Geomagnetic polarity reversals in a turbulent core

The behavior of the main magnetic field components during a polarity transition is investigated using the α²-dynamo model for magnetic field generation in a turbulent core. It is shown that rapid reversals of the dipole field occur when the helicity, a measure of correlation between turbulent velocity and vorticity, changes sign. Two classes of polarity transitions are possible. Within the first class, termed component reversals, the dipole field reverses but the toroidal field does not. Within the second class, termed full reversals, both dipole and toroidal fields reverse. Component reversals result from long term fluctuations in core helicity; full reversals result from short term fluctuations. A set of time-evolution equations are derived which govern the dipole field behavior during an idealized transition. Solutions to these equations exhibit transitions in which the dipole remains axial while its intensity decays rapidly toward zero, and is regenerated with reversed polarity. Assuming an electrical conductivity of 3 × 10⁵ mho m^?1 for the fluid core, the time interval required to complete the reversal process can be as short as 7500 years. This time scale is consistent with paleomagnetic observations of the duration of reversals. A possible explanation of the cause of reversals is proposed, in which the core's net helicity fluctuates in response to fluctuations in the level of turbulence produced by two competing energy sources—thermal convection and segregation of the inner core. Symmetry considerations indicate that, in each hemisphere, helicity generated by heat loss at the core-mantle boundary may have the opposite sign of helicity generated by energy release at the inner core boundary. Random variations in rates of energy release can cause the net helicity and the α-effect to change sign occasionally, provoking a field reversal. In this model, energy release by inner core formation tends to destabilize stationary dynamo action, causing polarity reversals.     

Equatorial paleopoles and behavior of the dipole field during polarity transitions

One of the reasons for performing paleomagnetic studies is to determine whether the geomagnetic field remains dipolar during a polarity transition. Data on 23 field reversals of Recent, Tertiary and Upper Mesozoic age are examined with regard to the longitudinal and latitudinal distribution of paleomagnetic poles during a polarity change. Both frequency distributions of the transitional pole positions are not random. The results suggest that some field reversals are characterized by the rotation of the dipole axis in the meridional plane and show that two preferential meridional bands of polarity transitions exist centered on planes through 40°E–140°W and 120°E–60°W respectively. The latitudinal distribution of transitional paleopoles shows that there is a decrease in the number of observed poles with decreasing latitude. This is interpreted as the result of an acceleration in the motion of the dipole axis when it approaches the equator. Comparison of transitional velocities and paleointensity magnitudes reveals that the dipole moment is very weak only for a short part of the transitional period when the paleopole position lies within the latitudes of 10°N and 10°S. The overall conclusion is that the geomagnetic field retains its dipolar character during polarity changes.     

A Quaternary geomagnetic instability time scale

Reversals and excursions of Earth's geomagnetic field create marker horizons that are readily detected in sedimentary and volcanic rocks worldwide. An accurate and precise chronology of these geomagnetic field instabilities is fundamental to understanding several aspects of Quaternary climate, dynamo processes, and surface processes. For example, stratigraphic correlation between marine sediment and polar ice records of climate change across the cryospheres benefits from a highly resolved record of reversals and excursions. The temporal patterns of dynamo behavior may reflect physical interactions between the molten outer core and the solid inner core or lowermost mantle. These interactions may control reversal frequency and shape the weak magnetic fields that arise during successive dynamo instabilities. Moreover, weakening of the axial dipole during reversals and excursions enhances the production of cosmogenic isotopes that are used in sediment and ice core stratigraphy and surface exposure dating. The Geomagnetic Instability Time Scale (GITS) is based on the direct dating of transitional polarity states in lava flows using the ⁴⁰Ar/³⁹Ar method, in parallel with astrochronologic age models of marine sediments in which oxygen isotope and magnetic records have been obtained. A review of data from Quaternary lava flows and sediments gives rise to a GITS that comprises 10 polarity reversals and 27 excursions that occurred during the past 2.6 million years. Nine of the ten reversals bounding chrons and subchrons are associated with ⁴⁰Ar/³⁹Ar ages of transitionally-magnetized lava flows. The tenth, the Gauss-Matuyama chron boundary, is tightly bracketed by ⁴⁰Ar/³⁹Ar dated ash deposits. Of the 27 well-documented geomagnetic field instabilities manifest as short-lived excursions, 14 occurred during the Matuyama chron and 13 during the Brunhes chron. Nineteen excursions have been dated directly using the ⁴⁰Ar/³⁹Ar method on transitionally-magnetized volcanic rocks and these form the backbone of the GITS. Excursions are clearly not the rare phenomena once thought. Rather, during the Quaternary period, they occur nearly three times as often as full polarity reversals.     

