0 20 40 60 80 100 120 140 160 Mid-age of sliding window (Ma)
Fig. 4.20. Estimated reversal rate for the geodynamo for the past 160 Myr. Constructed from the time scales of Kent and Gradstein (1986) and Cande and Kent (1995), following the methods of McFadden (1984a). From Merrill etal. (1996).
158 to 130 Ma and from 25 Ma to the present, with an intermediate nonstationary segment including the Cretaceous Superchron. In an innovative approach Constable (1999) uses a method that does not rely on the details of any specific probability density. Although she is unable to reject either model, the gross structure of her estimated reversal rate closely parallels that of Fig. 4.20.
The question arises as to whether the fine structure observed in curves such as shown in Fig. 4.20 is meaningful. For example, several studies (Negi and Tiwari, 1983; Mazaud et al., 1983; Mazaud and Laj, 1991; Marzocchi and Mulargia, 1990; Rampino and Caldeira, 1993; Raup, 1985; Stothers, 1986) have suggested either a 15- or a 30-million-year periodicity in the reversal chronology record. McFadden (1984b) showed that similar apparent periodicities were produced by the use of fixed-length sliding windows to analyze a Poisson process with a uniformly changing reversal rate. McFadden and Merrill (1984) did not observe these periodicities when using sliding windows with a fixed number of intervals. Lutz (1985), Stigler (1987), McFadden (1987), and Lutz and Watson (1988) all showed that the perceived periodicities are more likely an artifact of the methods of analysis than real geophysical phenomena.
McElhinny (1971) and Irving and Pullaiah (1976) introduced the concept of polarity bias, which incorporated the idea of differential stability in the normal and reverse polarity states. That is, it was perceived that during times of normal polarity bias the field remained normal most of the time because that polarity was substantially more stable than the reverse polarity and vice versa for times of reverse polarity bias. Cox (1982) formalized this into polarity bias superchrons. This concept was interesting in that it was at odds with one of the few obvious and truly robust conclusions from the dynamo equations. The equations are symmetric in the magnetic field. This means that the velocity field in the geodynamo is unable to sense the direction of the magnetic field and so the statistical properties of the normal and reverse polarity states should be identical (Merrill et al., 1979).
Using the analysis tools of McFadden (1984a), McFadden and Merrill (1984) were able to show that, at least since about 165 Ma, the normal and reverse polarity states do not exhibit any differences in their relative stabilities either before or after the Cretaceous Superchron (see also McFadden et al., 1987). Merrill and McFadden (1994) were able to show that the Cretaceous Superchron is so long that it cannot be a member of the typical process describing reversals (see also McFadden and Merrill, 1995; Opdyke and Channell, 1996). Thus, it would seem that the geodynamo has two basic states - a reversing state and a non-reversing state. Together with the observed nonstationarity in reversal rate this leads to a simple broad-scale interpretation consistent with theory and with the observed polarity data for the past 160 Myr. That is, the boundary conditions imposed on the core by the lowermost mantle gradually changed in such a way as to reduce the reversal rate until it eventually reached zero (sometime soon after the start of the Cretaceous Superchron). The superchron was then not a consequence of polarity bias but of the fact that the reversal process had ceased. The fact that it was of normal polarity was merely a matter of the polarity the field was in (with a 50% chance for either polarity) at the time the reversal process ceased. The boundary conditions continued to change, and at some time before the end of the superchron the reversal process started again; the reversal rate gradually increasing to the current rate of about 4Vi reversals per million years.
Kent and Olsen (1999) found that the interval lengths of their Late Triassic (Newark) GPTS (Fig. 4.11) have a mean duration of about 0.54 Myr, which corresponds to an average reversal rate of about 1.8 Myr"1 (§4.3.5). They concluded that the distribution of interval lengths, ranging from about 0.02 to about 2 Myr, is well approximated by a Poisson distribution (k « 1). Critically, they note that there is no discernible polarity bias. Thus there is little evidence in the Newark GPTS for a prominent interval of low reversal rate (Johnson et al., 1995) or strong normal polarity bias (Algeo, 1996). Kent and Olsen (1999) point out that the Hettangian was a time of widespread igneous activity and of thick accumulation of sediment during a time of predominantly normal polarity. Results from the Hettangian tend to be over-represented in paleomagnetic compilations and this may provide a more satisfactory explanation for the claims of Johnson et al. (1995) and Algeo (1996).
The suggestion by Champion et al. (1988) that there are several reverse subchrons in the Brunhes (§4.4.5) has fundamental implications for the reversal process because it would imply that the reverse polarity state has been substantially less stable during the Brunhes than the normal polarity state. Since the dynamo equations show that the two polarities must be statistically identical, such a difference in stability can only be produced by mantle-imposed boundary conditions. Because the two stabilities are the same throughout the rest of the GPTS, these boundary conditions would have had to have changed in much less
than 10 years. However, the mantle changes on a time scale of 10 -10 years, so there is a major incompatibility. Merrill and McFadden (1994) concluded that the evidence that the observed abnormal directions represent genuine field reversals is not sufficiently compelling for them to be included in the GPTS.
Short polarity subchrons during the Cretaceous or Kiaman Superchrons would have similar implications for the reversal process. Consequently, the evidence for any such subchrons during either superchron needs to be thoroughly tested. Within the Cretaceous Superchron Tarduno et al. (1992) observed seven reverse polarity zones in the middle of the Albian. However, the magnetization in these zones is carried by hematite and may be late diagenetic in origin. Furthermore, the reverse magnetization components are not antipodal to the normal magnetization components but are offset toward directions consistent with the Late Cretaceous or Paleogene. Opdyke and Channell (1996) conclude that it is doubtful these mid-Albian reverse polarity zones represent the geomagnetic field at the time of deposition of the sediments, and consequently they should not be incorporated into the GPTS.
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