TECTONICS BLOG Rev. 01/03/2026

Click on an image to enlarge it Figure 1. This NASA short video captures the variable nature of Earth’s geomagnetic field as it responds to magnetic induction from the solar winds. ole and positive north one Figure 2. The physical nature of Earth's external magnetic field is captured in this NASA video gained from their 1992-2004 SAMPEX mission. The radiation belts are mapped using false colors to highlight relative densities of trapped electromagnetic particles from the solar winds. Click on the image to watch the video. Figure 3. The geomagnetic field equipotential lines mapped over time showing wander of Earth's poloid dipole moment over the past four centuries. The rate of polar drift has increased over the past decade. Figure 4. The external magnetic-field expression includes inner and outer (Van Allen) radiation belts. The inner belt (poloid moment) is a pulsating, asymmetric loop surrounded by the steady outer belt (toroid moment). A SAMPEX image from 09/07/2012 was used as the basis to conduct a comparative 2D area and 3D volumetric analysis of the respective geomagnetic field components using the SketchUp Pro 2024 architectural computer-aided drafting program. Figure 5. The 2D components of the geomagnetic field were digitized using false-color L-shell mapping of Earth’s radiation belts by NASA. Each 2D component was then revolved around the z-rotation axis to generate the respective 3D elements. The various components of the inner and outer radiation belts were then correlated with the toroid and poloid dipole field components and associated outer core and mantle structures responsible for generating them. Inner and outer radiation belts extend outward beyond its surface to variable limits depending upon temporal induction from the Solar winds. On 09/07/2012, the visible limits extend to ~ 7 L. Figure 6. A SAMPEX base image for 10-29-2023 (A. and B.) was used to derive the respective poloid (C.) and toroid (D.) dipole moments of the total field. Volume totals for both dipole moments were calculated by subtracting the inner and outer components. Figure 7.  A graphical summary of the various 2D and 3D geospatial components of the total field from which the respective areas (km2) and volumes (km3) were derived (table 1). Figure 8. 3D volumetric shells representing Earth's external magnetic field were sliced in half in order to visualize their relative extents and overlapping, interfering nature. Figure 9. Click on the image to open a short video highlighting the 3D nature of Earth's electromagnetic field.   Figure 10. Outer-core structures from the top resemble a six-shooter cylinder. The surface traces of the outside cylinders form tear-drop shaped gyres at the core-mantle boundary where two core-anchor structures form the base of overlying mantle plumes. Click on the image to play a short video highlighting the 3D structure of Earth's core. Figure 11. The southern hemisphere holds about 70% of basic, electromagnetically conductive plume material. The W hemisphere also has more connected material then the E when split along the S68W-N68E longitudinal at a percentage of ~57:43. These volumetric dichotomies account for the normal polarity of the total field (negative south pole) and why the magnetic field pulsates on a daily basis.

Gregory Charles Herman, PhD
Flemington, New Jersey, USA

The Structure of Earth's Geodynamo

Earths external radiation belts * Correlation of Earths' core and mantle structures with the toroid and poloid dipole moments * Outer core structure and the toroid dipole moment * Mantle-plume hemispheric heterogeneity and the poloid dipole moment * Summary * References 

Introduction

Albert Einstein considered the nature of Earth's magnetic field to be one of the five most important unsolved problems in physics (Herndon, 2022). This blog uses NASA satellite imagery of Earth's external radiation belts to identify and volumetrically model the fixed toroid and variable poloid dipole components of its quadrupole total field (figs. 1 to 4). The respective dipole components are then compared with the volume of Earth's core and mantle structures that likely generate the two overlapping, dipole moments. A spinning, metallic sphere can potentially have three dipole moments arising from 1) intrinsic charges (Q) held in the solid parts, 2) by spinning a charged body about a rotation pole (rot), and 3) from the coordinated alignment of electron spin when possible (spin). The former two occur in solid and semi-solid media whereas the latter occurs more commonly in fluid media. The interior structure of Earth includes the solid inner core, the fluid outer core shell, and the semi-solid mantle shell that's 'wired' with basic mantle plumes physically connected to the outer core (fig. 5). Each of these structures have a corresponding electromagnetic dipole moment arising from some combination of the three potential moment sources. This is expressed mathematically using the following premises and approach. Computer modeling used Trimble Inc.'s SketchUp Pro 2024 (SUP) architectural software (SUP).

Geospatial and volumetric aspects of Earth's geomagnetic field based on NASA satellite sensing of its external radiation belts

The U.S. National Space and Aeronautical Administration (NASA) releases short videos that characterize the geospatial and temporal nature of Earth's external radiation belts gained from their 2012-2020 SAMPEX mission (figs. 1 and 2). The inner radiation belt pulsates on a daily basis and they continuously fluctuate in extent depending upon the intensity of the solar winds and Earth's inductive response (fig. 2). A snapshot of the SAMPEX-sampled radiation belts from 09/07/2012 was used to quantify their 2D and 3D components based on their false-color representation that highlights regions in space surrounding Earth where various atomic particles in the Solar winds get trapped and temporarily held by the radiation belts. My interpretation of the SAMPEX data into the two, main, poloid and toroid dipole components is summarized in figures 4 to 9. As summarized in figure 6, the toroid moment envelopes the smaller poloid and is estimated to be about three times as large. Figures 8 and 9 show how the respective total-field components overlap.