The late Pleistocene geomagnetic field as recorded by sediments from Fargher Lake,Washington, U.S.A.

Measurement of the remanent magnetization of a 6.88-m oriented core of soft sediments and tephras from Fargher Lake near Mount St. Helens in southwestern Washington State shows that no significant geomagnetic reversals were recorded in the sediments of the lake. Radiocarbon and palynological dating of the tephra layers from the lake bed indicates deposition during the interval 17, 000–34, 000 years B.P. although geochemical correlation of a prominent tephra layer in the core with tephra set C of Mount St. Helens could mean that the maximum age of the sediments may be at least 36, 000 years B.P. The core was divided into specimens 0.02 m long, each representing approximately 55 years of deposition assuming a constant rate of sedimentation. Pilot alternating field demagnetization studies of every tenth specimen indicated a strong, stable remanence with median destructive field of 15 mT, and the remaining specimens were subsequently demagnetized in fields of this strength. The mean inclination for all specimens exclusive of the unstably magnetized muck and peat from near the surface is 56.1° which is 8° shallower than the present axial dipole field at this site, perhaps because of inclination error in the detrital remanent magnetization of the sediments, although because of the variability in the data, this departure from the axial dipole field may not be significant. The ranges of inclination and declination are comparable to those of normal secular variation at northern latitudes. Although three isolated specimens have remanence with negative inclination, these anomalous directions are due to sampling and depositional effects. Measurement of a second core of 6.86 m length also revealed only normal magnetic polarity, but this result is of little stratigraphic value as this core failed to penetrate the distinctive tephra found near the base of the former core.Studies of a concentrate of the magnetic minerals in the sediments by optical microscopy and X-ray diffraction indicate that the primary magnetic constituent is an essentially pure magnetite of detrital origin. The magnetite occurs in a wide range of grain sizes with much of it of sub-multidomain size (< 15 μm).As a whole, this study provides substantial evidence against the existence of large-scale worldwide geomagnetic reversals during the time interval of Fargher Lake sedimentation, a segment of geological time for which many excursions and reversals have been reported elsewhere.     

Paleointensity variations of Earth's magnetic field and their relationship with polarity reversals

Power-spectral analyses of the intensity of Earth's magnetic field inferred from ocean sediment cores and archeomagnetic data from time scales of 100 yr to 10 Myr have been carried out. The power spectrum is proportional to 1/f where f is the frequency. These analyses compliment previous work which has established a 1/f² spectrum for variations at time scales less than 100 yr. We test the hypothesis that reversals are the result of variations in field intensity with a 1/f spectrum which occasionally are large enough to cross the zero intensity value. Synthetic binormal time series with a 1/f power spectrum representing variations in Earth's dipole moment are constructed. Synthetic reversals from these time series exhibit statistics in good agreement with the reversal record, suggesting that polarity reversals may be the end result of autocyclic intensity variations with a 1/f power spectrum.     

A direct test of the Vine-Matthews hypothesis

Paleomagnetic studies of the basalt samples of Mid-Atlantic Ridge recovered during DSDP Leg 45 and the FAMOUS Project have led to a revision of our view of the oceanic igneous crust as a recorder of geomagnetic field reversals. The discovery of several magnetic polarity reversals with depth in the crust has indicated that oceanic igneous basement should not necessarily be considered magnetized uniformly in direction, or even polarity, in a given vertical cross section. Statistical arguments, based on the ratio of the average time of crustal formation to the average length of a magnetic polarity interval, indicate that magnetic reversals with depth are to be expected in typical ocean crust, but also that this does not conflict with current theories of plate tectonics or exclude the upper layers of the crust from making a major contribution to the overlying linear magnetic anomalies. Certain ratios of average crustal formation time to average polarity interval do, however, result in an effective zero magnetization for the oceanic crust and these conditions may be responsible for the reduced amplitude of magnetic anomalies in some areas.     

