Neogaean paleomagnetism constraints on the processes at the core and surface of the Earth
D. M. Pechersky

#### Wavelet Analysis

Fourier analysis is commonly used to reveal periodicities in a time series. However, formal application of Fourier analysis to the geomagnetic field can produce various artifacts, false periods, etc. This problem can be solved through the application of wavelet analysis which compares a signal studied with a finite wave train rather than an infinite sinusoid employed in the Fourier analysis. The geomagnetic polarity time scale is described by a step function whose Fourier spectrum contains numerous multiple harmonics, whereas the wavelet analysis does not produce multiple harmonics and is efficient in studies of spectral properties of aperiodic signals [Holschneider, 1995].

Wavelets are a family of oscillating self-similar functions varying in scale that are localized in both physical and Fourier spaces. Wavelet analysis allows one to study spectrally nonstationary processes, examine the phase behavior of components of a quasi-periodic process, and estimate its energy characteristics. As compared with the Fourier analysis, resulting spectra are smoother and free from multiple and combination frequencies. Another advantage of the wavelet analysis is its applicability to time series with missing observations [Galyagin and Frik, 1996].

The choice of a specific wavelet depends on the purposes of analysis. In our case [Galyagin et al., 1999], the Morle and "Mexican hat" wavelets were employed. The wavelet transformation transfers a function of one variable t into the plane of two variables t and a. Here, t specifies the wavelet center position on the time axis, and the parameter a characterizes the time scale of oscillations and coincides with their period if the Morle wavelet is used. An analogue of the Fourier spectrum is the so-called integral wavelet spectrum obtained by integration of the squared wavelet modulus along the time axis.

##### Wavelet analysis of the reversal frequency in the Neogaea.

Periods of the integral wavelet spectrum F(t) (15, 30, 50-60, 70, 100-110, 130, 180, 220, 280, and 390 Myr) are essentially the same as those previously obtained [Marzocchi and Mulargia, 1992; McElhinny, 1971; Merrill and McElhinny, 1983; Pechersky and Nechaeva, 1988]. As distinct from other methods of spectral analysis, wavelet data provide time evolution of the spectrum. We consider the Neogaean evolution of the wavelet spectrum (Figure 4) [Galyagin et al., 1999]. First, the Vendian-Phanerozoic and Riphean patterns are drastically different. Second, an oscillation with a period of about 400 Myr is recognizable throughout the Vendian-Phanerozoic interval; this period decreases from more than 450 Myr in the Vendian to less than 400 Myr in the Late Cenozoic. The lifetime of remaining oscillations with periods of 70 to 200 Myr is much shorter. Thus, oscillations with periods of 90 and 180 Myr are traceable from 550 to 200 Ma, when both periods gradually decreased from 200 to 170 Myr and from 100 to 90 Myr, respectively. A 130-Myr period is stable and exists from 180 Ma to the present time, and its resolution markedly improves toward the Cenozoic; a 70-Myr period exists from 160 Ma to the present time and decreases from 70 to 55 Myr. Third, the Phanerozoic and Early Riphean exhibit a series of "pulses" (approximately at 1650, 540, 370, and 160 Ma) at the lower boundary of the wavelet plane, which indicates their characteristic times to be about 30 Myr.

The stability of the inferred results is corroborated by their similarity for wavelet processing procedures with smoothing windows varying from 5 to 30 Myr.

##### Wavelet analysis of the geomagnetic polarity time scale.

It is interesting to apply the wavelet analysis to the polarity scale proper [Galyagin et al., 1998, 1999]. The integral wavelet spectrum is relatively smooth and exhibits one pronounced peak ( a 180 Myr) and a number of weak peaks at 12, 23, 43, 60, 100, 180, 300, and 600 Myr [Galyagin et al., 1999]. The picture on the wavelet plane is considerably different from the reversal frequency spectrum (Figure 4). The oscillation with a 180-Myr period exists over the interval 1450-850 Ma. The period is 160 Myr in the middle of the interval and increases to 180-200 Myr at its ends. In the Phanerozoic, this pattern is changed by a rather stable oscillation, with its period gradually increasing from 250 to 300 Myr in the interval 450-100 Ma. The remaining "periods" observed in the integral spectrum are due to local events (pulses). Three intervals are recognized: (a) Vendian-Phanerozoic (630-0 Ma), includes five pulses, with average spacing between them being 125 Myr; (b) middle Middle Riphean-middle Late Riphean (1260-860 Ma), five pulses, average spacing of 80 Myr; and (c) Early-Middle Riphean (1670-1260 Ma), three pulses, average spacing of 140 Myr. A "quiescence" interval is confidently defined between 850 and 650 Ma (Figure 4).