Correlation of Earth's outer core and mantle plumes with the toroid and poloid dipole moments of the total geomagnetic field

The inner and outer radiation belts highlight two main components of Earth's geomagnetic field including the stable, larger toroid moment and the wandering, smaller poloid moment. The outer radiation belt is correlated with the toroid moment as its larger, steadier, and appears to be influenced by the smaller and variable poloid moment where the two field components overlap. The inner radiation belt is correlated with the poloid moment generated by rotating electrically-charged mantle plumes rising off the outer core about the planetary spin axis, because rotating volumes of charged Earth media about a central axis will produce various magnetic moments. The moment intensity and form relate to its size (radius r), how fast it rotates (angular velocity ꙍ) and the hemispheric volumes and distribution of charged, spherical media. 

Earth has three main interior structures: a solid, spherical inner core (ic), a liquid outer-core-shell (oc), and a semi-solid mantle shell (ms) rotating about a central, polar axis (fig. 10 ). For Earth’s spinning, outer-core shell of liquid we need only consider the dipole moment resulting from aligned electron spin (oc_spin), as solid, remnant charges are null. If we also assume that the dipoles resulting from electron spin in the inner core and mantle shell are negligible, then the main component dipoles to Earth’s total magnetic field (u_Earth) reduce to four dipoles with two each for the solid inner core and semi-solid mantle, but only one for the outer core:

Equation 1: u_Earth=(u_spinoc+u_rotms>>u_Qic+u_rotic+u_Qms)

A moving electric charge creates a magnetic dipole moment (u). A solid, ferrous sphere holding an intrinsic magnetic charge (Q in Joules per Tesla or Amperes/m² ) and rotating about a central axis can have three magnetic-dipole moments including one from the intrinsic magnetic charge (u_Q), one from rotating charged media about a fixed axis (urot), and one from rotation-induced electron-spin alignment (uspin is considered much larger (>>) than u_Q and urot). Therefore, the sphere’s total dipole (u_t) is therefore the sum of the three component dipoles: 

Equation 2.  u_t = u_Q+urot+uspin

The rotational dipole (urot) of uniformly charged sphere of volume-charge density (ρ) about a central axis can also be derived using the spheres radius (km) and its angular velocity ꙍ (km/sec):

Equation 3.    u_rot=1/5Qr²ꙍ

Equation 3 is typically derived using the definition of the magnetic dipole moment for a current distribution, which involves treating the rotating charge as a volume current density.

The volume-charge density (ρ) is simply Q divided by the spherical volume:

Equation 4.    ρ = Q/(4/3πr³) or Q = 4/3ρπr³

u_Q from Equation 2 can therefore also be expressed in terms of the sphere's charge density (ρ) and radius:

Equation 5. u_Q=1/5(4/3ρπr³)r²ꙍ=4/15ρꙍπr⁵

The dipole moment of rotating the solid, spherical mantle shell (urotms) holding a uniform, volume-charge density (ρ) with inner (r_min) and outer (r_max) radii, is the difference between the volume of each sphere; the larger one of radius r_max, and the smaller one, r_min " the inner hole". Therefore:

Equation 6. u_rotms=V_mantle=V_rmax–V_rmin, or,

Equation 7.   u_rotms=4/15ρꙍπr_max⁵-4/15ρꙍπr_min⁵=4/15πρ(r_max⁵-r_min⁵)

The uniform volume charge density spherical shell (ρ) is the total intrinsic charge (Q) divided by the spherical volume:

Equation 8.  ρ = Q/(4/3πr_max³ - 4/3πr_min³)

The dipole moment generated from rotating the charged, spherical, mantle shell is determined from substitution of equation 8 into equation 7:

urotms= 4/15 π(Q/(4/3πꙍ(rmax3-rmin3))) (rmax5- rmin5) or,

Equation 9.  urotms=Qmsꙍ(r5max- r5min)/(rmax3- rmin3)/5

The only unknown variable in equation 9 is the inherent electrical charge Q.

Earth's outer core structure and the toroid dipole moment

The toroid dipole moment of the total field is probably generated by the alignment of electron spin within circulating, ferrous fluids in Earth's outer-core shell. According to de Wijs and others (1998), fluids move under the Coriolis effect resulting in spinning, inner and outer cylindrical columns with radii comparable to the inner core (fig. 10). The outer-core columns are thought to occur in a hexagonal, closely-packed (h.c.p.) crystal form with adjacent columns spinning in opposing directions outward from the equator. The intersection of the outside columns form  tear-drop-shaped surface gyres at the mantle base where two core-anchor structures in opposing hemispheres form the roots of  overlying mantle plumes that are electromagnetically wired into the outer core (fig. 10) .

