The tachocline has values of the stratification or buoyancy frequency N two or more orders of magnitude greater than the Coriolis frequency. In this and other respects it is very like the Earth's atmosphere, viewed globally, except that the Earth's solid surface is replaced by an abrupt, magnetically-constrained ‘tachopause’ (Gough & McIntyre 1998). The tachocline is helium-poor through fast ventilation from above, down to the tachopause, on timescales of only a few million years. The corresponding sound-speed anomaly fits helioseismic data with a tachocline thickness (0.019 ± 0.001) R⊙, about 0.13 × 105 km (Elliott & Gough 1999), implying large values of the gradient Richardson number such that stratification dominates vertical shear even more strongly than in the Earth's stratosphere, as earlier postulated by Spiegel & Zahn (1992). Therefore the tachocline ventilation circulation cannot be driven by vertically-transmitted frictional torques, any more than the ozone-transporting circulation and differential rotation of the Earth's stratosphere can thus be driven. Rather, the tachocline circulation must be driven mainly by the Reynolds and Maxwell stresses interior to the convection zone, through a gyroscopic pumping action and the downward-burrowing response to it. If layerwise-two-dimensional turbulence is important, then because of its potential-vorticity-transporting properties the effect will be anti-frictional rather than eddy-viscosity-like. In order to correctly predict the differential rotation of the Sun's convection zone, even qualitatively, a convection-zone model must be fully coupled to a tachocline model.

The sun is a magnetic star whose variable activity has a profound effect on our technological society. The high speed solar wind and its energetic particles, mass ejections and flares that affect the solar-terrestrial interaction all stem from the variability of the underlying solar magnetic fields. We are in an era of fundamental discovery about the overall dynamics of the solar interior and its ability to generate magnetic fields through dynamo action. This has come about partly through guidance and challenges to theory from helioseismology as we now observationally probe the interior of this star. It also rests on our increasing ability to conduct simulations of the crucial solar turbulent processes using the latest generation of supercomputers.

Introduction

The intensely turbulent convection zone of the sun, occupying the outer 30% by radius or 200Mm in depth, exhibits some remarkable dynamical properties that have largely defied theoretical explanation. The most central issues concern the difierential rotation with radius and latitude that is established by the convection redistributing angular momentum, and the manner in which the sun achieves its 22-year cycles of magnetic activity. These dynamical issues are closely linked: the global dynamo action is most likely very sensitive to the angular velocity Ω profiles realized within the sun. It is striking that the underlying solar turbulence can be both highly intermittent and chaotic on the smaller spatial and temporal scales, and yet achieve a large-scale order that is robust in character (e.g. Brummell, Cattaneo & Toomre 1995).

Introduction

When the phrase solar–terrestrial activity is used, the intent is to describe those changes of energetic particles and electromagnetic fields that originate at the Sun, travel to the Earth's magnetosphere, and have drastic effects upon the Earth's atmosphere and geomagnetic field. The activity is on time scales that are short in the human perception of events. The Sun is said to be “active” when the magnitude of such changes is distinguishably large with respect to the average behavior over tens of years. A specific region or process on the Sun is said to be an active source region when a particle or field disturbance in the Earth's magnetosphere can be traced to some special change in that region of the Sun. The vagueness in these definitions should disappear as we become more specific in the description of such phenomena as sunspots, flares, coronal holes, coronal mass ejections, solar wind, geomagnetic storms, ionospheric disturbances, auroras, and substorm processes.

We call the moving plasma of ionized particles and associated magnetic fields that are expanding outward from the Sun the solar wind. Its associated field is the interplanetary magnetic field (IMF). The wind exists out past 150 times the Sun–Earth distance because the pressure of the interstellar medium is insufficient to confine the energetic particles coming from the hot solar corona. We call this solar-wind dominated region the heliosphere.

Outer space is filled with particles and fields originating from the formation of the universe and from stars.

International Unions and Programs

The following quotation was taken, with permission, from The National Geomagnetic Initiative copyright 1993 by the National Academy of Sciences, courtesy of the National Academy Press, Washington, D.C. Revisions of this quoted material have been provided by J.H. Allen in order to modernize the statement to year 2002.

The study of the Earth is intrinsically global. This was recognized by geologists, geodeticists, and geophysicists in the nineteenth century. During the past hundred years, the need for global collaboration in geosciences has become axiomatic; many mechanisms have been developed to encourage international cooperation in Earth sciences. Much international cooperation in science takes place under the non-governmental International Council for Science (ICSU).