Overall, wavelet planes of the polarity scale and reversal frequency (in essence, entirely different entities) yield similar evolution patterns of geomagnetic field in the Phanerozoic and Precambrian [Galyagin et al., 1999].

#### Summary Amplitude of Paleovariations in the Geomagnetic Field Direction.

The geomagnetic polarity time scale yields evidence of the field sign, i.e. maximum changes of the field direction. The paleomagnetic database [McElhinny and Lock, 1990, 1993] provides the possibility of estimating the summary amplitude of paleovariations in the field direction, amounting to a few tens of degrees. Theoretically, the summary amplitude is defined by the standard angular deviation S=81/K1/2 [Fisher et al., 1987; Khramov et al., 1982; Merrill and McElhinny, 1983], where K is the precision parameter of individual vector directions for their normal distribution on sphere. The S value was determined in this way for the whole Neogaea [Pechersky, 1996, 1997].

##### Index of paleomagnetic reliability.

Each paleomagnetic determination of the paleomagnetic database is characterized by its index of paleomagnetic reliability (IPR) varying from 0 to 1 and depending on the number of samples involved in a given determination, precision parameter of paleomagnetic directions, availability of thermal and alternating field demagnetization data, paleomagnetic reliability tests (baked contact, pebble, fold, and reversal tests), quality of laboratory paleomagnetic measurements and their processing, and age determinations of rocks and stable component of natural remanent magnetization (NRM). Age determination was shown to have the greatest effect on the IPR value (particularly for Precambrian rocks) and considerably increase the scatter in S values close in age.

The IPR value was taken as a weight in the calculation of S means for each 10-Myr intervals [Pechersky, 1996, 1997]. Weighted means of S from volcanic and sedimentary rocks younger than 10 Ma do not differ on a significant level; decreasing IPR results in an increase in DS from 3-4o at IPR > 0.6 to 8o at IPR 0.2. Therefore, low-IPR S means may be considered reliable, which is especially important in the case of Precambrian determinations dominated by IPR 0.2.

##### Rock types.

All rocks are subdivided into four groups according to their NRM origin: (a) volcanic rocks with the most probable primary thermal remanent magnetization (TRM); in the context of our study, the lava cooling and related acquisition of geomagnetic direction may be considered instantaneous; (b) intrusive rocks with probably dominating primary TRM; however, due to slow cooling of large bodies, variations may be averaged in a collection and even in an individual sample; (c) sedimentary rocks; they may preserve information about primary detrital remanent magnetization and exhibit marked averaging of variations within a sample due to slow deposition of sediments, postsedimentary processes, and early diagenesis; (d) "metamorphic" rocks; these are rocks that experienced various alterations, including the acquisition of secondary, often postfolding, crystallization or chemical remanent magnetization; acquisition time of ancient magnetization in this rock group can be long, and as a result the scatter in S values is largest. Evidently, metamorphism affects all groups of rocks, particularly ancient ones, which gives rise to a higher scatter in S values and thereby affects both the magnetization age and their relation to the variation amplitude.

Weighted averages of S insignificantly differ in young volcanic, intrusive, and sedimentary rocks, and relative variations in S, averaged over 10-Myr age intervals in the Phanerozoic and Precambrian are also similar [Pechersky, 1997]. In view of this similarity, data on all types of rocks are grouped in accordance with their IPR weight (Figure 1d). Information is irregularly distributed in time: data from the Phanerozoic are more representative, whereas Precambrian determinations are fewer, and their quality is worse (determinations with IPR 0.2 are predominant) [Pechersky, 1997].

##### Influence of geomagnetic reversals.

To include the possible effect of transitional reversal zones, collections with a constant polarity (S0) and those with both polarities (Sm) were separately analyzed. The probability of finding transitional-zone samples in the mixed-polarity collections was higher. Correspondingly, the S value from mixed-polarity collections of coeval rocks of one group is on average markedly higher than from single-polarity collections. This fact was accounted for through division by Sm/S0 averaged over rocks of a given age from a given group, which reduced the scatter in data but did not affect the general behavior of S, and the Precambrian pattern became better resolved [Pechersky, 1997].

