Anthony B. Davis,
Los Alamos National Laboratory
& Didier Sornette,
University of California - Los Angeles and CNRS - France
EOS 86 (46), 461,467 (November 15, 2005)
As 2005 -the International Year of Physics- comes to an end, two physicists working primarily in geophysical research reflect on how geophysics is not an applied physics. Although geophysics has certainly benefited from progress in physics and sometimes emulated the reductionist program of mainstream physics, it has also educated the physics community about some of the generic behaviors of strongly nonlinear systems. Dramatic examples are the insights we have gained into the "emergent" phenomena of chaos, cascading instabilities, turbulence, self-organization, fractal structure, power-law variability, anomalous scaling, threshold dynamics, creep, fracture, and so on. In all of these examples, relatively simple models have been able to explain the recurring features of apparently very complex signals and fields. It appears that the future of the intricate relation between physics and geophysics will be as exciting as its past has been characterized by a mutual fascination. Physics departments in our universities should capitalize on this trend to attract and retain young talent motivated to address problems that really matter for the future of the planet. A pressing topic with huge impact on populations and that is challenging enough for both physics and geophysics communities to work together like never before is the understanding and prediction of extreme events.
UNESCO has declared 2005 the International Year of Physics in celebration of the centennial of Einstein's annus mirabilis when, as a young clerk at the Swiss Patent Office in Berne, he published three short papers that changed physics forever by 1) introducing the Special Theory of Relativity and demonstrating the equivalence of mass and energy (E = mc2), 2) explaining the photoelectric effect with Planck's then still new and controversial concept of light quanta (E = h‡), and 3) explaining the curious macroscopic phenomenon of Brownian motion by invoking Boltzmann's molecular dynamics (E = kT), far from fully accepted at the time. Trained as physicists but working primarily in geophysics for two decades each, we thoroughly enjoy our research activity respectively in solid-earth geophysics and in atmospheric science. We know of surprisingly many others, and suspect the existence of yet many more, with this same background in all of AGU's Sections for whom we can speak with the same unmitigated enthusiasm. In the following, we take a very broad view in order to examine the past and future of the intimate and dynamic relation between physics and geophysics, or geosciences in general.
In the Preface to his Principles of Philosophy (1644), the 17th-century French philosopher, mathematician and physicist, Descartes described Philosophy as a tree rooted in metaphysics, whose trunk is physics and all the branches growing out are all the other scientific disciplines, such as medicine, mechanics, morals. This "Tree of Philosophy" constitutes an extreme presentation of the general perception (by many physicists) that Physics is the Queen of sciences and that all other (natural) sciences are essentially different incarnations of Applied Physics. Even the social sciences are not protected from the hegemonic ambitions of Physics, as witnessed for instance from the recent emergence of a growing number of physicists working in "econophysics" and "sociophysics." In 1972, P.W. Anderson, a condensed-matter physicist and Nobel laureate, contended in his essay More Is Different , that particle physics and indeed reductionism has only a limited ability to explain the world. Anderson argued that reality has a hierarchical structure, with each level independent, to some degree, of the levels above and below: "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one." Anderson noted "Psychology is not applied biology, nor is biology applied chemistry." Let us examine how geophysics, far from being just another field of applied physics, has driven physics itself to innovate in deep and lasting ways.
Geosciences are the aggregation of a broad set of disciplines, whose concerns span from the structure of the deep interior of the Earth, the source of the Earth magnetic field believed to stem from a dynamo in the core, the dynamics and composition of the mantle (source of minerals and oceanic water), the lithosphere and the outer solid crust (location of earthquakes, volcanic eruptions, landslides, etc.), to the study of geomorphology (landscapes, mountains, river networks, erosion, impacts, etc.), to the application of paleontology and microbiology to the study of the origin and evolution of life, to the fluid envelops of the Earth, its oceans and atmosphere and their mutual interactions shaping weather and climate, up to the outer atmosphere screening us from dangerous cosmic radiations, to the magnetosphere and Earth's radiation belts where magnetic storms occur as space weather unfolds.
