Eccentric Dipole Research Articles

Universal Time Variations in the Magnetosphere and the Effect of CME Arrival Time: Analysis of the February 2022 Event that Led to the Loss of Starlink Satellites

AbstractWe study Universal Time (UT) variations in the magnetospheric response to Coronal Mass Ejection (CME) impacts, using the example of the two CMEs that led to the destruction of 38 out of 49 Starlink satellites in early February 2022. We employ the Expanding‐Contracting Polar Cap model to analyze the variation in the size of the ionospheric polar caps and an eccentric dipole model of the geomagnetic field and thereby quantify the UT variations caused by the inductive effect of the diurnal motions of the geomagnetic poles in a “geocentric‐solar” frame of reference (i.e., a frame with an X axis that points from the center of the Earth to the center of the Sun). The results show that use of a quasi‐steady convection model predicts a similar global power deposition into the thermosphere as that inferred here, but does not give the same division of that power between the northern and southern hemispheres. We demonstrate that, through the combined effects of the Russell‐McPherron dipole‐tilt mechanism on solar‐wind magnetosphere coupling and of the diurnal polar cap motions in a geocentric‐solar frame, the power deposited varies significantly with the arrival UT of the CMEs at Earth. We also show that in the events of early February 2022, both CMEs arrived at almost the optimum UT to cause maximum thermospheric heating.

Universal Time variations in the magnetosphere

We study the dependencies of Earth’s magnetosphere on Universal Time, UT. These are introduced because Earth’s magnetic axis is not aligned with the rotational axis and complicated because it is eccentric, which makes the offset of the magnetic and rotation poles considerably greater in the Southern hemisphere and the longitudinal separation of the magnetic poles less than 180°: hence consequent UT variations in the two hemispheres are not in equal in amplitude nor in exact antiphase and do not cancel, as they would for a geocentric dipole. We use long series of a variety of geomagnetic data to demonstrate the inductive effect of motions of the polar caps in a “geocentric-solar” frame, which is phase-locked to the Russell-McPherron (R-M) effect on solar-wind magnetosphere coupling. This makes the response of the magnetosphere-ionosphere system different for the two polarities of the Y-component of the Interplanetary Magnetic Field in the GSEQ reference frame, explaining the difference in response to the March and September equinox peaks in solar wind forcing. The sunward/antisunward pole-motion effect is detected directly in satellite transpolar voltage data and is shown to have a greater effect on the geomagnetic data than the full dipole tilt effect which generates the equinoctial pattern, the potential origins of which are discussed in terms of the dipole tilt effect on ionospheric conductivities and the stability of the near-Earth tail. Persistent UT variations in Region-1 and Region-2 field-aligned currents and in partial ring current indices are presented: their explanation is an important challenge for numerical modelling of the magnetosphere-ionosphere-thermosphere system which we need to quantify the relative contributions of the various mechanisms and to give understanding of the effect of arrival time on the response of the system to large, geoeffective disturbances in interplanetary space.Plain language summary: The effect on terrestrial space weather of Earth’s magnetic axis not being aligned with the rotational axis is investigated. It is complex because not only do these two axes not align in direction (the “dipole tilt”), the magnetic axis does not pass through the centre of the Earth, which sets a requirement for an “eccentric” model of the field and not the commonly-used “geocentric” one. For many years, it has been known that the dipole tilt gives a peak in geomagnetic activity at the equinoxes (the semi-annual variation) through the “Russell-McPherron” (R-M) effect. However, although the variation with Universal Time is consistent with the R-M effect for the September equinox, it is not for the March equinox. We here solve this long-standing puzzle by investigating the effects of the motions of the two poles in a frame fixed with respect to both the Earth and the Sun for an eccentric dipole model. But solving one puzzle generates many others. We present observations of the Universal Time variations that these mechanisms combine to generate, which set an important challenge to the numerical modelling of the near-Earth space environment.