##### Latitude effect.

To analyze the dependence of S on the determination latitude of paleomagnetic direction, the deviation of paleomagnetic latitude from its actual value should be first found. Possible underestimation of paleomagnetic latitude was analyzed using paleomagnetic data over the past 10 Myr, when the true latitude of the stable NRM component acquisition, insignificantly disturbed by lateral movement of crustal blocks, is known [Pechersky, 1996]. Mean paleolatitudes, calculated from 10o intervals of the true latitude of sampling sites for both volcanic and sedimentary rocks from mixed- and single-polarity collections, deviate from the true latitude by no more than 10o. Thus, the paleolatitude underestimation is on average insignificant.

We consider the latitude dependence of S for two main states of the geomagnetic field: (a) stable normal or reversed polarity, and (b) frequent polarity reversals [Pechersky, 1996, 1997]. Averaging data over age intervals of the stable field (Figure 5) yields the inverse latitude dependence of S close to the dipole field model of secular variations, secular variation amplitude of the present field observed in the northern hemisphere [Kono and Tanaka, 1995; McElhinny and McFadden, 1997; Pesonen et al., 1994; Yanovskii, 1978], and paleovariation amplitude in the Permian and Carboniferous, when the field was stable [Khramov et al., 1982]. This dependence is not observed during the high reversal frequency intervals (Figure 5d), which allows the following conclusions to be drawn. (1) The latitude dependence of S implies that its average value yields adequate constraints on the summary amplitude of paleovariations in the field direction. (2) Field generation conditions in the 1700-Ma interval were similar in the periods of stable (normal and reversed) polarity. (3) The summary amplitude of direction variations did not depend on latitude in the high reversal frequency intervals. The mean amplitude of the unstable field behavior ( S 15o, Figure 5d) does not differ from the mean amplitude of the stable one near the equator (Figure 5i); therefore, the S independence of latitude is not due to an increase in the variation amplitude that would mask S variation with latitude, but it is a regularity inherent in a specific generation mode of the geomagnetic field. The example of secular variations in the present field direction has shown that, first, their latitude dependence is markedly different in the northern and southern hemispheres [McFadden et al., 1988; Merrill and McElhinny, 1983; Pesonen et al., 1994]; second, the secular variation amplitude depends not only on latitude but also, to large degree, on longitude [Shibuya et al., 1995; Tsunakawa, 1988]; and, third, the field that existed at the core surface during the past 300 years includes, in addition to the dipole part, a combination of stable constant, immobile fluctuating, and drifting components [Gubbins, 1987], which markedly smooth the average latitude dependence. The above indicates that the amplitude of secular variations in the field direction is dominated by a nondipole component which strongly varies at the Earth's surface during epochs of unstable geomagnetic field behavior, whereas during stable field periods the nondipole field variations are regular and symmetrical and, as a result, evidently depend on latitude. The two types of field behavior are also recognizable from the analysis of geomagnetic polarity over the past 1700 Myr, providing an independent argument for the result derived from the study of the variation amplitude. The accuracy and representativity of data are still insufficient for the analysis of intermediate field states between the two regimes considered above, transition time between those, and stability time intervals of each regime. The field stability intervals are likely to exist during very short times, alternating with and superimposing on one another [Pesonen et al., 1994].

Thus, similar to the geomagnetic polarity behavior (Figure 1d), two intervals, Phanerozoic and Precambrian, differing in the type of variations in S are recognized, and the boundary between them lies at about 600 Ma. This may be explained in part by the amount and quality of data, but the characteristic features discussed above suggest that these two types of polarity behavior are likely to have actually existed. Irrespective of paleolatitude, the value of S very smoothly increases from 13o to 16o in a 1450-450-Ma interval and afterward gradually decreases to 12o until presently. High-frequency S fluctuations within 1-4o occur against the background of this smooth variation in the amplitude of paleovariations.

##### Wavelet analysis of the summary amplitude of field direction variations [Galyagin et al., 1999].

The smooth integral wavelet spectrum of the S time series exhibits weak peaks at 45, 80, 160, 300, 450, and about 1000 Myr. As is evident from the wavelet plane (Figure 4), these periods are local maximums. The pattern is rather uniform at a> 100 Myr. The difference between the Phanerozoic and Precambrian generation modes is obvious at characteristic times smaller than 100 Myr: an interval of more intense Precambrian variations is observed at these times.

