html ).     

Geomagnetic field analysis—IV. Testing the frozen-flux hypothesis

Summary. We present a model of the magnetic field at the core–mantle boundary, for epoch 1959.5, based on a large set of observatory and survey measurements. Formal error estimates for the radial field at the core are 50 μT, compared with 30 and 40 μT for our previous MAGSAT (1980) and POGO (1970) models.
Current work on the determination of the velocity of the core fluid relies on the assumption that the core behaves as a perfect conductor, so that the field lines remain frozen to the fluid at the core surface. This frozen-flux condition requires that the integrated flux over patches of the core surface bounded by contours of zero radial field remain constant in time. A new method is presented for constructing core fields that satisfy these frozen-flux constraints. The constraints are non-linear when applied to main field data, unlike the case of secular variation which was considered in an earlier paper. The method is applied to datasets from epochs 1969.5 and 1959.5 to produce fields with the same flux integrals as the 1980 model.
The frozen-flux hypothesis is tested by comparing the changes in the flux integrals between 1980/1969.5, 1969.5/1959.5 and 1980/1959.5 with their errors. We find that the hypothesis can be rejected with 95 per cent confidence. The main evidence for flux diffusion is in the South Atlantic region, where a new null flux curve appears between 1960 and 1970, and continues to grow at a rapid rate from 1970 to 1980. However, the statistical result depends critically on our error estimates for the field at the core surface, which are difficult to assess with any certainty; indeed, doubling the error estimates negates the statistical argument. The conclusion is therefore, at this stage, tentative, and requires further evidence, either from older data, if good enough, or from future satellite measurements.     

Maximum entropy regularization of time-dependent geomagnetic field models

We incorporate a maximum entropy image reconstruction technique into the process of modelling the time-dependent geomagnetic field at the core–mantle boundary (CMB). In order to deal with unconstrained small lengthscales in the process of inverting the data, some core field models are regularized using a priori quadratic norms in both space and time. This artificial damping leads to the underestimation of power at large wavenumbers, and to a loss of contrast in the reconstructed picture of the field at the CMB. The entropy norm, recently introduced to regularize magnetic field maps, provides models with better contrast, and involves a minimum of a priori information about the field structure. However, this technique was developed to build only snapshots of the magnetic field. Previously described in the spatial domain, we show here how to implement this technique in the spherical harmonic domain, and we extend it to the time-dependent problem where both spatial and temporal regularizations are required. We apply our method to model the field over the interval 1840–1990 from a compilation of historical observations. Applying the maximum entropy method in space—for a fit to the data similar to that obtained with a quadratic regularization—effectively reorganizes the magnetic field lines in order to have a map with better contrast. This is associated with a less rapidly decaying spectrum at large wavenumbers. Applying the maximum entropy method in time permits us to model sharper temporal changes, associated with larger spatial gradients in the secular variation, without producing spurious fluctuations on short timescales. This method avoids the smearing back in time of field features that are not constrained by the data. Perspectives concerning future applications of the method are also discussed.     

Palaeointensity In the Pelagic Realm: Marine Sediment Data Compared With Archaeomagnetic and Lake Sediment Records

Summary. Four box cores collected from the Ontong—Java plateau during the Eurydice expedition have been used to make relative geomagnetic palaeo-intensity measurements. Rock magnetic measurements on the sediments show that they are characterized by a uniform magnetic mineralogy, and that they are suitable for relative intensity estimates. These are obtained by normalizing the NRM by an ARM imparted in a low DC bias field. the palaeoceanographic event known as the preservation spike is used to establish a crude time-scale for the record so that it may be compared with other data from the same region, and also with global palaeointensity estimates. the marine sediment data are quite similar to Australian intensity data from lake sediments and archaeomagnetic sources, but as might be expected exhibit some obvious differences from the global record.     

Anisotropic turbulence in weakly stratified rotating magnetoconvection

Numerical simulations of the 3-D MHD-equations that describe rotating magnetoconvection in a Cartesian box have been performed using the code NIRVANA. The characteristics of averaged quantities like the turbulence intensity and the turbulent heat flux that are caused by the combined action of the small-scale fluctuations are computed. The correlation length of the turbulence significantly depends on the strength and orientation of the magnetic field and the anisotropic behavior of the turbulence intensity induced by Coriolis and Lorentz force is considerably more pronounced for faster rotation. The development of isotropic behavior on the small scales—as it is observed in pure rotating convection—vanishes even for a weak magnetic field which results in a turbulent flow that is dominated by the vertical component. In the presence of a horizontal magnetic field the vertical turbulent heat flux slightly increases with increasing field strength, so that cooling of the rotating system is facilitated. Horizontal transport of heat is always directed westwards and towards the poles. The latter might be a source of a large-scale meridional flow whereas the first would be important in global simulations in case of non-axisymmetric boundary conditions for the heat flux.     

