Academic literature on the topic 'Paleomagnetism Mathematics'

The Rikitake two-disc system [10] has been proposed as a model of the Earth's magnetic dipole. Numerical integration of the system by Rikitake[10] and Allan [1] showed the phenomenon of polarity reversal which is seen in terrestrial paleomagnetic data [6]. Reversals in the simulations occurred at irregular and apparently unpredictable time intervals, in accord with the capricious character of the real data, though the agreement was qualitative rather than quantitative.

The introduction of modern methods for the mathematical processing of geological data is one of the promising areas of study and development in the field of geosciences. For example, today mathematical geology makes it possible to reliably identify astronomical cycles by measuring the scalar magnetic parameters of rocks (magnetic susceptibility). The main aim of this study is to develop a mathematical tool for identifying stable oscillation cycles (periods) in the dataset of the magnetic susceptibility of rocks in a geological section. The author’s method (algorithm) is based on the concept of discrete mathematical analysis—an innovative mathematical approach to the analysis of discrete geological and geophysical data. Its reliability is also demonstrated, by comparison with the results obtained by classical methods: Fourier analysis, Lomb periodogram, and REDFIT. The proposed algorithm was applied by the authors to analyze the material of field geological studies of the Zhelezny Rog section (Taman Peninsula). As a result, stable cycles were determined for the Pontian and Lower Maeotian sedimentary strata of the Black Sea Basin (Paratethys).

A thermodynamically consistent model for soft deformable viscoelastic magnets is formulated in actual space (Eulerian) coordinates. The possibility of a ferro-paramagnetic-type (or ferri-antiferromagnetic) transition exploiting the Landau phase-transition theory as well as mechanical melting or solidification is considered, being motivated and applicable to paleomagnetism (involving both thermo- and isothermal and viscous remanent magnetization) in rocks in Earth’s crust and to rock-magma transition. The temperature-dependent Jeffreys rheology in the deviatoric part combined with the Kelvin-Voigt rheology in the spherical (volumetric) part is used. The energy balance and the entropy imbalance behind the model are demonstrated, and its analysis is performed by time discretization, proving existence of weak solutions.

Summary We study predictions of reversals of Earth’s axial magnetic dipole field that are based solely on the dipole’s intensity. The prediction strategy is, roughly, that once the dipole intensity drops below a threshold, then the field will continue to decrease and a reversal (or a major excursion) will occur. We first present a rigorous definition of an intensity threshold-based prediction strategy and then describe a mathematical and numerical framework to investigate its validity and robustness in view of the data being limited. We apply threshold-based predictions to a hierarchy of numerical models, ranging from simple scalar models to 3D geodynamos. We find that the skill of threshold-based predictions varies across the model hierarchy. The differences in skill can be explained by differences in how reversals occur: if the field decreases towards a reversal slowly (in a sense made precise in this paper), the skill is high, and if the field decreases quickly, the skill is low. Such a property could be used as an additional criterion to identify which models qualify as Earth-like. Applying threshold-based predictions to Virtual Axial Dipole Moment (VADM) paleomagnetic reconstructions (PADM2M and Sint-2000) covering the last two million years, reveals a moderate skill of threshold-based predictions for Earth’s dynamo. Besides all of their limitations, threshold-based predictions suggests that no reversal is to be expected within the next 10 kyr. Most importantly, however, we show that considering an intensity threshold for identifying upcoming reversals is intrinsically limited by the dynamic behavior of Earth’s magnetic field.

Thesis: S.B., Massachusetts Institute of Technology, Department of Mathematics, 2014.
Author received an S.B. from the Department of Mathematics, but her thesis was submitted to the Department of Earth, Atmospheric and Planetary Sciences for the degree of S.B. Cataloged from PDF version of thesis.
Includes bibliographical references (pages 29-32).
Rapid India-Asia convergence has led to a major continental collision and formation of the Himalayas, the highest mountain range on Earth. Knowledge of the paleolatitude of the Kohistan-Ladakh Arc (KLA), an intermediate tectonic unit currently situated between the converging Indian and Eurasian continents in Western Himalaya, would constrain the tectonic history and dynamics of Himalayan orogenesis. We present new paleomagnetic data from the Khardung volcanic rocks of the Shyok-Nubra valley region of Ladakh, western Himalaya. Samples from all four sites (KP1-KP4) display high-temperature components indicating a roughly equatorial paleolatitude, with the average of site mean directions implying a paleolatitude of 5'N. We interpret results of a positive baked contact test at one site (KP3) to imply that the high-temperature components in the distal volcanic bedrock predate bedding tilt and dike formation. Previous studies of the Khardung unit (Bhutani 2009, Dunlap 2002) have measured 40Ar-39Ar and U-Pb dates of -52-67 Ma. Assuming these ages apply to our samples, our results support the two-stage collision model of Jagoutz and Royden (in prep), which indicates an approximately equatorial India-KLA collision at 50 Ma.
by Elizabeth A. Bailey.
S.B.