By the latter part of the nineteenth century, international expeditions and exchange of datawere common in the geosciences. This led to the development of international mechanisms for ongoing cooperation in geophysical and geological sciences. Seismic and magnetic observatories were being established worldwide. These de facto global networks of magnetic and seismic observatories led to international agreements on measurement standards and data exchange. These international activities led to the formation of an international organization that was the predecessor to the modern International Union of Geodesy and Geophysics (IUGG). The objectives of IUGG are the promotion and coordination of physical, chemical, and mathematical studies of the Earth and geospace environment. IUGG now consists of seven essentially autonomous associations: one of these, the International Association of Geomagnetism and Aeronomy (IAGA), is principally concerned with geomagnetism.

This second edition of Introduction to Geomagnetic Fields has been redesigned as a classroom textbook for a semester course in geomagnetism. Student exercises have been added at the end of each chapter. Outdated figures and tables are replaced with more modern equivalents. Recent discoveries, field information, and references have been added along with special websites and computer programs. The basic structure of the original edition remains, providing a condensed and more readable coverage of geomagnetic topics than is afforded by existing textbooks.

My intention has been to focus upon the basic concepts and physical processes necessary for understanding the Earth's natural magnetic fields. When mathematical presentation is required, I have tried to remove the mystery of the scientists' special jargon and to emphasize the meanings of important equations, rather than obscure the relationships with complex formulas. Because some formulas are needed to appreciate geomagnetism, I have included, in an appendix, a succinct review of the required mathematical definitions and facts. For those readers who are approaching the subject of Earth magnetic fields for the very first time it may be helpful to start with the small layman's presentation, devoid of all mathematical equations, that I provided as Earth Magnetism: A Guided Tour Through Magnetic Fields, Academic Press, San Diego, 151 pp, 2001.

The student reader is expected to have a familiarity with the elementary scientific concepts identified by words of specific meaning, such as “force, velocity, energy, temperature, heat, charge, light waves, and fields of electric, magnetic, and gravitational nature”.

Introduction

Man has no obvious sensation of the presence or change of the Earth's magnetic field such as he does for the sensation of rain, wind, or earthquakes. He must rely upon the field's interaction in other physical processes to produce measurable effects. In this chapter we will look at some methods of providing such geomagnetic information.

From a physicist's viewpoint the geomagnetic field we wish to measure has some interesting singular characteristics. It is ever-present; we must take deliberate action to create any required field-free environments. Because of the great spatial extent of the field with respect to available sensor dimensions, only single-point measurements are typically obtained. The natural field is constantly changing and cannot be stopped at will by the experimenter. A conglomeration of Earth-core, magnetospheric, ionospheric, and induced currents all contribute to the simple measurement of a geomagnetic field magnitude and direction at each instant of time; occasionally, special frequency-analysis techniques allow us to identify some of these contributing sources.

The Earth's field changes are not easily stoppered in a bottle and brought to the laboratory for testing like a paleomagnetic rock sample. Those who want the measurement usually must move to a sampling spot that they have selected with care in order to minimize unwanted “noise” and to indicate special upper-atmosphere or deep-Earth characteristics. Everywhere at the Earth's surface, the “steady” field (i.e., slowly varying with respect to the spectral components at active times) is quite strong compared to the relatively infinitesimal fields of rapid (micro) pulsations.

This appendix presents a number of mathematical topics that arise in the book. The review is not meant to be comprehensive; it is limited to only items that could be helpful for understanding the flow of ideas in the chapters of this book.

Variables and Functions

Variable is the name we give to a value of something that changes. When we call a variable independent we mean that it can be any size within a prescribed physical domain of realistic values. A dependent variable is the value that we call a function of the independent variable. On a daily magnetogram, the magnitudes of the scaled H (a “dependent” variable) are dependent upon the selection of the “independent” variable of daily hourly time that we can take to be any value (in the domain) from 0 to 24. Maxwell's equations (Chapter 1) allow a unique field value to be determined from a given source-current distribution; however, given the field values, a number of possible currents might be the source. The dependent-variable field is a function of the independent-variable current. The extreme highest and lowest values of the dependent variable that occur over the domain of the independent variable define the range of the dependent variable.

The term function has a very special meaning in mathematics. When we say, for example, “the variable y is a function of the variable x” it is written as y = f(x).