Borehole radiation and reception responses for azimuthal shear-wave reflection imaging with an off-centred dipole acoustic tool

Abstract Radiation and reception responses of a dipole acoustic logging tool placed eccentrically in borehole fluid are an interesting and important topic in acoustic reflection imaging. Herein, we present a thorough research study on these responses. We treat the wave incidence from the reflector as the radiation from a virtual source and use the cylindrical-wave expansion method to solve both the wave radiation and reception problems for the off-centred tool, which, by using the steepest-descent method, yields asymptotic solutions for modelling the radiation and reception wavefield characteristics. The modelling results from the analytical solution and the 3D finite-difference method were in good agreement. Specifically, we analysed the radiation directivity of an eccentric dipole source in a fluid-filled borehole. The results revealed that the radiation pattern was asymmetric with respect to the borehole, and the asymmetry was determined by the eccentric distance, source frequency and formation properties. In particular, for the typical 3 kHz dipole logging frequency, the radiation was stronger in the off-centred direction than in the opposite direction. The asymmetry of the eccentric radiation resulted in a significant amplitude difference relative to its centred counterpart, which provided a potential method for addressing the 180° azimuth ambiguity of the dipole source. We used a theoretical waveform modelling example to demonstrate this advantage. Therefore, the results of this study provide a theoretical foundation for the development and application of dipole shear-wave imaging technology.

A New Technique to Diagnose the Geomagnetic Field Based on a Single Circular Current Loop Model

AbstractThe geomagnetic field originates from interior dynamo currents and can be approximated well by a simple dipolar field in the vicinity of Earth's surface. Given that the dipolar field is induced by a current loop, it is possible to invert the loop parameters by tracing the sampled magnetic field geometry. Drawing on the analysis of field geometric structure with sampled field dataset, we develop, in this study, a new technique to invert the interior current source, which is based on a single circular current loop model. Unlike previous studies, this technique has the ability to separate and solve the optimal loop parameters successively, including the location of the loop center, the loop axis, the radius, and the carried electric current. Applications to the International Geomagnetic Reference Field and the sampled magnetic field dataset by the spacecraft of the Swarm mission demonstrate that our technique‐derived loop center, loop axis, and magnetic moment are consistent with previous estimations by the eccentric dipole model, which shows the reasonability and effectiveness of this technique. Moreover, our technique can be reduced to fit an eccentric dipole model and is particularly useful for inversions of the geometry of interior current sources. Thus, it could be applied widely in the fields of planetary magnetism and palaeomagnetism. Further applications and constraints are discussed, with some cautions given.

Eccentric Dipole Evolution during the Last Reversal, Last Excursions, and Holocene Anomalies. Interpretation Using a 360-Dipole Ring Model

The eccentric dipole (ED) is the next approach of the geomagnetic field after the generally used geocentric dipole. Here, we analyzed the evolution of the ED during extreme events, such as the Matuyama-Brunhes polarity transition (~780 ka), the Laschamp (~41 ka) and Mono Lake (~34 ka) excursions, and during the time of two anomalous features of the geomagnetic field observed during the Holocene: the Levantine Iron Age Anomaly (LIAA, ~1000 BC) and the South Atlantic Anomaly (SAA, analyzed from ~700 AD to present day). The analysis was carried out using the paleoreconstructions that cover the time of the mentioned events (IMMAB4, IMOLEe, LSMOD.2, SHAWQ-Iron Age, and SHAWQ2k). We found that the ED moves around the meridian plane of 0–180° during the reversal and the excursions; it moves towards the region of the LIAA; and it moves away from the SAA. To investigate what information can be extracted from its evolution, we designed a simple model based on 360-point dipoles evenly distributed in a ring close to the inner core boundary that can be reversed and their magnitude changed. We tried to reproduce with our simple model the observed evolution of the ED, and the total field energy at the Earth’s surface. We observed that the modeled ED moves away from the region where we set the dipoles to reverse. If we consider that the ring dipoles could be related to convective columns in the outer core of the Earth, our simple model would indicate the potential of the displacement of the ED to give information about the regions in the outer core where changes start for polarity transitions and for the generation of important anomalies of the geomagnetic field. According to our simple model, the regions in which the most important events of the Holocene occur, or in which the last polarity reversal or excursion begin, are related to the regions of the Core Mantle Boundary (CMB), where the heat flux is low.

