Data-Driven Numerical Modelling in Geodynamics: Methods and by Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

By Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

This booklet describes the tools and numerical ways for info assimilation in geodynamical versions and provides numerous purposes of the defined method in appropriate case experiences. The e-book begins with a short evaluate of the elemental ideas in data-driven geodynamic modelling, inverse difficulties, and knowledge assimilation tools, that's then through methodological chapters on backward advection, variational (or adjoint), and quasi-reversibility equipment. The chapters are followed via case experiences featuring the applicability of the equipment for fixing geodynamic difficulties; particularly, mantle plume evolution; lithosphere dynamics in and underneath distinctive geological domain names – the south-eastern Carpathian Mountains and the japanese Islands; salt diapirism in sedimentary basins; and volcanic lava circulate.
Applications of data-driven modelling are of curiosity to the and to specialists facing geohazards and hazard mitigation. rationalization of the sedimentary basin evolution advanced by way of deformations as a result of salt tectonics might help in oil and gasoline exploration; greater figuring out of the stress-strain evolution some time past and rigidity localization within the current grants an perception into huge earthquake practise techniques; volcanic lava stream tests can suggest on hazard mitigation within the populated components. The publication is a vital instrument for complicated classes on information assimilation and numerical modelling in geodynamics.

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Extra resources for Data-Driven Numerical Modelling in Geodynamics: Methods and Applications

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T/@T=@n at model boundary € 4 is assumed to be related to some (unknown as yet) temperature T D T2 D at model boundary € 2 , and temperature T * is a component of the solution (T *, u *, p *) to the auxiliary problem, when the temperature T D T2 at € 2 equals to * (Eq. T / @T =@n at 4 . Consider the cost functional for admissible functions determined at € 2 Z  k T J. 12) where T is the component of the solution (T , u , p ) of the auxiliary problem with the condition T D at € 2 in Eq. 9). The functional has its global minimum at value D and J .

To prove the statement, Ismail-Zadeh et al. 11) The gradient is derived by using the Gateaux derivative of the objective functional. 0; / : Thus, the solution of the backward heat problem is reduced to solutions of series of forward problems, which are known to be well-posed (Tikhonov and Samarskii 1990). The algorithm can be used to solve the problem over any subinterval of time in [0, ª]. 5 Solution Method Here the method for numerical solution of the inverse problem of thermal convection in the mantle is described.

Math Modeling 9:119–127 Schubert G, Turcotte DL, Olson P (2001) Mantle convection in the earth and planets. Cambridge University Press, Cambridge Sleep NH (1990) Hotspots and mantle plumes: some phenomenology. J Geophys Res 95:6715–6736 Tikhonov AN (1963) Solution of incorrectly formulated problems and the regularization method. Dokl Akad Nauk SSSR 151:501–504 (Engl. : Soviet Math Dokl 4:1035–1038) Tikhonov AN, Samarskii AA (1990) Equations of mathematical physics. Dover Publications, New York Trompert RA, Hansen U (1998) On the Rayleigh number dependence of convection with a strongly temperature-dependent viscosity.

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