Uniqueness of mainly dipolar magnetic fields recovered from directional data

We show that a knowledge of either the signed or the unsigned direction of a potential field on a given smooth surface S , which separates the space into a volume containing the sources and a volume free of sources, sometimes gives enough information for the whole field to be recovered within the free volume, except for a constant multiplier (positive, for the signed case). We show that the best parameter to be considered on the surface S is the number n of loci where the field is known to be either zero (no direction) or normal to the surface. In the case of sources lying outside S ('external-sources' directional problem) we prove that the dimension of the space of solutions is no larger than n –1. This implies uniqueness for the external-sources directional problem when n = 2. In the case of sources lying inside S ('internal-sources' directional problem), we distinguish fields with monopole sources (such as the gravitational field) from those without monopole sources (such as the magnetic field). For gravitational fields, we show that the dimension of the space of solutions cannot exceed n . We note that the only situation of interest is the one for which n = 1, which implies in practice that the surface S is an isopotential and that the problem has a unique solution. For magnetic fields, we show that the dimension of the space of solutions cannot exceed n –1. It follows that the problem has a unique solution when n = 2. This shows in particular that a geomagnetic field with only two poles (south and north magnetic poles) can be recovered, except for a constant multiplier (positive, for the signed case) from directional data gathered at the Earth's surface. Finally, we note that our results are not restricted to the 3-D space and can readily be extended to two dimensions and higher dimensions.     

The relation between magnetic range values and spectral power

Spectral power is shown to be proportional to the square of the range for variables with a normal distribution. Plots of log power versus log range for 3  hr intervals of data from Canadian magnetic observatories show a close fit to a straight line with a slope of 2. The same results are obtained from all sites in the Canadian magnetic observatory network, which extends from the polar cap to auroral and sub-auroral latitudes. This indicates that a square-law relation between spectral power and range is a general property of magnetic field variations.     

A pseudo-Thellier relative palaeointensity record, and rock magnetic and geochemical parameters in relation to climate during the last 276 kyr in the Azores region

In the pseudo-Thellier method for relative palaeointensity determinations (Tauxe et al. 1995) the slope of the NRM intensity left after AF demagnetization versus ARM intensity gained at the same peak field is used as a palaeointensity measure. We tested this method on a marine core from the Azores, spanning the last 276  kyr. We compared the pseudo-Thellier palaeointensity record with the conventional record obtained earlier by Lehman et al . (1996 ), who normalized NRM by SIRM. The two records show similar features: intensity lows with deviating palaeomagnetic directions at 40–45  ka and at 180–190  ka. The first interval is associated with the Laschamps excursion, while the 180–190  ka low represents the Iceland Basin excursion (Channell et al. 1997). The pseudo-Thellier method, in combination with a jackknife resampling scheme, provides error estimates on the palaeointensity.
  Spectral analysis of the rock magnetic parameters and the palaeointensity estimates shows orbitally forced periods, particularly 23  kyr for climatic precession. This suggests that palaeointensity is still slightly contaminated by climate. Fuzzy c -means cluster analysis of rock magnetic and geochemical parameters yields a seven-cluster model of predominantly calcareous clusters and detrital clusters. The clusters show a strong correlation with climate, for example samples from detrital clusters predominantly appear during rapid warming. Although both the pseudo-Thellier palaeointensity m _a and fuzzy clusters show climatic influences, we have not been able to find an unambiguous connection between the clusters and m _a .     

The role of seismicity models in probabilistic seismic hazard estimation: comparison of a zoning and a smoothing approach

Seismic hazard estimations are compared using two approaches based on two different seismicity models: one which models earthquake recurrence by applying the truncated Gutenberg-Richter law and a second one which smoothes the epicentre location of past events according to the fractal distribution of earthquakes in space ( Woo 1996 ). The first method requires the definition of homogeneous source zones and the determination of maximum possible magnitudes whereas the second method requires the definition of a smoothing function. Our results show that the two approaches lead to similar hazard estimates in low seismicity regions. In regions of increased seismic activity, on the other hand, the smoothing approach yields systematically lower estimates than the zoning method. This epicentre-smoothing approach can thus be considered as a lower bound estimator for seismic hazard and can help in decision making in moderate seismicity regions where source zone definition and estimation of maximum possible magnitudes can lead to a wide variety of estimates due to lack of knowledge. The two approaches lead, however, to very different earthquake scenarios. Disaggregation studies at a representative number of sites show that if the distributions of contributions according to source–site distance are comparable between the two approaches, the distributions of contributions according to magnitude differ, reflecting the very different seismicity models used. The epicentre-smoothing method leads to scenarios with predominantly intermediate magnitudes events (5 ≤ M ≤ 5.5) while the zoning method leads to scenarios with magnitudes that increase with the return period from the minimum to the maximum magnitudes considered. These trends demonstrate that the seismicity model used plays a fundamental role in the determination of the controlling scenarios and ways to discriminate between the most appropriate models remains an important issue.     