Semi-annual, annual and Universal Time variations in the magnetosphere and in geomagnetic activity: 4. Polar Cap motions and origins of the Universal Time effect

We use theam,an, asand theaσgeomagnetic indices to the explore a previously overlooked factor in magnetospheric electrodynamics, namely the inductive effect of diurnal motions of the Earth’s magnetic poles toward and away from the Sun caused by Earth’s rotation. Because the offset of the (eccentric dipole) geomagnetic pole from the rotational axis is roughly twice as large in the southern hemisphere compared to the northern, the effects there are predicted to be roughly twice the amplitude of those in the northern hemisphere. Hemispheric differences have previously been discussed in terms of polar ionospheric conductivities generated by solar photoionization, effects which we allow for by looking at the dipole tilt effect on the time-of-year variations of the indices. The electric field induced in a geocentric frame is shown to also be a significant factor and gives a modulation of the voltage applied by the solar wind flow in the southern hemisphere that is typically a ±30% diurnal modulation for disturbed intervals rising to ±76% in quiet times. For the northern hemisphere these are 15% and 38% modulations. Motion away from/towards the Sun reduces/enhances the directly-driven ionospheric voltages and reduces/enhances the magnetic energy stored in the tail and we estimate that approximately 10% of the effect appears in directly driven ionospheric voltages and 90% in changes of the rate of energy storage or release in the near-Earth tail. The hemispheric asymmetry in the geomagnetic pole offsets from the rotational axis is shown to be the dominant factor in driving Universal Time (UT) variations and hemispheric differences in geomagnetic activity. Combined with the effect of solar wind dynamic pressure and dipole tilt on the pressure balance in the near-Earth tail, the effect provides an excellent explanation of how the observed Russell-McPherron pattern with time-of-yearFandUTin the driving power input into the magnetosphere is converted into the equinoctialF-UTpattern in average geomagnetic activity (after correction is made for dipole tilt effects on ionospheric conductivity), added to a pronouncedUTvariation with minimum at 02–10 UT. In addition, we show that the predicted and observedUTvariations in average geomagnetic activity has implications for the occurrence of the largest events that also show the nettUTvariation.

Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic field models by dynamo simulations

The IGRF offers an important incentive for testing algorithms predicting the Earth’s magnetic field changes, known as secular variation (SV), in a 5-year range. Here, we present a SV candidate model for the 13th IGRF that stems from a sequential ensemble data assimilation approach (EnKF). The ensemble consists of a number of parallel-running 3D-dynamo simulations. The assimilated data are geomagnetic field snapshots covering the years 1840 to 2000 from the COV-OBS.x1 model and for 2001 to 2020 from the Kalmag model. A spectral covariance localization method, considering the couplings between spherical harmonics of the same equatorial symmetry and same azimuthal wave number, allows decreasing the ensemble size to about a 100 while maintaining the stability of the assimilation. The quality of 5-year predictions is tested for the past two decades. These tests show that the assimilation scheme is able to reconstruct the overall SV evolution. They also suggest that a better 5-year forecast is obtained keeping the SV constant compared to the dynamically evolving SV. However, the quality of the dynamical forecast steadily improves over the full assimilation window (180 years). We therefore propose the instantaneous SV estimate for 2020 from our assimilation as a candidate model for the IGRF-13. The ensemble approach provides uncertainty estimates, which closely match the residual differences with respect to the IGRF-13. Longer term predictions for the evolution of the main magnetic field features over a 50-year range are also presented. We observe the further decrease of the axial dipole at a mean rate of 8 nT/year as well as a deepening and broadening of the South Atlantic Anomaly. The magnetic dip poles are seen to approach an eccentric dipole configuration.