The geodynamo as a bistable oscillator

Abstract

Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating α reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ∝(1 ? a ²)², subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2?3) × 10⁵ year, is shown to imply a secular variation of the axial dipole moment of ～ 15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data.     

Geomagnetic reversal frequency since the Late Cretaceous

Models of geomagnetic reversals as a stochastic or gamma renewal process have generally been tested for the Heirtzler et al. [1] magnetic polarity time scale which has subsequently been superseded. Examination of newer time scales shows that the mean reversal frequency is dominated in the Cenozoic and Late Cretaceous by a linearly increasing trend on which a rhythmic fluctuation is superposed. Subdivision into two periods of stationary behavior is no longer warranted. The distribution of polarity intervals is visibly not Poissonian but lacks short intervals. The LaBrecque et al. [2] polarity time scale shows the positions of 57 small-wavelength marine magnetic anomalies which may represent short polarity chrons. After adding these short events the distribution of all polarity intervals in the age range 0–40 Myr is stationary and does not differ significantly from a Poisson distribution. A strong asymmetry develops in which normal polarity chrons are Poisson distributed but reversed polarity chrons are gamma distributed with indexk = 2. This asymmetry is of opposite sense to previous suggestions and results from the unequal distribution of the short polarity chrons which are predominantly of positive polarity and concentrated in the Late Cenozoic. If short-wavelength anomalies arise from polarity chrons, the geomagnetic field may be more stable in one polarity than the other. Alternative explanations of the origin of short-wavelength marine magnetic anomalies cast doubt on the inclusion of them as polarity chrons, however. The observed behavior of reversal frequency suggests that core processes governing geomagnetic reversals possess a long-term memory.     

Constraints on the origins of lunar magnetism from electron reflection measurements of surface magnetic fields

Apollo 15 and 16 subsatellite measurements of lunar surface magnetic fields by the electron reflection method are summarized. Patches of strong surface fields ranging from less than $\text{1}\text{4}$° to tens of degrees in size are found distributed over the lunar surface, but in general no obvious correlation is observed between field anomalies and surface geology. In lunar mare regions a positive statistical correlation is found between the surface field strength and the geologic age of the surface as determined from crater erosion studies. However, there is a lack of correlation of surface field with impact craters in the mare, implying that mare do not have a strong large-scale uniform magnetization as might be expected from an ancient lunar dynamo. This lack of correlation also indicates that mare impact processes do not generate strong magnetization coherent over ～ 10 km scale size. In the lunar highlands fields of >100 nT are found in a region of order 10 km wide and >300 km long centered on and paralleling the long linear rille, Rima Sirsalis. These fields imply that the rille has a strong magnetization (>5 × 10^?6 gauss cm³ gm^?1 associated with it, either in the form of intrusive, magnetized rock or as a gap in a uniformly magnetic layer of rock. However, a survey of seven lunar farside magnetic anomalies observed by the Apollo 16 subsatellite suggests a correlation with inner ejecta material from large impact basins. The implications of these results for the origin of lunar magnetism are discussed.     

Magnetic lineations in the Pacific Jurassic quiet zone

Magnetic anomalies of low amplitude (<100 gammas) are present in the Jurassic magnetic quiet zone of the western Pacific Ocean. These small anomalies are lineated and can be correlated among the Phoenix, Hawaiian and Japanese lineation patterns. Thus, they represent seafloor spreading that recorded some sort of magnetic field phenomena prior to magnetic anomaly M25 at 153 m.y. B.P. The most likely possibility is that they represent a series of late Jurassic magnetic field reversals that occurred during a period of anomalously low magnetic field intensity. We propose a time scale of magnetic reversals between 153 and 158 m.y. B.P. to account for these anomalies and suggest that the dipole magnetic field intensity increased by a factor of about four from 160 to 140 m.y. B.P. in the late Jurassic.     

