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Progress in Geomathematics Bringing the Sun Down to Earth Earth springer.com/librarybooks Springer News 9/2008 Earth Sciences/Geography 103 G. Bonham-Carter, Geological Survey of Canada, D. R. Brooks, Institute for Earth Science Research and A. G. Camacho, Universidad de Madrid, Spain; Ottawa, ON, Canada; Q. Cheng, York University, Education, PA, USA J. I. Díaz, Universidad Complutense Madrid, Spain; Toronto, ON, Canada (Eds.) J. Fernández, Universidad de Madrid, Spain (Eds.) Bringing the Sun Progress in Geomathematics Down to Earth Earth Sciences and Designing Inexpensive Instruments for Mathematics Volume I Monitoring the Atmosphere Celebrating Frits Agterberg’s half-century of publication activity in geomathematics, this A Complutense International Seminar on “Earth volume’s 28 timely papers, written by his friends Sciences and Mathematics” was organised and held and colleagues, treat a variety of subjects of The book first presents some science background in Madrid at the Facultad de Ciencias Matemáticas current interest, many of them also studied by about the sun and Earth’s atmosphere and then of the Universidad Complutense de Madrid Frits, including spatial analysis in mineral resource describes the kinds of measurements that can be September, 13th-15th, 2006. Scientists from both assessment, quantitative stratigraphy, nonlinear made with inexpensive equipment to study how fields, Mathematics and Earth Sciences, took part multifractal models, compositional data analysis, solar radiation interacts with the atmosphere on in this International Seminar, addressing scientific time series analysis, image analysis, and geosta- its way to Earth’s surface. Such measurements problems related with our planet from clearly tistics. Professor Agterberg published his first are critical to understanding the forces that will complementary approaches, seeking to gain and paper as a graduate student in 1958 and has since modify Earth’s climate during the 21st century. learn from this dual approach and proposing a produced (and continues to publish) a steady The book describes in detail how to design, build, closer collaboration in the near future. This volume stream of research papers on a wide variety of calibrate, and use inexpensive instruments for is the first one of a Topical Issue on “Earth Sciences subjects of interest to geomathematical practitio- measuring solar radiation, ranging from total and Mathematics” and contains papers addressing ners. Most of the papers included here address radiation from the entire sky to narrow spectral different topics as deformation modelling applied methodology and feature practical case studies, bands of radiation travelling along a path directly to natural hazards, inverse gravimetric problem so that the book likely has broad appeal to those from the sun. Students and their teachers will learn to determine 3D density structure, advanced interested in mathematical geosciences, both to a great deal about weather, the seasons, and the differential SAR interferometry, climate change, academic researchers seeking a comprehensive atmosphere, and they will develop a much better geomagnetic field, earthquake statistics, meteo- overview and to practitioners of geomathematical understanding of how to measure the physical rological studies using satellite images, climate approaches in industry. world around them. energy balance models, study of soils properties, and multifractal data sets. Features Features Reviews the development of mathematical Provides an enhanced understanding of the Features applications in the geosciences over the last fifty sun, weather and climateA combination of Interdisciplinary research articles from years using Prof. Agterberg’s research as an anchor theory and applications show how to measure Mathematics and Earth Sciences and reference pointPresents the state of the the interaction of solar radiation with Earth’s art including resource assessment, nonlinear atmosphereProvides detailed information for From the contents modeling, geostatistics and time series analysis designing, building, and calibrating inexpensive Introduction: Linking Earth Sciences and Math- Serves as both an account of 50 years of instruments to monitor the atmosphereA ematics (Camacho, Díaz, Fernández).- A review geomathematics and as a survey of current meth- unique project sourcebook for teachers, students, of Earthquakes Statistics: Fault and Seismicity odology with case studies and citizen scientists Based Models, ETAS and BASS (Holliday, Turcotte, Rundle).- A finite element algorithm of a nonlinear Fields of interest From the contents diffusive climate energy balance model (Bermejo, Math. Applications in Geosciences; Statistics for 1. Introduction.- 2. Earth’s Sun and Atmosphere.