Spatial features of geomagnetic cutoff rigidity secular variation using analytical approaches

The secular variation spatial pattern of geomagnetic cutoff rigidity, Rc, is analyzed considering analytical expressions. Störmer analytic Rc equation in terms of geomagnetic latitude is used considering a pure dipolar field for the centered and eccentric dipole coordinates, together with a dipole-quadrupole superposition simplified equation. Linear Rc time trend for the period 1900–2020 in a 5 ° × 15 ° latitude-longitude grid is assessed in each case and a comparative analysis is made with trends based on trajectory based Rc estimations. Common features with some analytic approaches are the two patches of Rc positive and negative trends in the western hemisphere, even though maximum and minimum trend values are underestimated in all analytical cases. Global mean values are almost coincident, except for the dipole-quadrupole superposition case. The salient patches pattern may be due mainly to the dipole axis rotation, more than to its center displacement, its decreasing momentum or the increasing quadrupolar component role. Even though with the advent of better computational tools the trajectory based estimation would be a natural choice to analyze Rc variations, we still consider that an appropriately modified Störmer equation, with its natural advantages of its analytical form and extremely fast way of computation, is sufficient for many applications.

Two-dipole model of the asymmetric Sun

The large-scale photospheric magnetic field is commonly thought to be mainly dipolar during sunspot minima, when magnetic fields of opposite polarity cover the solar poles. However, recent studies show that the octupole harmonics contribute comparably to the spatial power of the photospheric field at these times. Also, the even harmonics are non-zero, indicating that the Sun is hemispherically asymmetric with systematically stronger fields in the south during solar minima. We present here an analytical model of two eccentric axial dipoles of different strength, which is physically motivated by the dipole moments produced by decaying active regions. With only four parameters, this model closely reproduces the observed large-scale photospheric field and all significant coefficients of its spherical harmonics expansion, including the even harmonics responsible for the solar hemispheric asymmetry. This two-dipole model of the photospheric magnetic field also explains the southward shift of the heliospheric current sheet observed during recent solar minima.

On the Influence of the Earth's Magnetic Dipole Eccentricity and Magnetospheric Ring Current on the Magnetopause Location

AbstractWe investigate the influence of two typically unconsidered parameters—Earth's magnetic dipole eccentricity and ring current—on the location of the magnetopause. Although empirical magnetopause models generally assume the Earth's magnetic field to be axially symmetric, the terrestrial magnetic dipole is shifted by as much as 500 km out of the Earth's center. Additionally, the magnetic field at the magnetopause is further modified by magnetospheric currents, most importantly by the ring current. In order to quantify the effects related to these phenomena on the magnetopause location, we compare observed magnetopause distances with model distances calculated using a model, which does not take them into account. International Geomagnetic Reference Field is used to describe the dipole eccentricity and relevant multipoles, which results in a statistically observable magnetopause displacement (≈0.2RE) at locations where the magnetic field strength increases/decreases as compared to the dipole field. Additionally, the magnetic field at the magnetopause is modified by the ring current, becoming stronger at the times of a stronger ring current. We use the corrected Dst* index to describe the ring current strength, and we demonstrate that its variation results in a change of the magnetopause stand‐off distance as large as about 0.8RE. We further use the T96 magnetic field model to estimate the total contribution of magnetospheric currents to the magnetic field at the magnetopause and their effects on the magnetopause location. We suggest empirical relations that can be used to incorporate the obtained dependences into existing empirical models of magnetopause location.

Weak Measurement of Elliptical Dipole Moments by C-Point Splitting.

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric dipoles, the C points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-field polarization basis. Projecting the far field onto a spatially varying postselected polarization state reveals the angular separation and the helicity of the C points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the C points in its far field.

An Update on the Centered and Eccentric Geomagnetic Dipoles and Their Poles for the Years 1980–2015