The palaeogeomagnetic field strength,variations in reversal frequency,and geomagnetic dynamo models

Abstract

The geomagnetic field and its frequent polarity reversals are generally attributed to magnetohydrodynamic (MHD) processes in the Earth's metallic and fluid core. But it is difficult to identify convincingly any MHD timescales with that over which the reversals occur. Moreover, the geological record indicates that the intervals between the consecutive reversals have varied widely. In addition, there have been superchrons when the reversals have been frequent, and at least two, and perhaps three, 35-70 Myr long superchrons when they were almost totally absent. The evaluation of these long-term variations in the palaeogeophysical record can provide crucial constraints on theories of geomagnetism, but it has generally been limited to only the directional or polarity data. It is shown here that the correlation of the palaeogeomagnetic field strength with the field's protracted stability during a fixed polarity superchron provides such a constraint. In terms of a strong field dynamo model it leads to the speculation that the magnetic Reynolds number, and the toroidal field, increase substantially during a superchron of frequent reversals.     

Magnetic studies on Kilauea Iki lava lake,Hawaii

Ground surveys made during August, 1961, show large vertical magnetic intensity anomalies associated with the partly lava filled crater of Kilauea Iki. A vertical magnetic variation of 11,600 gammas occurs along a north-south profile across the crater, the maximum being on the north rim of the crater and the minimum on the south edge of the encrusted lava lake below the south rim. An east-west profile shows less vertical magnetic variation, with lake-surface measurements 1500 to 2500 gammas lower than measurements on the east rim of the crater. Computed anomalies using two-dimensional potential field graticules are in good agreement with the observed anomalies and support the following conclusions: 1) Average measured values of remanent magnetization of 10^?2 cgs units and susceptibilities of 10^?3 cgs units give reasonable magnitudes to the computed anomalies. 2) The remanent magnetization is parallel to the earth’s present magnetic field. 3) The maximum vertical magnetic field value in the north-south profile is the result of reinforcement of the positive terrain effect of the north rim of the crater and the positive edge effect of the north side of the lava lake. 4) The minimum value in the same profile is the result of reinforcement of the negative terrain effect at the base of the south rim of the crater and the negative edge effect of the south side of the lava lake. 5) Variation in the east-west magnetic profile is less because the terrain and edge effects of the horizontal components of the earth’s magnetic field and remanent magnetization approach zero. Changes in vertical magnetic field values as the lake solidifies will be maximum at the north edge of the lava lake, but more consistent changes of the opposite sign will occur on the south side of the lava lake. Total change will be approximately + 2300 gammas between the August 1961 measurement at station S6 and the value at that point when the entire lava lake has cooled below 400° C. The maximum rate of change at station S6 will occur when the 500° C isotherm is 35 to 65 meters below the surface and will be about 28 gammas per meter of lowering of the 500°C surface. Because of the steep magnetic anomalies associated with the lava lake and crater rims, the permanent magnetization presently forming in the cooling lake crust will have inclinations as much as 12° less than the average 37.5° inclination in the Kilauea area.     

Oxfordian magnetostratigraphy of Poland and its correlation to Sub-Mediterranean ammonite zones and marine magnetic anomalies

A nearly continuous magnetostratigraphic polarity pattern was compiled from several ammonite-zoned carbonate successions of southern Poland and from a composite magnetostratigraphy from the Iberian Range of Spain. The array of sections spans the middle two-thirds of the Oxfordian within the Sub-Mediterranean Province (Cordatum through Bifurcatus ammonite zones). The average paleopole calculated from eight of these Polish sections is at 78.5°N, 184.9°E (δp = 2.6°, δm = 3.5°). The Sub-Mediterranean polarity pattern is consistent with an independent polarity pattern derived from the Boreal-realm sections of the British Isles, and improves the inter-correlation between these faunal realms. Cycle stratigraphy published for these ammonite subzones from southern France enabled temporal scaling of the polarity pattern, thereby facilitating correlation to marine magnetic anomalies M28 through M33 as modeled from deep-tow magnetometer surveys in the Western Pacific. The bases of the Middle and Upper Oxfordian substages as defined in the Sub-Mediterranean zonation in Poland correspond approximately to chrons M33 and M29 of that Pacific M-sequence model.     

