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Development of effective code for earthquake dynamic source simulations
Premus, Jan ; Gallovič, František (advisor) ; Zahradník, Jiří (referee)
Title: Development of effective code for earthquake dynamic source simulations Author: Bc. Jan Premus Department: Department of Geophysics Supervisor: doc. RNDr. František Gallovič, Ph.D, Department of Geophysics Abstract: Dynamic rupture modeling coupled with strong motion data fitting offers an insight into physical mechanisms behind earthquake sources [Gallovic et al., 2019]. Running a large number of dynamic model simulations is required due to the nonlinearity of the inverse problem. The goal of this Thesis is a development of an efficient forward solver for the dynamic inversions. The fi- nite difference staggered grid code FD3D by Madariaga and Olsen [1998] served as a basis for the development, offering sufficient speed, but rather low accu- racy. Traction at split node implementation of the fault boundary condition and perfectly matched layers as the absorbing boundary condition were required to obtain desirable accuracy. In addition to the slip weakening friction law, fast ve- locity weakening friction law has been implemented, increasing the applicability of the code. We test the new code FD3D TSN using USGS/SCEC benchmarks TPV5 (slip-weakening friction) and TPV104 (fast rate weakening friction) [Harris et al., 2018], showing very good agreement with results calculated by advanced numerical...
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On the Optimization of Initial Conditions for a Model Parameter Estimation
Matonoha, Ctirad ; Papáček, Š. ; Kindermann, S.
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The core idea resides in the maximization of a sensitivity measure, which depends on the initial condition. Numerical experiments show that the discretized optimal initial condition attains only two values. The number of jumps between these values is inversely proportional to the value of a diffusion coefficient D (characterizing the biophysical and numerical process). The smaller value of D is, the larger number of jumps occurs.
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Alternative mathematical notation and its applications in calculus
Marian, Jakub ; Pick, Luboš (advisor) ; Zahradník, Miloš (referee)
We explore the possibility of formalizing classical notions in calculus without using the notion of variable. We provide a new mathematical 'language' capable of performing all classical computations (namely computing limits, finite differences, one-dimensional derivatives, and indefinite and definite integrals) without any need to introduce a variable. Equations written using our notation contain only func- tion symbols (and as such are completely rigorous and don't leave any room for vague interpretations). They also tend to be much shorter and more mathemati- cally transparent than their traditional counterparts (for example, there is no need for introduction of new symbols in integration, and definite integration is formalized in such a way that all rules (including 'substitution' rules) for indefinite integration translate directly to definite integration). We also fully formalize the Landau little-o notation in a way that makes computation of limits using it fully rigorous. 1
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