We present a global 1‐D conductivity model which is obtained by analysis of five years (2001–2005) of simultaneous magnetic data from the three satellites Ørsted, CHAMP and SAC‐C. After removal of core and crustal fields as predicted by a recent field model we used non‐polar scalar and vector observations from the night‐side sector, and interpret the field residuals in terms of a large‐scale contribution from the magnetospheric ring current and its induced counterpart. We then derive transfer functions between internal (induced) and external expansion coefficients of the magnetic potential and provide globally‐averaged C‐responses in the period range between 14 hours and 4 months. Since the satellite responses are probably influenced by induction in the oceans for periods shorter than a few days, we correct the data for this effect. Interpreting the corrected responses yields a 1‐D conductivity model which is rather similar to models derived from ground‐based data.

We present a new global electrical conductivity model of Earth's mantle. The model was derived by using a novel methodology, which is based on inverting satellite magnetic field measurements from different sources simultaneously. Specifically, we estimated responses of magnetospheric origin and ocean tidal magnetic signals from the most recent Swarm and CHAMP data. The challenging task of properly accounting for the ocean effect in the data was addressed through full three‐dimensional solution of Maxwell's equations. We show that simultaneous inversion of magnetospheric and tidal magnetic signals results in a model with much improved resolution. Comparison with laboratory‐based conductivity profiles shows that obtained models are compatible with a pyrolytic composition and a water content of 0.01 wt % and 0.1 wt % in the upper mantle and transition zone, respectively.

A 3‐D frequency‐domain solution based on a volume integral equation approach has been implemented to simulate induction log responses. In our treatment of the problem, we assume that the electrical properties of the bedding as well as the borehole and invasion zones can exhibit transverse anisotropy. The solution process uses a Krylov subspace iteration to solve the scattering equation, which is based on the modified iterative dissipative method. Internal consistency checks and comparisons with mode matching and finite‐difference solutions for vertical borehole models demonstrate the accuracy of the solution. There are no known analytical solutions for induction log responses arising from deviated boreholes intersecting horizontal bed boundaries. To simulate such responses requires the numerical solution of Maxwell's equations in three dimensions along with independent tests to validate the solution approach and its accuracy. In this paper, we compare two independent 3‐D frequency‐domain solutions for the problem, based on finite differences and the integral equation technique. Specific examples in the quasi‐static limit are studied, including a 45° deviated borehole that intersects formation bed boundaries as well as cases where the bedding exhibits transverse anisotropy. All comparisons made in this paper show very good agreement and demonstrate, for the first time, verifiable induction log responses in the presence of deviated boreholes. We also show that responses arising from deviated boreholes can be significant and must be accounted for properly when interpreting induction logs.

S U M M A R YDuring the last decade a number of one-dimensional (1-D) conductivity profiles have been constructed for the upper and mid-mantle of the North Pacific Ocean region. These profiles differ significantly, and from our point of view it is still unclear which profile is the best candidate for the upper and mid-mantle conductivity reference model for this region. Keeping the differences in mind, and inspired by recent findings that the ocean effect is a major contributor to the anomalous behaviour of C-responses up to the period of 20 days (especially at coastal observatories), the goal of this paper has been three-fold: (1) to understand, on the basis of systematic model studies using 3-D ocean models, which of the published 1-D upper and mid-mantle profiles is in best agreement with the available observations. (2) To try to reduce the misfit between the observed and modelled responses by using dense grids in modelling, by considering 3-D models which include not only an inhomogeneous surface layer but also inhomogeneous deeper structures. (3) To derive an alternative 1-D upper and mid-mantle section for the North Pacific Ocean by carefully selecting the data for interpretation and by using 3-D models that are as realistic and detailed as possible.In order to perform the simulations using realistic 3-D models on a routine basis a novel 3-D 'spherical' forward solution has been elaborated in this paper. The solution combines the modified iterative-dissipative method with a conjugate gradient iteration and allows one to compute efficiently the electromagnetic fields in full 3-D spherical models with very high lateral contrasts of conductivity and for very dense grids.During the 3-D simulations a systematic shift of observed C-responses at Honolulu compared with those at other observatories was detected. The reason for this shift is still unclear. Even if a very detailed grid of 0.3 • × 0.3 • is used, the 3-D simulations using a model of the inhomogeneous surface has no notable ocean effect to C-responses at this site.An attempt has been made to reduce the misfit between observed and modelled C-responses by incorporating a 3-D model with inhomogeneous lithosphere and upper mantle. However, this has resulted only in a slight change in responses.The main conclusion drawn from our 3-D model studies is that there exists a significant disagreement between observed and 3-D modelled C-responses if the published 1-D sections with conducting uppermost 400 km are considered as the upper and mid-mantle sections. Our 3-D simulations and reinterpretation of the data also confirm the recent finding that the upper and mid-mantle beneath North Pacific Ocean in the depth range down to 400 km is much more resistive than hitherto assumed.