#### Variation in the Paleointensity (Modulus of the Field Intensity)

The absolute value of paleointensity is mostly determined by using heating methods (Thellier, Wilson-Burakov, van Zijl, Shaw, and others [Khramov et al., 1982; Merrill and McElhinny, 1983; Pechersky, 1985]). The Thellier method with controllable mineral alterations is believed to be most reliable. In addition to determinations of the paleointensity Ha and related estimates of the magnetic dipole moment (DM) incorporated in the Database [Tanaka and Kono, 1994], we used data on the Paleozoic and Precambrian that were not included in this database [Harcombe-Smee et al., 1994; Mikhailova et al., 1994, 1996; Oppenheim et al., 1994; Pavlov et al., 1992; Starunov et al., 1996; Thomas, 1993; Thomas and Piper, 1995; Thomas et al., 1995; Ueno, 1995].

The Ha and DM determinations are distributed very irregularly in time. Thus, in many intervals occasionally reaching a length of 100 Myr, the determinations are absent at all (Figure 1e) [Pechersky, 1998]. Coverage of a 400-0-Ma interval (1058 determinations) is on the whole satisfactory, whereas only 89 determinations are available for the Early Paleozoic-Precambrian. 681 of 1063 determinations from the Phanerozoic and 83 of 84 in the Riphean were made by using the Thellier method [Pechersky, 1998].

The values of paleointensity and related DM vary within a wide range, from < 5 to > 100 m T (Figures 1e-1g). (The majority of Ha> 100 m T values were obtained with the help of the Shaw method!) The scatter (standard deviation) in the Ha and DM determinations close in age was taken as a characteristic of the paleointensity variation amplitude.

##### Reliability index of paleointensity determination.

Similar to the analysis of data on paleomagnetic directions used for estimation of the amplitude of paleovariations, reliability indexes of paleointensity determinations (RIPs), ranging from 0 to 1, are introduced. The maximum RIP = 1 characterizes samples from baking zones and rapidly cooling lavas; maximum RIPs of 1, 0.6, 0.6, and 0.5 are given by the methods of Thellier, Shaw, Wilson-Burakov, and van Zijl, respectively; and RIP values of not more than 0.2 characterize other methods and paleointensity estimates obtained from relative values of thermoremanent magnetization (TRM) created in laboratory in a given external magnetic field and natural remanent magnetization (NRM). If data on paleomagnetic direction are unavailable, a value of 0.3 is subtracted from the pertinent RIP. RIP values reduced by 0.2-0.3 are commonly adopted for determinations made before 1970 and, finally, lower RIP values are assigned to less accurately dated determinations. Most authors assume that ages of rocks and stable natural remanence component coincide, provided the component is a primary TRM, the Database [Tanaka and Kono, 1994] provides very little information about the validity of the primary thermal origin of remanence. Calculation of mean paleointensities includes a RIP as a weight of each determination.

The majority of determinations have RIP 0.5 (RIPs are close to unity for many of those) mostly due to numerous Thellier determinations from baked rocks, performed by G. M. Solodovnikov and covering a 400-0-Ma interval. RIP does not exceed 0.2 in the age intervals 70-80, 170-180, 220-230, and 360-370 Ma; most Riphean determinations have RIP = 0.4-0.5 mainly due to lacking information about paleomagnetic directions and inaccuracy of datings [Pechersky, 1998].

##### The influence of geomagnetic reversals.

Paleointensity is known to considerably decrease during geomagnetic reversals and excursions, but we are not interested in the field behavior during reversals. For this reason we did not consider Database determinations that were attributed by their authors to reversal zones, as well as abnormally low Ha values whose directions are untypical of their time and site.

##### Latitude effect.

A close linear relation between Ha and DM (Figure 6) [Pechersky, 1998] reflects obvious predominance of the dipole component in Ha. The Ha value changes across the Ha (DM band by about 35%, yielding variation in the present dipole field intensity from equator to pole. The band length which reflects the amplitude of variations in both Ha and DM considerably overlaps the possible latitude dependence of Ha.