Inner core anisotropy, anomalies in the time-averaged paleomagnetic field, and polarity transition paths

The diffusion of the dynamo-generated magnetic field into the electrically conducting inner core of the Earth may provide an explanation for several problematic aspects of long-term geomagnetic field behavior. We present a simple model which illustrates how an induced magnetization in the inner core which changes on diffusive timescales can provide a biasing field which could produce the observed anomalies in the time-averaged field and polarity reversals. The Earth's inner core exhibits an anisotropy in seismic velocities which can be explained by a preferred orientation of a polycrystalline aggregate of hexagonal close-packed (hcp) iron, an elastically anisotropic phase. Room temperature analogs of hcp iron also exhibit a strong anisotropy of magnetic susceptibility, ranging from 15 to 40% anisotropy. At inner core conditions the magnetic susceptibility of hcp iron is estimated to be between 10⁻⁴ and 10⁻³ SI. We speculate here that the anisotropy in magnetic susceptibility in the inner core could produce the observed anomalies in the time-averaged paleomagnetic field, polarity asymmetry, and recurring transitional virtual geomagnetic pole (VGP) positions.     

Quantitative description of the geomagnetic field during the Matuyama-Brunhes polarity transition

A model of the reversing geodynamo based on the assumptions (1) that reversals start in a localized region of the core and (2) that upon its onset this reversed region extends, or “floods”, both north-south and east-west until the entire core is affected, has recently been shown to provide a generally successful simulation of existing paleomagnetic records of the Matuyama-Brunhes transition (Hoffman, 1979). In this paper the modelled solution is analyzed so as to reveal the behavior of the dominant Gauss coefficients during the transition. At the time of total axial dipole decay the controlling components are found to be a zonal octupole (g₃⁰) and a non-axisymmetric quadrupole (g₂¹, h₂¹). Given the distribution of sites corresponding to the available records of the Matuyama-Brunhes, the existence of a significant zonal quadrupole field component cannot be ruled out; however, the role of any equatorial dipole component can be neglected.Due to the presence of a significant low-order non-axisymmetric term in the analyzed transition field, the predicted minimum intensity experienced during the Matuyama-Brunhes is found to be dependent on both site latitude and longitude. In particular, over a mid-northern circle of latitude, the predicted minimum intensity is found to vary by more than a factor of three, averaging about 10% of the full polarity field strength.Although not a unique solution, the applicability of the findings from this analysis is not tied to the phenomenological model from which they were derived. More specifically, whether the above two-component non-dipole transitional field arises from assumed configurational changes of the reversing geodynamo (as is the case for the flooding model) or, alternatively, is considered to be a stationary (non-reversing) portion of the field during axial dipole decay and regeneration, has little effect on either the calculated path locality of the virtual geomagnetic pole or the minimum intensity experienced at a given site. These two possible situations, in principle, should be distinguishable given the future attainment of detailed paleomagnetic data corresponding to back-to-back (R → N and N → R) polarity transitions.     

A theoretical analysis of the observed variability of the geomagnetic dipole field

We present a detailed analysis of the Sint-800 virtual axial dipole moment (VADM) data in terms of an Ω mean field model of the geodynamo that features a non-steady generation of poloidal from toroidal magnetic field. The result is a variable excitation of the dipole mode and the overtones, and there are occasional dipole reversals. The model permits a theoretical evaluation of the statistical properties of the dipole mode. We show that the model correctly predicts the distribution of the VADM and the autocorrelation function inferred from the Sint-800 data. The autocorrelation technique allows us to determine the turbulent diffusion time τ_d=R²/β of the geodynamo. We find that τ_d is about 10–15 kyr. The model is able to reproduce the observed secular variation of the dipole mode, and the mean time between successive dipole reversals. On the other hand, the duration of a reversal is a factor 2 too long. This could be due to imperfections in the model or to unknown systematics in the Sint-800 data. The use of mean field theory is shown to be selfconsistent.     