Forward modelling of direct current and low-frequency electromagnetic fields using integral equations

We present a semi-analytical, unifying approach for modelling the electromagnetic response of 3-D bodies excited by low-frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell's equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green's function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipoledipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR-TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR-TE, where the mode of conduction is predominantly perpendicular to the profile.     

Limitations on the parameters of the solar wind in modelling lunar electromagnetic induction

Summary. A striking feature of the day-side response of the Moon to periodic fluctuations in the solar wind is the rapid rise, and subsequent fall, in the amplitude of the transfer function as the inducing field frequency increases. This behaviour can be characterized by the amplitude values at the two frequencies 24 and 40 mHz. Before the response of a conductivity model representing the Moon can be calculated at a given frequency, the parameters (ν, θ) (where ν is the solar wind speed and θ is the angle between the solar wind velocity and the magnetic field propagation direction) have to be specified. By applying some results due to Parker (1972) to the above two data points, we have determined constraints on the parameter space (ν, θ). In particular, we determine the region of the (ν, θ) space in which conductivity models may be found that satisfy our data pair. Outside this region, there are no conductivity models satisfying the data pair, and hence many (ν, θ) values are inconsistent with the original data and the model assumptions.     

Interpreting magnetic data by integral moments

The use of the integral moments for interpreting magnetic data is based on a very elegant property of potential fields, but in the past it has not been completely exploited due to problems concerning real data. We describe a new 3-D development of previous 2-D results aimed at determining the magnetization direction, extending the calculation to second-order moments to recover the centre of mass of the magnetization distribution. The method is enhanced to reduce the effects of the regional field that often alters the first-order solutions. Moreover, we introduce an iterative correction to properly assess the errors coming from finite-size surveys or interaction with neighbouring anomalies, which are the most important causes of the failing of the method for real data. We test the method on some synthetic examples, and finally, we show the results obtained by analysing the aeromagnetic anomaly of the Monte Vulture volcano in Southern Italy.     

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.     

Quantitative Analysis of Scale of Aeromagnetic Data Raises Questions About Geologic-Map Scale

A recently published study has shown that small-scale geologic map data can reproduce mineral assessments made with considerably larger scale data. This result contradicts conventional wisdom about the importance of scale in mineral exploration, at least for regional studies. In order to formally investigate aspects of scale, a weights-of-evidence analysis using known gold occurrences and deposits in the Central Lapland Greenstone Belt of Finland as training sites provided a test of the predictive power of the aeromagnetic data. These orogenic-mesothermal-type gold occurrences and deposits have strong lithologic and structural controls associated with long (up to several kilometers), narrow (up to hundreds of meters) hydrothermal alteration zones with associated magnetic lows. The aeromagnetic data were processed using conventional geophysical methods of successive upward continuation simulating terrane clearance or ‘flight height’ from the original 30 m to an artificial 2000 m. The analyses show, as expected, that the predictive power of aeromagnetic data, as measured by the weights-of-evidence contrast, decreases with increasing flight height. Interestingly, the Moran autocorrelation of aeromagnetic data representing differing flight height, that is spatial scales, decreases with decreasing resolution of source data. The Moran autocorrelation coefficient scems to be another measure of the quality of the aeromagnetic data for predicting exploration targets.     

Study and observation of the great solar event in July 2000 at cusp latitude

A series of solar flare and coronal mass ejection (CME) event occurred in July 2000, particularly the largest flare (X5.7/3B) with CME on 14th of July since 1989, which stimulated a great geomagnetic storm with D st index reaching -300 nT. A number of data have been obtained from the Chinese Antarctic Zhongshan Station (ZHS, INT Lat. 74.5°, L≈14), which is located at cusp latitude, and from the ACE satellite. After analyzing these data we have got the results as follows: a lot of solar high energy particles penetrated into the polar ionosphere and ionized it, which significantly increased the cosmic noise absorption (CNA) and blanked the DPS-4 data for more than two days. The magnetic pulsation in Pc 3/5 frequency band on the ground has a high relation with the fluctuation of interplanetary magnetic field (IMF) B z, which shows the contribution of interplanetary magnetohydrodynamical (MHD) waves to the Pc 3/5 pulsation on the ground. The Pc 3/5 pulsation was intensified much during the great magnetic storm. The H component of the magnetic field at ZHS varied with the southern value of IMF B z but lagged behind for about 8 10 h. While D st index responded to the variation of the IMF B z very quickly, which suggested that the magnetic storm occurred at low latitude firstly and then effected the ionospheric current at high latitude.