AbstractThis paper is an update and extension of an earlier study of the centered and eccentric dipole models of the Earth's magnetic field. We use the 1980–2015 IGRF Gauss coefficients to recalculate the magnetic dipole moments and pole positions for both the centered and eccentric dipoles for an additional 35 years. The changes that have taken place are mostly extensions of the trends described earlier. Interestingly, the earlier weak suggestion of an accelerated decline in the magnetic moment over the interval 1975–1985 persists in the more recent data; if the current decline for the years 2000–2015 continues, the Earth's field is projected to decline to nothing around the year 3797 A.D. This projected decline to zero field will almost certainly not occur on this date, but it is of interest because the timescale for the decline is remarkably short compared with the timescales derived for past field reversals. The asymmetry of the Earth's field continues to increase quite rapidly, with the offset of the equivalent dipole from the Earth's center now close to 9% of the Earth's radius. Since we now know that all the planets in our solar system with global magnetic fields have asymmetric fields that can be modeled more accurately as eccentric dipole fields, and not as centered dipole fields, the eccentric dipole analysis reported here can now be viewed more generally as an approach to planetary magnetic fields and not just to the magnetic field of our own planet.

The South Atlantic Anomaly throughout the solar cycle

The Sun–Earth's interaction is characterized by a highly dynamic electromagnetic environment, in which the magnetic field produced in the Earth's core plays an important role. One of the striking characteristics of the present geomagnetic field is denoted the South Atlantic Anomaly (SAA) where the total field intensity is unusually low and the flux of charged particles, trapped in the inner Van Allen radiation belts, is maximum. Here, we use, on one hand, a recent geomagnetic field model, CHAOS-6, and on the other hand, data provided by different platforms (satellites orbiting the Earth – POES NOAA for 1998–2014 and CALIPSO for 2006–2014). Evolution of the SAA particle flux can be seen as the result of two main effects, the secular variation of the Earth's core magnetic field and the modulation of the density of the inner radiation belts during the solar cycle, as a function of the L value that characterises the drift shell, where charged particles are trapped. To study the evolution of the particle flux anomaly, we rely on a Principal Component Analysis (PCA) of either POES particle flux or CALIOP dark noise. Analysed data are distributed on a geographical grid at satellite altitude, based on a L-shell reference frame constructed from the moving eccentric dipole. Changes in the main magnetic field are responsible for the observed westward drift. Three PCA modes account for the time evolution related to solar effects. Both the first and second modes have a good correlation with the thermospheric density, which varies in response to the solar cycle. The first mode represents the total intensity variation of the particle flux in the SAA, and the second the movement of the anomaly between different L-shells. The proposed analysis allows us to well recover the westward drift rate, as well as the latitudinal and longitudinal solar cycle oscillations, although the analysed data do not cover a complete (Hale) magnetic solar cycle (around 22 yr). Moreover, the developments made here would enable us to forecast the impact of the South Atlantic Anomaly on space weather. A model of the evolution of the eccentric dipole field (magnitude, offset and tilt) would suffice, together with a model for the solar cycle evolution.

THE DECADE-LONG INSTABILITIES IN EARTH’S ROTATION AS EVIDENCE OF LITHOSPHERIC DRIFT OVER THE ASTENOSPHERE

The decade instabilities in Earth’s rotation (DIER) are usually explained by the interactions of the Earth’s core and mantle. This hypothesis explains well a close correlation between DIER and the variations in the rate of the westward drift of the geomagnetic eccentric dipole; it corresponds quite reasonably to the possible redistribution of the angular momentum between the fluid core and the mantle of the Earth. however, the hypothesis can not explain the close correlations of DIER with the observable variations in the masses of the Antarctic andGreenlandice sheets, with the decade oscillations of the types of synoptic processes (the epochs of the atmospheric circulation), with the anomalies of the global temperature, regional anomalies of the cloudiness, precipitation, and other climatic characteristics. It is supposed that the DIER are the fluctuations of the velocity of the lithosphere driftage along the asthenosphere. The sliding of the lithosphere over the asthenosphere is possible due to of the vibratory displacement mechanism by tidal forces. The consequences following from this hypothesis are discussed.