The commonly perceived work of a geoscientist consists in applying knowledge of basic scientific principles to make sense of existing observations, while hypothesizing theories on the cause of still unresolved complicated structures and dynamics. There is a long history of famous examples of which we cite a few. In 1752, Benjamin Franklin performed his famous kite-flying experiment which established that lightning is a naturally-occurring electrical spark. In the 19th century, the work of Tyndall on the radiative properties of gases contributed greatly to the understanding of how these gases affect the heating and cooling of the Earth's atmosphere. S. Arrhenius, Nobel prize in Chemistry, presented a groundbreaking paper to the Stockholm Physical Society in 1895 "On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground," a question coming back as a major concern to Earth scientists and the broader community, today. In the first decades of the 20th century, the Serbian astrophysicist M. Milankovitch developed a mathematical theory of climate based on the seasonal and latitudinal variations of solar radiation received by the Earth, due to variations of the Earth-Sun geometry (changes in orbital eccentricity’ obliquity’ and precession). This theory still stimulates today many researchers both from an applied but also fundamental physical and mathematical view point. Using his pioneering interdisciplinary approach, A. Wegener wrote one of the most influential and controversial books in the history of science, The Origin of Continents and Oceans, first published in 1915, in which he offered his theory of drifting continents and widening seas to explain the evolution of Earth's geography. The theory waited almost 55 years to be rejuvenated as the theory of Plate Tectonics, established on the solid basis of modern geophysical data (rock magnetism, mantle convection and seismology). More recently, J. Martin studied the basic chemical processes that govern life in the ocean and proposed his "iron hypothesis:" by sprinkling a relatively small amount of iron into certain areas of the ocean, one could create large blooms of algae that could take in so much carbon from the atmosphere that they could reverse the greenhouse effect and cool the Earth. These are just a few examples of how geophysicists have, like physicists, reduced complex phenomena to elementary processes -and even used them to propose global engineering projects- thus reinforcing the notion that geophysics is an applied field dependent on more general science.
However, there are also many instances in which the geosciences have inspired or forced scientists on their way to discoveries that can be considered "fundamental," even by the criteria of the purest physicists. In the early decades of the 20th century, V. Bjerknes, considered by many to be one of the founders of modern meteorology and weather forecasting, discovered the circulation theorems that led him to a synthesis of hydrodynamics and thermodynamics applicable to large-scale motions in the atmosphere and oceans, opening the road to the computation of the future state of the atmosphere carried out by integrating the governing equations forward in time, starting from the observed, initial state of the atmosphere (an initial value problem in mathematical physics). Bjerknes, his son Jacob, and others established the mechanism that controls the behavior of mid-latitude cyclones that ultimately resulted in the theory of air masses and fronts. Motivated in part by the high pressure and shear stresses applied to rocks within the Earth interior, P. Bridgman in 1935 and later the Russian N.S. Enikolopyan made ground-breaking works on the effect of combined hydrostatic pressure and shear applied to a wide variety of materials. This research continues actively today at the interface between the quest for fundamental new properties of minerals under high pressures (up to megabars) and high temperatures (up to thousands of degrees), and the study of physical and chemical properties of geological materials, including rocks, minerals, chemical compounds (oxides and silicates), metals, alloys, silicate melts, glasses, and so on. These studies have potential impacts in finding and evaluating sources of oil or geothermal energy, investigation of the structure of silicate melts and glasses on a molecular level, and prediction of the properties of materials at high pressures and temperatures. Solid friction studied by Amonton, then formalized by Coulomb in 1773, has received a recent boost in the discovery of state- and velocity-dependent friction coefficients often associated with the names of J. Dieterich and A. Ruina, motivated by its application to earthquake ruptures. A strong research effort now attempts to unravel its microscopic physical origin in a variety of materials and to decipher its broad consequences on the dynamics of sliding and rupture in materials from the atomic scale to faults of hundreds of kilometers. The wavelet transform or wavelet analysis is probably the most recent solution to overcome the signal-cutting problem of the Fourier transform in signal analysis, by the use of fully scalable modulated windows. The wavelet transform, in its present form, was discovered by J. Morlet in 1975 under the name "cycle-octave transform" (later published in Geophysics, Vol. 47, 1982) while working for a large oil company, with the goal of enhancing the resolution of seismic signals while processing field data. The wavelet transform basically made the Fourier transform obsolete after 200 years of uses and abuses. This novel mathematical tool proved to be at once universal and useful, particularly in data compression where significant savings in storage and transmission costs were obtained, but also in numerical simulation, data processing, communications, image analysis, and many other engineering problems. It can also be stated that the concept of fractals, developed by the physicist/mathematician B. Mandelbrot in the 1960s, owes a significant debt to geosciences as a source of inspiration, and without doubt as maybe the richest and most varied domain of applications (mountain ranges, fault networks and earthquake ruptures, rocks, lightning bolts, river networks, coastlines, patterns of climate change, clouds, etc.). There is a good reason why geologists always include a scale or reference-object when taking a picture of geologic interest? If they did not, the actual size or scale of the pictured object could not be determined because most geo-formations are self-similar, i.e., a 1 cm fold looks quite the same as if it were 10 m or 10 km in size. The discovery of deterministic chaos by Ed Lorenz, a meteorologist, in 1963 extended the modern qualitative theory of dynamical systems developed by Poincaré to study the stability of the solar system. This breakthrough triggered more than two decades of intense exploration in mathematics and physics to understand the mechanisms of chaos. Fractals and chaos are sweeping concepts now widely used in non-equilibrium physics at large. These are just a few examples of how geoscience as influenced mainstream physics and thus enabled it to progress in its own endeavors (e.g., quantum chaos, chaotic behavior in lasers, multifractality in turbulence and in statistical physics).