I consider the latitude dependence of paleointensity for two cases of geomagnetic field regime: (1) unstable, with frequent reversals, and (2) stable, with very rare reversals. The time intervals 45-0 Ma and 310-260 Ma will be examined where paleointensity data are sufficiently representative and cover a wide range of paleolatitudes. In both cases, irrespective of the reversal regime, Ha averages over latitude intervals are close to the line representing the latitude dependence of field intensity of the central axial dipole (Figure 7a); therefore, the paleointensity is close to the central axial dipole field irrespective of the reversal regime. The closeness of the DM to the central axial dipole is substantiated by the comparison of average DMs in the southern and northern hemispheres in the age interval 7-0 Ma. Such an interval is chosen because it is the only one in which the numbers of DM determinations in the southern (56 collections) and northern (127 collections) are more or less comparable and cover a sufficiently wide interval of latitudes. Average DMs in the northern and southern hemispheres are differ insignificantly: (7.4 3.6)1022 A m 2 (RIP=0.65) and (8.5 2.7)1022 A m 2 (RIP=0.77), respectively. To verify stability of these results, the age interval was divided into the intervals 0.9-0 and 7-1 Ma, which gave nearly the same values [Pechersky, 1998]. Thus, one may state that the geomagnetic field is close to that of a central axial dipole.

The latitude dependence of Ha variations is quite different (Figure 7b): the high reversal frequency period is characterized by an increase of the variation amplitude with latitude, which does not agree with the dipole field behavior, whereas the amplitude decreases with latitude, in accordance with the dipole field, during the stable field period.

##### Smoothing.

To reduce the scatter in data connected with dating uncertainties and systematic errors, all results were subdivided into 10-Myr intervals in which Ha and DM averages and standard deviations dH were calculated, with weights taken in accordance with RIP indexes. The 10-Myr averages were then smoothed both with and without weighting. Smoothing windows of 30 Myr and more in length and a step of 10 Myr were used [Pechersky, 1998].

##### Wavelet analysis of paleointensity.

In contrast to the geomagnetic polarity scale, the time series of the intensity modulus includes noticeable breaks (Figure 1) [Pechersky, 1998]. A specific wavelet analysis procedure was developed to analyzed such series [Galyagin and Frik, 1996; Galyagin et al., 1999]. The integral spectrum of Ha exhibits peaks of 45, 140, 260, and 560 Myr. The wavelet plane of Ha (Figure 1) [Galyagin et al., 1999] differs from those discussed above. Only two oscillations with relatively long periods of 230-260 Myr (from about 500 Ma until present time) and 135 Myr (approximately from 1200 to 1000 Ma) are more or less reliably recognized, and a series of local maximums with periods of 30 to 80 Myr is additionally observed. Two areas of 1600-1450 and 850-450 Ma, clearly observed on the plane, are related in part to lacking data (Figure 1e); on the other hand, they resemble similar areas of other field characteristics, not related to lacking data (Figure 1). This mostly concerns the boundary region between the Riphean and Phanerozoic (circa 850-450 Ma).

##### Wavelet analysis of paleointensity variations.

To analyze the paleointensity variation, I consider the time behavior of the standard deviation dH and ratio dH/Ha. The integral spectrum of dH is very close to the Ha spectrum and has only one additional peak yielding a period of 60 Myr. The spectrum dH/Ha is somewhat different and exhibits peaks with 40, 100, 180, 320, and 500 Myr. Like integral spectra, the wavelet spectra of Ha and dH are on the whole similar [Galyagin et al., 1999]. Thus, the higher the intensity of an oscillation, the stronger its variation. The wavelet plane of dH/Ha has generally the same pattern as those of Ha and dH.

##### The general pattern of paleointensity behavior.

The above data on the paleointensity behavior reveal three tendencies: (1) The Ha and dH scatter within comparatively narrow time limits is likely to reflect the paleointensity variation amplitude. (2) Relatively smooth long-period cyclic variations in Ha and DM are observed (with periods ranging from several tens to several hundreds of millions of years). (3) The average paleointensity level in Precambrian (DM averages 6.51022 A m 2 ) is higher than in Phanerozoic (DM averages 4.81022 A m 2 ); the Riphean is characterized by a general drop in paleointensity, and its general increase is observed in the Phanerozoic.