Introduction

It is the nature of geomagnetic fields to not divulge their sources simply. The observatory magnetometers (Earth-field measuring devices described in Chapter 5) respond to all the fields reaching the local environment, add them together, and limit recording only by the frequency response designed into the instruments. A large part of research in geomagnetism concerns the dissection of field variation recordings to isolate the individual contributing sources, discover the physical processes that cause these currents, and thereby understand another feature of our global environment. Occasionally, a newly revealed feature becomes immediately important and useful to society's needs; usually, its utility is discovered only after many years. One of the first field sources to be discovered (Stewart, 1883; Schuster, 1889, 1908) was a current driven by tidal forces and winds in a conducting region above the Earth that was subsequently named the ionosphere. Such currents are indicated by a recurring field pattern on quiet-time daily recordings. The accurate determination of quiet-day field variation now finds utility in improvement of satellite main-field modeling, in profiling the Earth's electric conductivity, and in establishment of baselines from which magnetospheric disturbances are quantified.

The purpose of this chapter is to explain the origin and behavior of the regularly recurring field variations that have periods of a day or less. Because the principal source for these currents lies in a naturally ionized layer above the Earth, we will examine the basic features of this ionosphere.

Introduction

The science of geomagnetism developed slowly. The earliest writings about compass navigation are credited to the Chinese and dated to 250 years B.C. (Figure 1.1). When Gilbert published the first textbook on geomagnetism in 1600, he concluded that the Earth itself behaved as a great magnet (Gilbert, 1958 reprint) (Figure 1.2). In the early nineteenth century, Gauss (1848) introduced improved magnetic field observation techniques and the spherical harmonic method for geomagnetic field analysis. Not until 1940 did the comprehensive textbook of Chapman and Bartels bring us into the modern age of geomagnetism. The bibliography in the Appendix, Section B.7, lists some of the major textbooks about the Earth's geomagnetic field that are currently in use.

For many of us the first exposure to the concept of an electromagnetic field came with our early exploration of the properties of a magnet. Its strong attraction to other magnets and to objects made of iron indicated immediately that something special was happening in the space between the two solid objects. We accepted words such as field, force field, and lines of force as ways to describe the strength and direction of the push or pull that one magnetic object exerted on another magnetic material that came under its influence. So, to start our subject, I would like to recall a few of our experiences that give reality to the words magnetic field and dipole field.

Introduction

In this chapter we will look at some of the ways in which geomagnetism finds utility in today's world. The main subjects are the impact of the geomagnetic field on modern technological systems and the application of geomagnetism to the discovery of the physical nature of our world. I also include interesting observations for which geomagnetic connections imply future application directions.

Each period range of natural geomagnetic field fluctuations can be identified with special utilization topics. For example, consider the following:

1. (a) For the period range from 0.25 seconds to 1 minute the primary subjects of interest are Earth crust exploration, detection of hidden conductivity anomalies, electric power transformer failures, studies of hydromagnetic wave propagation, and discovery of magnetospheric processes.

2. (b) For the range from 1 minute to 24 hours, studies include the structure of magnetospheric deformation and currents, thermospheric heating and winds, ionospheric currents and tides, and conductivity characteristics of the Earth's lower crust, mantle, and continental coastlines. Geomagnetic storms in this time scale affect a multitude of man-made systems such as satellites, communication systems, electric-power grids, and long pipelines (see Heirtzler et al., 2002).

3. (c) From the range 1 day to 1 year we obtain information about the fluid motions within the Earth's core and at the core–mantle boundary, solar activity and solar sector changes, tropospheric weather changes, and magnetospheric deformation. Our main field magnetic navigation charts are obtained from data in this period range.

Below is a description of computer program files, mentioned throughout this textbook, that may be obtained by the readers in two ways: (1) free of charge at the website prepared by Susan McLean of NGDC/NOAA (http://www.ngdc.noaa.gov/seg/potfld/geomag.shtml) or (2) on a high-density (1.4 Mb) floppy disk sold by NGDC/ NOAA.

At the website main page, select the highlighted “useful computer programs.” The executable files are designed for a DOS-compatible, personal computer. The programs were designed to assist the user in understanding the subject of geomagnetic fields; no claim is made regarding the suitability of the software for any other purpose. No restriction has been placed on the sharing of these programs; also, no warranty (expressed or implied), no endorsement, no guarantee of accuracy, and no responsibility for the program's functioning, can be made by the program authors, the author or publisher of this book, or by the National Geophysical Data Center. The files ending in. EXE are the executable programs; all the other files provide necessary input for some of the programs and must also be copied for proper operation of the set. If the files have been downloaded from the NGDC website, then copy all of them to a disk on your computer before running.

Geomagnetic Coordinates 1940–2005

The GMCORD program provides a determination of the geomagnetic coordinates for any selected global location. The program uses a polynomial fit (see the POLYFIT program below) of the dipole Gauss coefficients from the geomagnetic reference field models (see file ALL-IGRF.TAB below).