- Carpio, Diaz, Galan del Sastre). Engineering, Physics, Computer Science, Chem- 3. Measuring Atmospheric and Surface Proper- istry & Geosciences; Computer Applications ties.- 4. Instrument Design Principles 1: Radiom- Fields of interest eters.- 5. Instrumennt Design Principles II: Sun Geosciences, general Target groups Photometers.- 6. Concluding Remarks. Academic and professional geoscientists special- Target groups izing in the use of mathematical applications in the Fields of interest Students and researchers interested in mathemat- geosciences and in mineral and oil exploration Meteorology/Climatology; Applied Geosciences; ical methods for solving problems from the earth Teacher Education sciences (e.g., climate change, earthquake statistics, Discount group meteorological studies) P Target groups Science teachers, students, instructors teaching Discount group environmental science/engineering, scientists, P citizen scientists, practitioners Discount group P Due October 2008 Due September 2008 Due October 2008 2009. Approx. 570 p. 228 illus., 28 in color. Hardcover 2008. XII, 150 p. 15 illus. in color. Hardcover 2009. VI, 234 p. (Pageoph Topical Volumes) Softcover $259.00 $79.95 $74.95 ISBN 978-3-540-69495-3 ISBN 978-1-4020-8693-9 ISBN 978-3-7643-8906-2 104 Earth Sciences/Geography Springer News 9/2008 springer.com/booksellers W. Freeden, University of Kaiserslautern, Germany; K. Glaßmeier, TU Braunschweig, Germany; H. Soffel, New Series M. Schreiner, University of Buchs NTB, Switzerland LMU München, Germany; J. F. Negendank, GFZ Potsdam, Germany (Eds.) Spherical Functions of Mathematical Geosciences Geomagnetic Field Variations Advances in Geophysical A Scalar, Vectorial, and Tensorial Setup and Environmental Mechanics Earth’s magnetic field is currently changing and Mathematics dramatically. Is the observed decrease of the dipole This book collects all material developed by the moment indicating a future polarity transition? Series editor: K. Hutter Geomathematics Group, TU Kaiserslautern, during What would be the effects of such a drastic change the few last years to set up a theory of spherical on system Earth? Can any positive or nega- functions of mathematical (geo-)physics. The tive effects on our biosphere or even humans be The series Advances in Geophysical and Environ- work shows a twofold transition: First, the natural expected? mental Mechanics and Mathematics (AGEM2) transition from the scalar to the vectorial and This book gives a first overview about the geomag- reports new developments on all topics of tensorial theory of spherical harmonics is given in netic field in general and serves as an introduc- geophysical, environmental and astrophysical coordinate-free representation, based on new vari- tion into geomagnetism. As the topic of the book mechanics and mathematical research and ants of the addition theorem and the Funk-Hecke covers a wide range of scientific disciplines, teaching – quickly and informally, but with high formulas. Second, the canonical transition from the first chapter summarises basic principles quality and the explicit aim to summarize and spherical harmonics via zonal (kernel) functions to of geomagnetism and related fields including a communicate current knowledge in an accessible the Dirac kernel is presented in close orientation to historic overview, instruments and measurements, way. Books published in this series are conceived an uncertainty principle classifying the space/ paleomagnetic fields, basics of dynamo theory, etc. as bridging material between upper level textbooks frequency (momentum) behavior of the functions The contributed chapters review major results of and the forefront of research to serve the following for purposes of constructive approximation and international activities aiming at understanding purposes: (1) to be a compact and up-to-date data analysis. In doing so, the whole palette of the causes and effects of geomagnetic field varia- source of reference on a well defined topic; (2) to spherical (trial) functions is provided for modeling tions in view of the questions above. serve as an accessible introduction to a specialized and simulating phenomena and processes of the field to advanced students and non-specialized Earth system. Features researchers from related areas; (3) to be a source of Topic of high scientific and public interest advanced teaching material for specialized semi- Contents Serves as introduction and review of current nars, courses and schools. 1 Introduction.- 2 Basic Settings and Spherical research on geomagnetic field variations Nomenclature.- 3 Scalar Spherical Harmonics.- Green Functions and Integral Theorems.- Contents 5 Vector Spherical Harmonics.- 6 Tensor Spherical 1. The Geomagnetic Field.- 2. The Recent Geomag- Harmonics.- 7 Scalar Zonal Kernel Functions.- netic Field and its Variations.-
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