#### Main Features of the Geomagnetic Field Behavior in the Neogaea

1. The Neogaea is evidently dominated by the reversed geomagnetic polarity, but the normal polarity percentage increases, against the background of marked fluctuations, from the Early Paleozoic to the present time; the whole Phanerozoic is a transitional, unstable-polarity interval. This instability appears as a marked increase in reversal frequency and the shortening of single-polarity magnetic zones. The mean reversal frequency is less than 1 reversal every 10 Myr in the Precambrian (magnetic zones 1 to 100 Myr long are predominant), about 6 reversals every 10 Myr in the Paleozoic (magnetic zones 0.5 to 5 Myr long), over 8 reversals every 10 Myr in the Mesozoic (0.2 to 2.5 Myr), and about 30 reversals every 10 Myr in the Cenozoic (0.05 to 1 Myr), the frequency increasing from 12 per 10 Myr in the Early Cenozoic to 43 in the last 10-Myr interval. The aforementioned asymmetry of the field, as well as the regular distributions of its reversal frequency and lengths of constant-polarity intervals indicate that at least two field generation modes existed over the past 1700 Myr. The first mode was typical of the Precambrian and Paleozoic, when long stable-field intervals of mostly reversed polarity prevailed; the second mode characterized by frequent reversals was typical of Mesozoic and especially Cenozoic. Activities of both modes largely overlapped in time. Long stable field intervals of constant polarity were rather uniformly distributed in the Neogaea: their centers (Figure 1a, b) at about 1680, 1520,, 1360, 1150, 1100, 900, 700, 630, 470, 290, and 100 Ma are spaced by 160-200 Myr except for two anomalies between 1150 and 1100 Ma and between 700 and 630 Ma, whereas the reversal frequency between these intervals considerably increases in the Phanerozoic.

The reversal sequence is fractal, with the dimensions d 0.5-0.6 and 0.9, i.e., has the property of self-similarity of large-scale processes in accordance with the observed reversal distribution: alternation of high reversal frequency zones with fairly long intervals of rare reversals. On the other hand, their distribution within intervals of high reversal frequency is nearly chaotic (d<0.6).

2. The summary amplitude behavior of field direction paleovariations is on the whole characterized by the same regularities as the reversal frequency variations; the Riphean amplitudes vary between 10o and 14o and occasionally reach 20o ; their general level weakly rises, whereas an inverse situation is observed in the Phanerozoic: against the background of weak fluctuations, S smoothly falls from 18o in the Vendian to 11o in the Cretaceous. The analysis of latitude dependence of S from three main states of the geomagnetic field (stably normal polarity, stably reversed polarity, and frequent reversals) leads to the following conclusions. (a) The variation in S with latitude implies that the paleovariations in the summary amplitude of geomagnetic field, prevailing in the Precambrian and Paleozoic, are consistent with a central axial dipole, and (b) this amplitude was on average independent of the paleolatitude in high reversal frequency zones. Furthermore, average amplitudes of unstable and stable regimes virtually coinciding, the invariability of S with latitude is evidence of a different mode of geomagnetic field generation.

Mean paleolatitudes calculated from paleomagnetic inclinations provided by collections of young volcanic and sedimentary rocks of single or mixed polarity differ from the true latitude by less than 10o, which implies that, on average, the paleolatitude is not overly underestimated.

3. Three tendencies are recognizable in the intensity behavior during the Neogaea:

(a) The scatter in Ha and DM (standard deviation dH ) within relatively narrow time limits is likely to reflect the amplitude of intensity paleovariations; the dH/Ha value appears to correlate with intervals of predominant reversed polarity (especially noticeable in the Riphean) and with reversal frequency.

(b) Relatively smooth long-period cyclic variations in Ha and DM are observed (over times of few tens to few hundreds of millions of years). Correlated extremums being nearly as frequent as anticorrelated ones, the time distribution of extremums of both types is rather chaotic except for the correlation between the DM and polarity asymmetry: correlation of extremums is almost everywhere normal in the Phanerozoic and inverse in the Riphean. The dH and dH/Ha values correlate with the polarity asymmetry and reversal frequency F, and the polarity asymmetry is anticorrelated with F and S in the Riphean (the correlation is mostly positive in the Mesozoic and Cenozoic). Most noticeable is the correlation, observed throughout the Neogaea, between the lower amplitude relative variation of the paleointensity dH/Ha and Neogaean intervals of lower frequency or absence of reversals (Figure 1).

