Christopher Barton (Advisor), Mateen Rizki (Committee Member), Sarah Tebbens (Committee Member)
Master of Science (MS)
The geologic record documents that the Earth's magnetic field has reversed 284 times over the past 160 Myr. This study uses two methods to analyze the scaling properties of the pattern of geomagnetic reversals and to analyze the scaling properties of reversals output by two mathematical self-reversing dynamo models, the Rikitake (1958) two-disk dynamo and the magnetohydrodynamic (MHD) model of Driscoll and Olson (2011). The first analysis method plots the duration versus cumulative probability for geomagnetic polarity intervals ranging between 0.01 and 35 Myr. The Kolmogorov-Smirnov statistic is used to determine the optimal minimum value of xmin at which power scaling begins, followed by the method of maximum likelihood estimation which estimates the scaling exponent α. For the geomagnetic field, xmin ≈ 0.26 Myr and α ≈ 2.22 for all polarity intervals greater than xmin. Polarity intervals < 1.0 Myr are shown to follow a gamma distribution. The second method analyses the temporal clustering of the reversals using box-counting. For the geomagnetic field, box-counting reveals power scaling behavior in the temporal clustering for box sizes from 1.0 Myr to 20.0 Myr. The scaling exponent DB is determined to be 0.88 for all polarity intervals. A roll-off observed for box sizes less than ∼1.13 Myr for the geodynamo leads to splitting of the polarity interval data set into two subsets, one < 1.0 Myr and the other ≥ 1.0 Myr. The method of maximum likelihood returns xmin ≈ 1.13 Myr and α ≈ 2.46 for intervals ≥ 1.0 Myr. Box-counting on synthetic occurrence times generated from the polarity intervals ≥ 1.13 Myr returns DB ≈ 0.69. The two analysis methods are also applied to the output of the Rikitake (1958) two-disc dynamo model and the MHD model of Driscoll and Olson (2011). For all polarity intervals in the Rikitake (1958) dynamo, the maximum likelihood method returns xmin≈ 2.0 synthetic time units and α ≈ 2.7. Box-counting returns a scaling exponent DB ≈ 0.83 for all box sizes. No roll-off is observed in any of the plots for the Rikitake (1958) model. For the Driscoll and Olson (2011) model, xmin ≈ 0.47 Myr and α ≈ 2.62 for all polarity intervals. Box-counting returns a scaling exponent DB ≈ 0.92. A roll-off observed at ∼1.0 Myr in the box-counting plot for Driscoll and Olson (2011) prompts splitting of the data set; maximum likelihood produces xmin ≈ 1.09 simulated Myr and α ≈ 2.50 for polarity intervals ∼1.0 simulated Myr. Box counting returns DB ≈ 0.72 for box sizes ≥ 1.09 simulated Myr. Box sizes < 1.0 simulated Myr also follow a gamma distribution. Taken together, the two analysis methods 1) show that the MHD model of Driscoll and Olson (2011) successfully reproduces the scaling behavior of the geomagnetic reversal pattern, and 2) verify that there are two "modes" operating within the Earths interior to produce reversals, one a "reversing" state producing reversals at a higher rate with an independent probability distribution, and a "non-reversing" state producing reversals whose occurrence rates are lower and whose distribution is statistically self-similar and dependent.
Department or Program
Department of Earth and Environmental Sciences
Year Degree Awarded
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