The mathematics of chaos and the geometry of fractals are now standard tools used in the broad field loosely called "complexity theory." They have played similar paradigmatic roles for the theory of complex systems as Einstein's 1905 foundation of relativity theory and in quantum mechanics did for the evolution of physics in the first half of the 20th century, and that of the double helix by Crick and Watson in 1953 for the progress of the life sciences in its second half. Arguably, Einstein's 1905 investigation into Brownian motion marks the first deep physical insight into an inherently complex phenomenon which, as it turns out, is a prime example of a fractal.
The theory of complexity, very much in the making, is the archetype of a new way of doing science in which the geosciences (as well as many other natural sciences) are both users as well as builders of fundamental principles. Indeed, the concept of complex systems and the importance of systemic approaches is pervasive to the geosciences which constitute one of the best natural "laboratories" for the following concepts: systems with a large number of mutually interacting parts, often open to their environment, self-organize their internal structures, and their dynamics with novel and sometimes surprising ("emergent") macroscopic properties. The complex system approach involves seeing inter-connections and relationships, i.e., the whole picture as well as the component parts. Complexity manifests in linkages between space and time, generally producing patterns on many scales, and often including a hierarchy of interactions, cascades -both direct (from large to small scales) and inverse (micro to macro)- and the emergence of fractal structures. Complex systems are generally sensitive to initial conditions; they may be robust with respect to certain types of perturbations, and fragile with respect to others, and exhibit transitions from different classes of order to chaos, turbulence, or even complete randomness. Concrete examples of fundamental concepts in statistical physics inspired by the geosciences include block-spring models and self-organizing sandpile models for earthquakes and rupture under threshold dynamics .
Complementing and feeding the quest for new concepts and novel understanding, the geosciences are witnessing a race towards accumulation of data with unprecedented accuracy, frequency and resolution, in order to address pressing societal problems associated with the sustainability of the Earth biosphere. For instance, NASA's EOS program is gathering new climatological data from space while DOE's ARM program has taken world-leadership in establishing ground-based climate observatories around the globe. Particularly challenging long-term measurements and assessments are needed to understand the ramifications of the temporal and spectral variability of solar irradiance, as well as aerosols, humidity, clouds, precipitation, and the sensitive cryosphere on global warming and reciprocally. The intricate processes of air pollution, ozone depletion, El Niño, and so on, are thus coming into sharper focus with NASA missions such as Terra, Aqua and Aura. NSF, together with USGS and other agencies, are launching the EarthScope, a project for monitoring and understanding the lithosphere at spatial and temporal scales undreamed off until recently, that will stimulate the scientific community in its quest for seismic and volcanic hazard control, earthquake risk management, mineral formation, and so on. The Earth's surface and interior will thus be probed by novel arrays of instruments and a rich crop of new fundamental understanding is expected in the physics of earthquakes, volcanoes, mantle convection and plate tectonics. Do we need to recall that the fundamental theory of plate tectonics unifies, in good Physics tradition, much of the geosciences into a coherent and logical framework to understand the Earth as a system? It is quite remarkable that, Plate Tectonics, "the" fundamental theory of the geosciences was finally accepted no sooner than in the late 1960s, decades after physicists understood most of the atomic and sub-atomic world as well as the fine details of solar energy production (hydrogen fusion, via Bethe's CNO cycle). The reason is not that geoscientists are any less clever than physicists, but lies in the fact that gathering and making sense of data at the scale of the Earth requires time, commitment, resources and ingenuity beyond those usually applied on most well-controlled experiments carried out in the narrow confines of a clean laboratory. The new wave of intensive data acquisition can thus be expected to deeply rejuvenate the geosciences and therefore the physical sciences.