Late Cretaceous magnetic anomalies in the North Atlantic

An identification of anomalies 31–34 is presented for the North Atlantic. North of the Azores-Gibraltar Ridge this implies a revision of the identification of the magnetic anomalies older than anomaly 26. DSDP site 10 in the western North Atlantic appears to be located on the old end of anomaly 33. The relative spacings of anomalies 29–34 in the North and South Atlantic, North and South Pacific and Indian Oceans are compared and the estimated relative widths of the magnetic polarity intervals in the Late Cretaceous are revised.     

High-frequency polarity swings during the Gauss-Matuyama reversal from Baoji loess sediment

Paleomagnetic records of the Gauss-Matuyama reversal were obtained from two loess sections at Baoji on the Chinese Loess Plateau. Stepwise thermal demagnetization shows two obvious magnetization components. A low-temperature component isolated between 100 and 200–250°C is close to the present geomagnetic field direction, and a high-temperature component isolated above 200–250°C reveals clearly normal, reversed, and transitional polarities. Magnetostratigraphic results of both sections indicated that the Gauss-Matuyama reversal consists of a high-frequency polarity fluctuation zone, but the characteristic remanent magnetization directions during the reversal are clearly inconsistent. Rock magnetic experiments demonstrated that for all the specimens with normal, reversed, and transitional polarities magnetite and hematite are the main magnetic carriers. Anisotropy of magnetic susceptibility indicates that the studied loess sediments have a primary sedimentary fabric. Based on virtual geomagnetic pole latitudes, the Gauss-Matuyama reversal records in the two sections are accompanied by 14 short-lived geomagnetic episodes (15 rapid polarity swings) and 12 short-lived geomagnetic episodes (13 rapid polarity swings), respectively. Our new records, together with previous ones from lacustrine, marine, and aeolian deposits, suggest that high-frequency polarity swings coexist with the Gauss-Matuyama reversal, and that the Gauss-Matuyama reversal may have taken more than 11 kyr to complete. However, we need more detailed analyses of sections across polarity swings during reversals as well as more high-resolution reversal records to understand geomagnetic behavior and inconsistent characteristic remanent magnetization directions during polarity reversals.     

Absolute geomagnetic paleointensity as recorded by ∼1.09 Ga Lake Shore Traps (Keweenaw Peninsula, Michigan)

Absolute geomagnetic paleointensity measurements were made on 255 samples from 38 lava flows of the ～1.09 Ga Lake Shore Traps exposed on the Keweenaw Peninsula (Michigan, USA). Samples from the lava flows yield a well-defined characteristic remanent magnetization (ChRM) component within a ～375°C–590°C unblocking temperature range. Detailed rock magnetic analyses indicate that the ChRM is carried by nearly stoichiometric pseudo-single-domain magnetite and/or low-Ti titanomagnetite. Scanning electron microscopy reveals that the (titano)magnetite is present in the form of fine intergrowths with ilmenite, formed by oxyexsolution during initial cooling. Paleointensity values were determined using the Thellier double-heating method supplemented by low-temperature demagnetization in order to reduce the effect of magnetic remanence carried by large pseudosingle-domain and multidomain grains. One hundred and two samples from twenty independent cooling units meet our paleointensity reliability criteria and yield consistent paleofield values with a mean value of 26.3 ± 4.7μT, which corresponds to a virtual dipole moment of 5.9 ± 1.1×10²² Am². The mean and range of paleofield values are similar to those of the recent Earth’s magnetic field and incompatible with a “Proterozoic dipole low”. These results are consistent with a stable compositionally-driven geodynamo operating by the end of Mesoproterozoic.     

Large intensity changes of the non-dipole field during a polarity transition

Directional and paleointensity data for the Steens Mountain geomagnetic polarity transition do not agree with the two simplest models of reversals: rotation of undiminished dipole or gradual diminution followed by change in polarity of the dipole moment. Instead, large and rapid changes in the intensity and direction of the field occur, probably as a result of non-dipole variations.