Rethinking the polar cap: Eccentric dipole structuring of ULF power at the highest corrected geomagnetic latitudes

AbstractThe day‐to‐day evolution and statistical features of Pc3‐Pc7 band ultralow frequency (ULF) power throughout the southern polar cap suggest that the corrected geomagnetic (CGM) coordinates do not adequately organize the observed hydromagnetic spatial structure. It is shown that that the local‐time distribution of ULF power at sites along CGM latitudinal parallels exhibit fundamental differences and that the CGM latitude of a site in general is not indicative of the site's projection into the magnetosphere. Thus, ULF characteristics observed at a single site in the polar cap cannot be freely generalized to other sites of similar CGM latitude but separated in magnetic local time, and the inadequacy of CGM coordinates in the polar cap has implications for conjugacy/mapping studies in general. In seeking alternative, observationally motivated systems of “polar cap latitudes,” it is found that eccentric dipole (ED) coordinates have several strengths in organizing the hydromagnetic spatial structure in the polar cap region. ED latitudes appear to better classify the local‐time ULF power in both magnitude and morphology and better differentiate the “deep polar cap” (where the ULF power is largely UT dependent and nearly free of local‐time structure) from the “peripheral polar cap” (where near‐magnetic noon pulsations dominate at lower and lower frequencies as one increases in ED latitude). Eccentric local time is shown to better align the local‐time profiles in the magnetic east component over several PcX bands but worsen in the magnetic north component. It is suggested that a hybrid ED‐CGM coordinate system might capture the strengths of both CGM and ED coordinates. It is shown that the local‐time morphology of median ULF power at high‐latitude sites is dominantly driven by where they project into the magnetosphere, which is best quantified by their proximity to the low‐altitude cusp on the dayside (which is not necessarily quantified by a site's CGM latitude), and that variations in the local‐time morphology at sites similar in ED latitude are due to both geographic local‐time control (relative amplification or dampening by the diurnal variation in the local ionospheric conductivity) and geomagnetic coastal effects (enhanced power in a coastally mediated direction). Regardless of cause, it is emphasized that the application of CGM latitudes in the polar cap region is not entirely meaningful and likely should be dispensed with in favor of a scheme that is in better accord with the observed hydromagnetic spatial structure.

Kelvin's article on the magnetic centre and Schmidt's one on the optimal eccentric dipole, revisited

Thomson's formulas (1872) that give the position of the magnetic centre of a magnet and the first results on the global geomagnetic field were sufficient to show that the source of this field had a disymmetry in the equatorial plane. To confirm this with Schmidt's (1934) explicit formulas giving the position of the optimal eccentric dipole, numerical calculus was necessary. To obtain their relatively simple formulas, Thomson and Schmidt used lengthy algebra that was avoidable.

Comparison of equatorial plasma mass densities deduced from field line resonances observed at ground for dipole and IGRF models

AbstractThe technique to remotely sense the plasma mass density in magnetosphere using field line resonance frequencies detected by ground‐based magnetometers has become more and more popular in the last few years. In this paper we examine the error that would be committed at low and middle latitudes (L < 4) in estimating the equatorial plasma mass density if dipole field lines are assumed instead of the more realistic representation given by International Geomagnetic Reference Field (IGRF) lines. It is found that the use of the centered dipole model may result in an error in the inferred density appreciably larger than what is usually assumed. In particular, it has a significant longitudinal dependence being, for example, greater than +30% in the Atlantic sector and about −30% at the opposite longitude sector for field lines extending to a geocentric distance of 2 Earth radii. This may result in an erroneous interpretation of the longitudinal variation in plasmaspheric density when comparing results from ground‐based arrays located at different longitudes. We also propose simple modifications of the standard technique, such as the use of an effective dipole moment or the eccentric dipole model, which allow to keep using the dipole field geometry but with a significant error reduction.

Dipole sources of the main geomagnetic field

The parameters of 15 arbitrary dipoles that, in aggregate, represent the main geomagnetic field (MGF) are estimated to obtain information on the distribution of MGF sources within the Earth in the form of dipoles with an arbitrary position and value of the magnetic moment vector. For an adequate estimation of the results, the method of obtaining the data is described, including: the eccentric dipole model and the derivation of the basic formulas for the magnetic field components of an arbitrary dipole; the method of estimating the parameters of these dipoles, including the computational scheme and optimization method; necessary constraints on the dipoles parameters and a justification of the choice of the initial values in the optimization fitting of the parameters. The results are presented as a map of the location of the centers of the dipoles and their northern axial poles for the epochs 1955 and 2005 and plots of changes in all six parameters of 15 dipoles for 50years. Most of the dipole centers are located in the lower mantle. The results suggest the existence of current systems in the lower mantle that produce dipole magnetic fields. These currents are provided by the high conductivity of wustite, an important component of the mantle, which, at a depth of 1000-2200km, transforms to the low-spin state of iron with increased density and electrical conductivity.