Earth's mantle-plume hemispheric heterogeneity and the poloid dipole moment

The poloid dipole moment of the total field is probably generated by electromagnetically conductive mantle plumes spinning about the planetary rotation axis. The mantle plumes are anchored to the outer core and weave upward through the mantle as portrayed in figure 11. The mantle plumes were built as a 3D CAD model using Moulik and Ekström (2014) global shear-wave velocity (Svel) model (Herman, 2022). Their Svel global data set are discretized, shear-wave velocity points having geographic coordinates (latitude, longitude) and depths from sea level (km) provided in tabular, ASCII form.  Data for thirteen different mantle depths were downloaded and processed using QGIS to map mantle heterogeneity. The 35% slowest shear-wave values were contoured at each depth using 2D polylines that were then used for building 3D mantle plumes as solid objects using triangular integrated networks called TINS (fig. 10). The 35% fastest Svel values were also processed, contoured, and built into TIN objects to compliment this effort, with the results reported in a 2023 blog entry titled Structure of Earth's Mantle Plumes and Core Accretion. The uneven distribution of the mantle plumes accounts for the pulsating nature of the poloid moment as seen in the SAMPEX data (fig. 2). The disproportionate concentration of plume mass in the southern hemisphere also agrees with having normal magnetic polarity.

A 3D computer model was used to quantify the volume of Earth’s external radiation belts and electromagnetically charged body structures that generate the toroid and poloid dipoles of its quadrupole geomagnetic field. 3D objects representing the inner and outer radiation belts were modeled in 3D and their volumes computed using a 09/07/2012 snapshot of the NASA SAMPEX satellite data with the SketchUp Pro 2024 computer-aided drafting (CAD) system.  The smaller, more variable and weaker inner belt was computed to be about 35% the volume of the outer belt, pulsates on a daily basis, and is correlated to the Earth's poloid dipole moment generated by rotating electrically-charged mantle-plume about a central axis. A 3D CAD model of the mantle plumes was built using the 35% slowest values in Moulik and Ekström (2014) S362ANI+M global shear-wave velocity model. The toroid is the stronger, steadier dipole moment that's spatially fixed to the planetary spin axis and generated in the outer core where six, cylindrical fluid columns spiral upward and downward from the equator and form tilted surface gyres at the outer-core and mantle interface. The toroid moment therefore likely arises from aligned electron spin in fluid media. The mantle plumes that generate the poloid dipole are anchored to the outer core by two, basal structures situated in opposing, longitudinal hemispheres. The overlying, evolving plumes weave upward through the mantle and into the crust beneath magmatically active oceanic spreading centers and crustal hot spots.  Daily pulsations of the poloid results from plumes having longitudinal heterogeneity (West:East = 55:45%). Earth’s total field is south negative, and the total field is skewed southward because ~70% of the plume bulk resides in the southern hemisphere. Poloid fluxes probably result when km-scaled bolide impacts suddenly produce large igneous provinces that alter hemispheric volumes of charged and connected mantle media. Large northern impacts could thereby potentially induce temporary, poloid-moment polarity reversals that could, in turn induce total-field polarity fluxes. The distribution of protons and electrons in the external radiation belts reflects intensity variations in the total field from having overlapping and interfering dipole moments. The dipole moments resulting from rotating spherical, charged body components about a rotation axis are expressed algebraically.

References

de Wijs, G.A, Kresse, G., Voc., L., Dobson, D., Alfe, D., Gillan, M.J., and Price, G.D., 1998, The viscosity of liquid iron at the physical conditions of the Earth’s core, Nature, vol. 392, p. 305-307.

Herndon, J. M., 2022, Origin of Earth’s Magnetic Field, its Nature and Behavior, Geophysical Consequences, and Danger to Humanity: A Logical Progression of Discoveries Review. European Journal of Applied Sciences, vol. 10, no. 6, p. 529-562.

Herman, G.C., 2022, Punctuated Tectonic Equilibrium, www.impacttectonics.org. 202 p. Amazon Books, https://www.amazon.com/dp/B0BHSZDXDS?ref_=pe_3052080_397514860.

Moulik, P. & Ekström, G., 2014. An anisotropic shear velocity model of the Earth's mantle using normal modes, body waves, surface waves and long-period waveforms, Geophysical Journal International, vol. 199, no.3, p. 1713-1738, http://geoweb.princeton.edu/people/pm5113/Research/3D/S362ANI+M/model.php

NASA SAMPEX Orbiter 1992-2004; 9/7/2012 Charged magnetic particles.
https://svs.gsfc.nasa.gov/vis/a000000/a003900/a003950/RBSPbeltprofile_HD1080.mp4

NOAA polar-wander maps 1590 to 2025, https://maps.ngdc.noaa.gov/viewers/historical_declination/

Introduction * Earths external radiation belts * Correlation of Earths' core and mantle structures with the toroid and poloid dipole moments * Outer core structure and the toroid dipole moment * Mantle-plume hemispheric heterogeneity and the poloid dipole moment * Summary * References