Mathematics announced the decision of the main tasks of Geophysics
Mathematician Andras washi from Stanford University (USA) announced the decision one of the most important problems of seismology — dimensional inverse kinematic problem.
Performed in conjunction with two colleagues, as reported in the publication Nature News, scientists presented at a seminar held last week at University College London (UK).
Three-dimensional inverse kinematic problem is a definition of high-speed characteristics of the environment known at the time of wave propagation along geodesic lines (shortest curves between two points in a metric space) with the known coordinates of the source and receiver.
Scientists approach involves representation of the environment in which distributed indignation, in a kind of layers. Gradually determining the speed for each of them, the scientists were able, in their words, to prove the existence and uniqueness of the solution and also to obtain its explicit form in space dimension three and higher.
Its study authors plan on posting soon in the library of e-preprints arXiv.org and guide, depending on the reactions of the experts for publication in peer-reviewed journal. According to Vasey, currently a 50-page paper explores a few specialists.
The solution of the inverse kinematic task in the General three-dimensional case, it is important to Geophysics, in particular seismology. It will allow much higher accuracy than at present, to determine the internal structure of the Earth (lithosphere, mantle layer and core).
Seismologist Maarten de Hoop from rice University in Houston (USA) believes that the work of Vasi and his colleagues conceptually not change existing perceptions and approaches, however, will lead to a deeper understanding of the nature of mantle plumes beneath Iceland and Hawaii, as well as the opening of new geophysical formations.
Three-dimensional inverse kinematic problem has interested scientists for over a century. Existing work mainly on private solutions to the problem, in particular, the special two-dimensional cases. One of the authors Vasey, mathematics günter Ullmann from the University of Washington (USA) is working on this task since the late 1990-ies.