First results of operational ionospheric dynamics prediction for the Brazilian Space Weather program

It is shown the development and preliminary results of operational ionosphere dynamics prediction system for the Brazilian Space Weather program. The system is based on the Sheffield University Plasmasphere–Ionosphere Model (SUPIM), a physics-based model computer code describing the distribution of ionization within the Earth mid to equatorial latitude ionosphere and plasmasphere, during geomagnetically quiet periods. The model outputs are given in a 2-dimensional plane aligned with Earth magnetic field lines, with fixed magnetic longitude coordinate. The code was adapted to provide the output in geographical coordinates. It was made referring to the Earth’s magnetic field as an eccentric dipole, using the approximation based on International Geomagnetic Reference Field (IGRF-11). During the system operation, several simulation runs are performed at different longitudes. The original code would not be able to run all simulations serially in reasonable time. So, a parallel version for the code was developed for enhancing the performance. After preliminary tests, it was frequently observed code instability, when negative ion temperatures or concentrations prevented the code from continuing its processing. After a detailed analysis, it was verified that most of these problems occurred due to concentration estimation of simulation points located at high altitudes, typically over 4000km of altitude. In order to force convergence, an artificial exponential decay for ion–neutral collisional frequency was used above mentioned altitudes. This approach shown no significant difference from original code output, but improved substantially the code stability. In order to make operational system even more stable, the initial altitude and initial ion concentration values used on exponential decay equation are changed when convergence is not achieved, within pre-defined values. When all code runs end, the longitude of every point is then compared with its original reference station longitude, and differences are compensated by changing the simulation point time slot, in a temporal adjustment optimization. Then, an approximate neighbor searching technique was developed to obtain the ion concentration values in a regularly spaced grid, using inverse distance weighting (IDW) interpolation. A 3D grid containing ion and electron concentrations is generated for every hour of simulated day. Its spatial resolution is 1° of latitude per 1° of longitude per 10km of altitude. The vertical total electron content (VTEC) is calculated from the grid, and plotted in a geographic map. An important feature that was implemented in the system is the capacity of combining observational data and simulation outputs to obtain more appropriate initial conditions to the ionosphere prediction. Newtonian relaxation method was used for this data assimilation process, where ionosonde data from four different locations in South America was used to improve the system accuracy. The whole process runs every day and predicts the VTEC values for South America region with almost 24h ahead.

Wavefield simulation and analysis with the finite-element method for acoustic logging while drilling in horizontal and deviated wells

We developed a frequency-domain finite-element method (FFEM) in conjunction with a complex-frequency-shifted perfectly matched layer (CFS-PML) boundary to effectively study the wavefield generated by acoustic multipole logging-while-drilling (LWD) tools in horizontal and highly deviated wells. With such an FFEM, the sources and receivers can be easily set symmetrically in the simulation to model the real tools exactly, while this is very difficult to deal with in the finite-difference method. In addition, the CFS-PML boundaries can be implemented more efficiently in this algorithm. We applied this method to study the effects of tool eccentricity on the measurements in slow formations that most likely need 3D solutions for LWD in horizontal and highly deviated wells. We found that because the tool cannot be centralized in these wells, some nonmonopole modes could appear in monopole measurements and the Stoneley mode could appear in dipole measurements; the flexural collar wave could become increasingly strong with an increase of tool eccentricity, and the Stoneley mode may be the later arriving event, especially in the case of a severely eccentric quadrupole tool. Based on these studies, we introduced a method to quantify the extent and the angle of the tool eccentricity with the phase difference in eccentric dipole measurements. These parameters are very useful for the analysis of the bottom-hole assembly performance in geosteering.