3-D velocity models transformation from general to natural splines

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

3-D velocity models transformation from general to natural splines

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

3-D velocity models transformation from general to natural splines

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10500 - Earth and related environmental sciences

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Studia Geophysica et Geodaetica

ISSN

0039-3169

e-ISSN

—

Svazek periodika

63

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

10

Strana od-do

137-146

Kód UT WoS článku

000459512900008

EID výsledku v databázi Scopus

2-s2.0-85059852061