Mesozoic Dipole Low in Relation to the Cretaceous Normal Superchron

Abstract
The behavior of a Mesozoic dipole low and a long interval of normal polarity in the Cretaceous can be described in relation to the geodynamo. Paleomagnetic data has been critical in understanding the behavior of the Earth’s geomagnetic polarity reversals during the Mesozoic. Looking into the Cretaceous Normal Superchron in relation to the Mesozoic dipole low is may potentially help understand the behaviors of the geomagnetic polarity reversals in the future and better understand the geodynamo. Numerous studies and hypotheses work to understand the extrinsic mechanisms that could affect the behavior in a way that is predictable. Studies include researching electromagnetism, geomagnetic polarity reversal evidence, theories for polarity reversal behaviors, and models to understand the complexities through studying the Cretaceous Normal Superchron. Understanding polarity reversals is important to understanding the geodynamo.

Introduction
In the Earth’s history, there is evidence of magnetic polarity reversals occurring throughout time. The Mesozoic Dipole Low (MDL) s a period dominantly characterized by a low-field state of the Earth’s magnetic field. During the Cretaceous period, there is an interval of approximately 40 Ma where there are no reversals occurring, but rather a relatively long period of normal polarity. This is also known as the Cretaceous Normal Superchron (CNS), where it is characterized by the absence of geomagnetic reversals. Reasons for this behavior are sought to be explained through the system the geodynamo, and the variables and constraints that could possibly be affecting the interval of normal polarity. A common implicit assumption of geomagnetic theories is theories is the long-term constancy of the average moment of the dipole field (Prévot 1990).

Geomagnetic reversals are defined by the change in the planet’s magnetic field in with the North-South dipoles are switched while the geographic North and South remain the same. Although this phenomenon is observed in our galaxy, the Sun for example, it is not as clearly defined for the Earth. The Earth’s magnetic field is more complex than a simple dipole, also being the reason for understanding the complexities of the magnetic reversal behaviors.

Cartoon depiction of the Geodynamo

Dynamo Theory
A dynamo process is believed to be the source of intrinsic generation of the Earth’s magnetic field. The dynamo in particular to the earth is thought to occur from the coupling of the solid inner core and liquid inner core. Heat from the inner core, mainly produced by the decay of radioactive isotopes, creates rapid convection movements in the liquid outer core. Due to the Earth’s rotation, the planet’s spin adds twist to the convection currents, which stirs electrically conducting low viscous, iron-rich liquid in the outer core. These convection currents create magnetic flux lines, which results in a magnetic field generated by the geodynamo coupling of the inner core and outer core (Grotzinger 2010). Figure 1 is a cartoon depiction of the geodynamo and the formation of the magnetic field. The magnetic field produced is more complex than a simple dipole field and is constantly changing over time.

Mathematically, electromagnetism can be described by a set of partial differential equations also known as Maxwell’s equations. These equations work together with the Lorentz force law and form the foundation of electrodynamics. The equations are listed below with a brief definition of each equation.

Gauss’s Law:

\begin{equation} \oint_{S}{\vec{E}\cdot d\vec{A}=\frac{1}{{\varepsilon_{0}}}}Q_{enc}\nonumber \\ \end{equation}

The electric flux leaving a volume is proportional to the charge inside. E is the electric field, A is the differential element of area, epsilon is a constant called ”The Permittivity of Free Space,” and Q is the enclosed charge.

Gauss’s Law for Magnetism:

\begin{equation} \oint{\vec{B}\cdot d\vec{A}}=0\nonumber \\ \end{equation}

There are no magnetic monopoles. B is the magnetic flux density and dA is the differential element of area.

Faraday’s Law of Induction:

\begin{equation} {\oint_{C}{\vec{E}\cdot d\vec{\ell}}=-\frac{d}{{dt}}}\int_{S}{\vec{B}_{n}d\vec{A}}\nonumber \\ \end{equation}

The voltage induced in a closed circuit is proportional to the rate of change of the magnetic flux it encloses. E is the electric field, dl is differential element of the path length, B is the magnetic flux density, and dA is the differential element of area.

Ampère’s Circuital Law:

\begin{equation} \oint_{C}{\vec{B}d\vec{\ell}=\mu_{0}I_{C}}\nonumber \\ \end{equation}

The magnetic field integrated around a closed loop is proportional to the electric current plus displacement current (rate of change of electric field) it encloses. B is the magnetic flux density, dl is the differential element of the path length, mu is a constant called ”The Permeability of Free Space,” and I is the enclosed current.

Lorentz Force:

\begin{equation} \vec{F}=q(\vec{v}\times\vec{B})\nonumber \\ \end{equation}

The Lorentz force is defined as the magnetic force on a moving charged particle through an electric and magnetic field. q is the electric charge with an instantaneous velocity v , and B is the magnetic flux density or field. The cross product corresponds to the computation being a vector quantity rather than scalar.

Though there are multiple mathematical equations helping to define electromagnetism, the geodynamo is complex and difficult to understand. There are spontaneous reversals of the magnetic field with large amounts of evidence being found in the geologic record. Lab experiments of the magnetic field reversals being generated by turbulent swirling flow of liquid sodium (von Kármán sodium or VKS) have been observed in laboratory experiments (Petrelis 2010), but the earth is a self-organized natural system. The self-organized natural system being one whose behavior is not predetermined by external constraints, but emerges from interaction from within the system (Grotzinger 2010).