Associated with the complexity of the data and of the interactions between the many subsystems, it is true that geophysics is messy, with little or no experimental control. It is also true that computers help a lot. These attributes it shares with astrophysics and, more specifically, with cosmology because there is only one Universe and, so far, only one Earth (at least that can be investigated at will and in situ). Just one big experiment unfolding, and very limited sampling in spite of the abovementioned heroic efforts of NASA, DOE, NSF, and other organizations. Unlike astrophysics and cosmology however, the first inkling of a physics-based prediction can be immediately confronted with hard data. So geophysics is a world of paradox and struggle, not the least because the lack of control implies that complex models of natural systems cannot be truly validated in the usual sense because model validation by the confirmation of some of its outputs with the natural world does not confirm the underlying scientific conceptualization. There have indeed been many cases of models that made accurate, quantitative predictions, but were later shown to be conceptually flawed . The geosciences thus pose a qualitatively different class of problems in order to understand Nature's processes and structures. Far from being an applied physics, geophysics has mutated the role of scientists who, in addition to staying abreast in their traditional discipline, are now required to develop novel and still mostly undiscovered ways of validating their models and theories.
In this vain, a very important direction of research in geophysics concerns the prediction and, possibly, control of Nature's weapons of mass destruction (earthquakes, volcanic eruptions, landslides, tsunamis, hurricanes, floods, tornadoes, etc.) which leave in their wake the collapse of critical infrastructure, socioeconomic crises and environmental disasters. These studies reside at the frontiers of modern mathematics and theoretical physics. They have wide applications to emergency management, public safety, civil engineering standards, insurance underwriting, and many economic, social, and political issues. As we emphatically stated, the science of chaos, fractals and complexity considers large systems of elements, interacting in a complicated nonlinear ways. Such strongly nonlinear systems sometimes self-reorganize, often abruptly, possibly with a disastrous impact. Extreme events are often "outliers" ("kings" or "black swans") with statistically different properties than the rest of the population and resulting from different physical mechanisms that could include the amplification of critical cascades, as occurs for instance in the rupture of heterogeneous materials, in great earthquakes, in turbulence and in abrupt changes of weather regimes, in floods and droughts, in financial crashes, and in human parturition (birth) . As humanity saturates the planet, it has to apply its science to the urgent socio-economic problem of limits of growth. We live in a planet and society with highly nonlinear dynamics rather than at an equilibrium point, so there is a growing need to sensitize students and citizens to the importance and impacts of extreme events in their multiple forms and to connect the different scientific disciplines, including the purest physics and mathematics, needed to understand them.
The challenge is to understand humanity's global environment, formed of interacting systems atmosphere, ocean, land surface and biosphere whose combined complexity exceeds that of any system previously considered by the physical, life or social sciences. We therefore applaud AGU and EGU for paving the way with their respective group/section in nonlinear geophysics that cuts across the traditional geophysical disciplines, and for their connections with societies representing mainstream Physics. Every year, talented youth graduates from our high-schools are motivated to contribute to solving environmental problems, while also excited by the correct perception that much fundamental science is also there to harvest. We therefore urge Physics Departments world-wide to engage their counterparts in Geosciences, Geophysics, Meteorology, Environmental, Atmospheric and/or Oceanic Sciences which are already networking to support Earth System Science -the ultimate interdisciplinary project.
 Anderson, P. W., More is different, Science, 177, 393-396 (1972).
 Bak, P., How Nature Works: The Science of Self-Organized Criticality. Springer-Verlag (1996).
 Oreskes, N., K. Shraderfrechette and K. Belitz, Verification, validation and confirmation of numerical models in the Earth sciences, Science, 263, 641-646 (1994).
 Sornette, D., Predictability of catastrophic events: Material rupture, earthquakes, turbulence, financial crashes and human birth, Proc. Nat. Acad. Sci., 99 (SUPP1), 2522-2529 (2002).
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