3-D velocity models transformation from general to natural splines

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404492" target="_blank" >RIV/00216208:11320/19:10404492 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=f10OmzQDB-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=f10OmzQDB-</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11200-018-0933-5" target="_blank" >10.1007/s11200-018-0933-5</a>

Result language
angličtina
Original language name
3-D velocity models transformation from general to natural splines
Original language description
The functions describing material parameters and structural interfaces in velocity models are frequently represented by splines. The general cubic splines differ from the natural cubic splines by the boundary conditions at the outermost gridpoints. The general cubic splines have a general curvature at the outermost gridpoints used for interpolation, whereas the natural splines have a zero normal curvature at the outermost gridpoints. It is thus very useful to employ a simple algorithm for the transformation between the general and natural splines. The transformation from the natural to general (bi-) (tri-) cubic splines is straightforward, because the natural splines represent a special case of the general splines. This paper is devoted to the algorithm of transformation from the general to natural (bi-) (tri-) cubic splines. We present the formulae necessary for the transformation together with their derivation.We illustrate the presented formulae on the example of fitting a 1-D quadratic function by natural cubic splines, and on the example of a velocity model of a layered structure with two 3-D structural interfaces.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10500 - Earth and related environmental sciences

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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