(c) The mean level of paleointensity in the Precambrian (DM = 6.51022 A m 2 ) was higher than in the Phanerozoic (DM = 4.81022 A m 2 ); the Riphean is characterized by a general drop in the paleointensity, and the Phanerozoic, by its rise. The general Phanerozoic rise in paleointensity correlates with an increase in the summary amplitude of field direction paleovariations, in the reversal frequency, and in the percentage of normal polarity. On the whole, higher paleointensity and its smooth decrease in the Riphean correlate with the evident predominance of reversed polarity and very low reversal frequency in the same period.

The paleointensity is close to the field of a central axial dipole irrespective of the reversal regime, whereas variations in Ha show quite different latitude dependences: with increasing latitude, the amplitude of paleointensity variations increases in the case of the high reversal frequency regime and decreases in intervals of a stable field.

4. The Riphean trend of all geomagnetic characteristics changes to the Phanerozoic one at about 600 Ma.

5. Datasets providing constraints on the reversal frequency and polarity asymmetry, on dH/Ha and DM, and on S are virtually independent (this is especially true for the first two sets). This is an argument confirming the validity of the correlations between these parameters.

6. Wavelet analysis of the reversal frequency, field sign, paleointensity, variations in the field direction and intensity, and their Neogaean evolution indicated that the geomagnetic field was generally unstable, i.e., its evolution involved no periodical processes. The following facts support this conclusion (Figure 4) [Galyagin et al., 1999].

(a) A marked difference between the general patterns of wavelet spectra of all geomagnetic parameters considered above is observed. For example, if the reversal frequency F is markedly more pronounced in the Phanerozoic, the summary amplitude of variations in the field direction S, as well as change in the polarity sign P, are considerably more "active" in the Precambrian.

(b) The majority of derived periods are represented by short "events" whose length amounts to one or two full oscillations. Only four of about one hundred of such events include three to five oscillations of a given period; these are the oscillations of the reversal frequency F at a period of 100-110 Myr in the age interval from 550 to 160 Ma, oscillations of the single-polarity magnetic zone length at a period of 160-200 Myr observed from 1500 to 850 Ma, oscillations of relative variation in paleointensity dH/Ha at a period of 90-100 from 450 to 100 Ma, and oscillations of the summary amplitude of variations in the field direction S at a period of 75-90 Myr from 1450 to 1150 Ma.

(c) Oscillations of various characteristics at close periods are commonly asynchronous. A Riphean interval of 1500 to 800 Ma is noticeable in which oscillations of field sign and paleointensity variations with close periods of 140-180 Myr are grouped. In the Vendian, they continue as oscillations of the same characteristics and reversal frequency at a period of about 220-300 Myr (Figure 4). Moreover, oscillations of F, P, dH/Ha, and S at a period of about 100 Myr are grouped in the Phanerozoic interval between 500 and 100 Ma. The remaining preferred intervals of "periods", without regard to the occurrence time of related oscillations, are as follows: 40-45 Myr ( F, P, Ha, dH, dH/Ha, S ); 60-70 Myr ( F, P, dH ); 80-100 ( F, dH/Ha, S ); 130-140 Myr ( F, Ha, dH ); 160-180 Myr ( F, P, dH/Ha, S ); 250-260 Myr ( Ha, dH ): 300-320 Myr ( dH/Ha, S ); and 500-600 Myr ( P, Ha, dH, dH/Ha ).

(d) Oscillation periods often smoothly vary with time (Figure 4), which is largely responsible for wide ranges of periods indicated in item "c". Most periods decrease with time concordantly with the general acceleration of the process; thus the F period falls from 100 to 85 Myr over a 470-160-Ma interval and from 70 to 60 Myr over a 150-0-Ma interval, and the S period falls from 90 to 70 Myr during the time from 1500 to 1100 Ma. The cases of an increase in periods, consistent with the slowing-down of the process are less frequent. For example, the P and dH/Ha periods increase, respectively, from 200 to 280 Myr and from 80 to 100 Myr over a 450-150-Ma interval (Figure 4).

(e) The boundary between Phanerozoic and Riphean, best expressed on the wavelet plane of reversal frequency, is recognizable in all time series (Figure 4).

7. The general behavior of main parameters of the geomagnetic field in the Neogaea (paleointensity and its variations, and summary amplitude of variations in the field direction, polarity, and reversal frequency) provides a basis for the modeling of geomagnetic field generation and characterizes processes in the core that are comparable with processes in the lithosphere and at the Earth's surface.

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