Geomathematics

Geomathematics is a branch of mathematics. She has to stretch an object, a bridge between the mathematical theory and the geotechnical application. The special attraction of this daughter of mathematics is based in lively exchange of ideas between the interested more in modeling, theoretical foundation and approximate and numerical problem-solving group of applied mathematicians and more familiar with instrumentation, methodology of data analysis, implementation of routines and software application set geoengineers and physicists.

Geomathematics as a cultural

The oldest surviving writing of certificates of mathematics emerged in the Sumerian Babylon from the practical tasks of measuring, counting and calculating for field management and stockpiling. Your first boom was dealt with geoscience issues relevant mathematics in antiquity, eg with the calculation of the radius of the earth by the Alexandrian Eratosthenes ( 176-195 BC). From the Arabs 827 AD, has been handed a northwest Baghdad degree carried out by measuring peak around the year. Other key stages geomathematischer research lead us through the Orient into Western Middle Ages and modern times. Nicolaus Copernicus (1473-1543) manages the transition from the geocentric system of Ptolemy to the heliocentric system. Johannes Kepler (1571-1630) is the laws of planetary motion. Other milestones from a historical perspective are for example the justification for the doctrine of the earth's magnetism by W. Gilbert (1544-1608), the development of triangulation with graticule provisions by Tycho Brahe (1547-1601) and Willibrord van Roijen Snell (1580-1626), the case law of Galileo Galilei (1564-1642 ) and the broad spread of seismic waves by Christiaan Huygens ( 1629-1695 ). The by Englishman Isaac Newton (1643-1727) formulated laws of gravity make it clear that the force of gravity decreases with the distance from the earth (also called severity ). In the 17th and 18th century France takes over a major role through the establishment of the Academy in Paris ( 1666). Success are the stages theory of isostatic adjustment of the mass distribution in the Earth's crust by Pierre Bouguer (1698-1758), the calculation of the figure of the earth, particularly the Polabplattung, by PL Maupertuis (1698-1759) and Alexis Claude Clairaut (1713-1765) and the development of the calculus of spherical functions by Adrienne -Marie Legendre (1752-1833) and Pierre Simon Laplace ( 1749-1829 ). The 19th century is much influenced by the work of Carl Friedrich Gauss ( 1777-1855 ). Particularly noteworthy are the calculation of the first Fourier coefficients of the spherical harmonic expansion of the geomagnetic field, the hypothesis of electric currents in the ionosphere and the definition of the level surface of the geoid (the term " geoid " however comes from the Gaussian pupil Johann Benedict Listing ( 1808-1882 ) ). End of the 19th century, the basic idea of ​​the dynamo theory in the geomagnetic by B. Stewart ( 1851-1935 ) was born, and many others This incomplete ( not even the last century containing ) list already shows that historically Geomathematics is one of the great achievements of mankind.

Geomathematics as task and goal

Geomathematics from today's perspective focuses on the qualitative and quantitative properties of the currently existing or potential structures of our Earth system. She is guarantor and sponsor at the same time for the concept of scientific rigor in the Earth System. The Earth system consists of a number of elements that are themselves again systems. The complexity of the whole Earth system is determined by interacting physical, biological and chemical processes, energy, material and information transform and transport. It is characterized by natural, social and economic processes that lead to mutual interference. Consequently, a simple cause-and- effect thinking is totally unsuitable for an understanding. What is needed is a way of thinking in dynamic structures and awareness of multiple, unpredictable and sometimes undesirable effects during interventions. Inherent networks must be identified and utilized, self-regulation is observed. All these aspects make a mathematics essential, which must be more than a collection of theories and numerical methods.

The geosciences to widmende mathematics is essentially nothing more than the organization of the complexity of the Earth system. These include graphic thinking to illustrate abstract complex issues, correct simplification of complex interactions, an appropriate mathematical term system to describe and accuracy in thinking and formulating. Geomathematics thus becomes the key science of the complex system Earth. Wherever there is data and observations, such as in the various scalar, vectorial and tensorial clusters of satellite data, it is mathematically. Statistics used, for example, the denoising, constructive approximation of the compression and evaluation, special systems approach of geo-relevant functions provide graphical and numerical representations - all based on mathematical algorithms.

The spectrum of modern geosciences, which is the focus of Geomathematics is, not least because of wide-ranging grew stronger observation diversity. Simultaneously, the "box" mathematical tools enlarged. A special feature is that Geomathematics primarily concerned with those areas of the world that are not accessible ( by remote sensing methods themselves ) inadequate or for direct measurements. Inverse methods for mathematical analysis are then inevitable. These usually run down to is that a physical field is measured near the surface or at satellite altitude, to then continue with mathematical methods in the interest depth ranges (English " downward continuation ").

Geomathematics as a potential solution

The previous methodology of applied measurement and evaluation methods will vary greatly depending on the studied variable ( acceleration due to gravity, electric and magnetic field strength, temperature and heat flow, stress-strain behavior, etc. ), the observed frequency range and the occurring basic " field characteristic " ( potential field, diffusion field or wave field, which will depend on the underlying differential equations). In particular, the differential equation has great influence on the evaluation process. Potential method ( potential fields, elliptic differential equations) in gravimetry, geomagnetism, geo-electric, geothermal, ..., diffusion processes (diffusion fields, parabolic differential equations) in magnetotelluric, : the typical mathematical exploration methods listed by the appropriate box Characteristic - Therefore are here - as in the geosciences usual Geoelektromagnetik, ..., wave method ( wave fields, hyperbolic differential equations) in seismology and seismic, ground penetrating radar, ....

The benefit and the benefit of this mathematical procedure consist in better, faster, cheaper and safer problem solving, with the means of simulation, visualization and data reduction floods.

The Geomathematics is closely correlated with Geoinformation, Geological Engineering and Geophysics. But Geomathematics also differs fundamentally from these disciplines. Engineers and physicists need the mathematical language as a tool and the tool. Content of Geomathematics is also the development of the language itself the subject of the Geoinformatics is design and architecture of processors and computers, databases and programming languages ​​, etc. in georeflektierten environment. For Geomathematics However, computers are not objects of study, but technical tools for solving mathematical problems of Georealität.