At coastal sites, geomagnetic variations for periods shorter than a few days are strongly distorted by the conductivity of the nearby sea-water. This phenomena, known as the ocean (or coast) effect, is strongest in the magnetic vertical component. We demonstrate the ability to predict the ocean effect of geomagnetic storms at geomagnetic observatories. The space-time structure of the storm is derived from the horizontal components at worldwide distributed observatories from which we predict the vertical component using a model of the Earth's conductivity that a) only depends on depth, and b) includes the conductivity of the sea-water. The results for several strong geomagnetic storms (including the "Bastille Day" event of July [14][15] 2000) show much better agreement (improvement by up to a factor of 2.5) between the observed and the modeled magnetic vertical component at coastal sites if the oceans are considered. Our analysis also indicates a significant local time asymmetry (i.e., contributions from spherical harmonics other than P 0 1 ), especially during the main phase of the storm.

Ocean flow moves sea water through the Earth's magnetic field, inducing electric fields, currents and secondary magnetic fields. These motionally induced magnetic fields have a potential for the remote sensing of ocean flow variability. A first goal must be to gain a better understanding of magnetic field generation by tidal ocean flow. We predict the motionally induced magnetic fields for the six major tidal constituents and compare their amplitudes with the spectra of night time observatory and satellite magnetic measurements for the Indian Ocean. The magnetic variations at the solar S2, K1, and P1 periods turn out to be dominated by unrelated external fields. In contrast, observed lunar M2 and N2 tidal signals are in fair agreement with predictions from motional induction. The lunar diurnal O1 signal, visible at some observatories, could be caused by ocean flow but disagrees in amplitude with our predictions.

We present a new, accurate, high-performance, wide-band three-dimensional (3-D) solver for the electromagnetic (EM) field scattering problem in an isotropic earth. The solver relates to those based on the volume integral equation (IE) approach and exploits a modified Neumann series (MNS) technique to solve Maxwell's equations. The solver allows for the conduction, polarization and displacement currents to be taken into account and admits for 3-D earth excitation by arbitrary electric or/and magnetic sources.We estimate the solver efficiency for scatterers discretized into N x N,, x N. prisms, where it requires only about 6NXNYNZ (log2(2NN) log2(2Ny) + 6N) multiplications to get one term of the MNS expansion and about 200 NXNVNZ2 bytes of memory. Our experience show that the number of terms N which are to be summed up to get the solution to 1% accuracy doesn't exceed fifty for the models with the conductivity contrast of up to 100.We demonstrate the solver versatility for magnetotellurics (MT) and controlled-source simulations. EM fields arising from a 3-D model with two high-contrast thin layers residing in layered earth were simulated due to a 10 Hz electric dipole located at the surface. When the layers were discretized into 16,384 prisms our code on a Pentium-100 MHz took T ti 58 minutes, M -7 Mbytes and N -280. We also modeled the 0.1 Hz and 0.01 Hz MT responses within 3-D model with 1 ftm and 100 1Lm blocks. When the blocks were discretized into 8,000 prisms the code took T -5 minutes, M -8 Mbytes, and N n-25. Finally fields for a crosswell model including a 3-D conducting target were simulated for 0.1 kHz and 10 kHz electric and magnetic dipoles in the wellbores. While the target was discretized into 6,250 prisms the code took T '-16 minutes, M -' 13 Mbytes, and N -24. All simulations showed from very good to excellent agreement with those of the other 3-D solvers.

Swarm, a satellite constellation to measure Earth's magnetic field with unpreceded accuracy, has been selected by ESA for launch in 2009. The mission will provide the best ever survey of the geomagnetic field and its temporal evolution, in order to gain new insights into the Earth system by improving our understanding of the Earth's interior and climate. An End-to-End mission performance simulation was carried out during Phase A of the mission, with the aim of analyzing the key system requirements, particularly with respect to the number of Swarm satellites and their orbits related to the science objectives of Swarm. In order to be able to use realistic parameters of the Earth's environment, the mission simulation starts at January 1, 1997 and lasts until re-entry of the lower satellites five years later. Synthetic magnetic field values were generated for all relevant contributions to Earth's magnetic field: core and lithospheric fields, fields due to currents in the ionosphere and magnetosphere, due to their secondary, induced, currents in the oceans, lithosphere and mantle, and fields due to currents coupling the ionosphere and magnetosphere. Several independent methods were applied to the synthetic data to analyze various aspects of field recovery in relation to different number of satellites, different constellations and realistic noise sources. This paper gives an overview of the study activities, describes the generation of the synthetic data, and assesses the obtained results.