Introduction to Mathematics and Geosciences: Global and Local Perspectives, Volume I

3 Mathematics plays a fundamental role in all scientific fields and, of course, in the Geosciences. This has been especially well known since, for example, the beginning of geodesy in the Greek era (VANI´Č EK and KRAKIWSKY 1992) or in the pioneering studies of planet Earth's interior and the description of the Earth's potential fields (geomagnetic and gravimetric). We can remember that Johann Carl Friedrich Gauss (1777–1855), who is recognized as one of the history's most influential mathematicians, had a remarkable influence in many fields of mathematics and science. He contributed significantly to the development of modern geophysics. In the field of geomagnetism, he developed the first method to obtain absolute geomagnetic measurements, worked out the mathematical theory for separating the inner and outer sources of Earth's magnetic field, and founded the ''Magnetischer Verein'' (Magnetic Union). Another pioneering natural topic was exploring Earth's interior using seismic waves for analyzing the Earth's inner structure and discovering underground resources. For instance, in 1936, the Danish mathematician Inge Lehman was the first to interpret P wave arrivals, which inexplicably appeared in the P wave shadow of the Earth's core as reflections at an inner core, and discovered the Earth's solid inner core by studying these anomalies. Now it is natural to use geophysical methods and remote sensing in exploring our soils to find water, oil, minerals, etc., and to use advanced mathematical tools for interpreting observation results. Therefore, as described by CAMACHO et al. (2008a, b), mathematics is one of the branches of science, together with physics, chemistry, and Information Technology that studies and furthers knowledge of the Earth's structure and dynamics. This research is conducted in multidisciplinary studies that use and incorporate the most advanced methods of those sciences, in the framework of, or in close cooperation with, the different branches of Earth sciences such as geology, geophysics, and geodesy. The international dimension of this collaboration is evident (see, e. The presentations at that meeting were published in two Pure and Applied Geophysics topical issues (CAMACHO et al. 2008c, d). Since 2006, Earth sciences and, therefore, their ''mathematical needs'' have evolved, marked to a very significant extent by the consolidated use of artificial satellites for the observation of Earth, which plays a more important role everyday (e. scale coverage at ultra-high resolution. This evolution is bringing new needs of techniques/methodologies for data fusion (to obtain a unique, new data set by combining …