One-Way Wave Equation Derived from Impedance Theorem

The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, th...
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Autor*in:	Oskar Bschorr [verfasserIn] Hans-Joachim Raida [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum

Übergeordnetes Werk:	In: Acoustics - MDPI AG, 2019, 2(2020), 1, Seite 164-170
Übergeordnetes Werk:	volume:2 ; year:2020 ; number:1 ; pages:164-170

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/acoustics2010012

Katalog-ID:	DOAJ042132207

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allfields	10.3390/acoustics2010012 doi (DE-627)DOAJ042132207 (DE-599)DOAJ59fdb2674eff496899f02651cfec92ca DE-627 ger DE-627 rakwb eng QC1-999 Oskar Bschorr verfasserin aut One-Way Wave Equation Derived from Impedance Theorem 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived. one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum Physics Hans-Joachim Raida verfasserin aut In Acoustics MDPI AG, 2019 2(2020), 1, Seite 164-170 (DE-627)1049287479 2624599X nnns volume:2 year:2020 number:1 pages:164-170 https://doi.org/10.3390/acoustics2010012 kostenfrei https://doaj.org/article/59fdb2674eff496899f02651cfec92ca kostenfrei https://www.mdpi.com/2624-599X/2/1/12 kostenfrei https://doaj.org/toc/2624-599X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_34 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2020 1 164-170
spelling	10.3390/acoustics2010012 doi (DE-627)DOAJ042132207 (DE-599)DOAJ59fdb2674eff496899f02651cfec92ca DE-627 ger DE-627 rakwb eng QC1-999 Oskar Bschorr verfasserin aut One-Way Wave Equation Derived from Impedance Theorem 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived. one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum Physics Hans-Joachim Raida verfasserin aut In Acoustics MDPI AG, 2019 2(2020), 1, Seite 164-170 (DE-627)1049287479 2624599X nnns volume:2 year:2020 number:1 pages:164-170 https://doi.org/10.3390/acoustics2010012 kostenfrei https://doaj.org/article/59fdb2674eff496899f02651cfec92ca kostenfrei https://www.mdpi.com/2624-599X/2/1/12 kostenfrei https://doaj.org/toc/2624-599X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_34 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2020 1 164-170
allfields_unstemmed	10.3390/acoustics2010012 doi (DE-627)DOAJ042132207 (DE-599)DOAJ59fdb2674eff496899f02651cfec92ca DE-627 ger DE-627 rakwb eng QC1-999 Oskar Bschorr verfasserin aut One-Way Wave Equation Derived from Impedance Theorem 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived. one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum Physics Hans-Joachim Raida verfasserin aut In Acoustics MDPI AG, 2019 2(2020), 1, Seite 164-170 (DE-627)1049287479 2624599X nnns volume:2 year:2020 number:1 pages:164-170 https://doi.org/10.3390/acoustics2010012 kostenfrei https://doaj.org/article/59fdb2674eff496899f02651cfec92ca kostenfrei https://www.mdpi.com/2624-599X/2/1/12 kostenfrei https://doaj.org/toc/2624-599X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_34 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2020 1 164-170
allfieldsGer	10.3390/acoustics2010012 doi (DE-627)DOAJ042132207 (DE-599)DOAJ59fdb2674eff496899f02651cfec92ca DE-627 ger DE-627 rakwb eng QC1-999 Oskar Bschorr verfasserin aut One-Way Wave Equation Derived from Impedance Theorem 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived. one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum Physics Hans-Joachim Raida verfasserin aut In Acoustics MDPI AG, 2019 2(2020), 1, Seite 164-170 (DE-627)1049287479 2624599X nnns volume:2 year:2020 number:1 pages:164-170 https://doi.org/10.3390/acoustics2010012 kostenfrei https://doaj.org/article/59fdb2674eff496899f02651cfec92ca kostenfrei https://www.mdpi.com/2624-599X/2/1/12 kostenfrei https://doaj.org/toc/2624-599X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_34 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2020 1 164-170
allfieldsSound	10.3390/acoustics2010012 doi (DE-627)DOAJ042132207 (DE-599)DOAJ59fdb2674eff496899f02651cfec92ca DE-627 ger DE-627 rakwb eng QC1-999 Oskar Bschorr verfasserin aut One-Way Wave Equation Derived from Impedance Theorem 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived. one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum Physics Hans-Joachim Raida verfasserin aut In Acoustics MDPI AG, 2019 2(2020), 1, Seite 164-170 (DE-627)1049287479 2624599X nnns volume:2 year:2020 number:1 pages:164-170 https://doi.org/10.3390/acoustics2010012 kostenfrei https://doaj.org/article/59fdb2674eff496899f02651cfec92ca kostenfrei https://www.mdpi.com/2624-599X/2/1/12 kostenfrei https://doaj.org/toc/2624-599X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_34 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2020 1 164-170
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topic_facet	one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum Physics
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callnumber-first	Q - Science
author	Oskar Bschorr
spellingShingle	Oskar Bschorr misc QC1-999 misc one-way wave equation misc 1st order wave equation misc two-way wave equation misc 2nd order wave equation misc impedance theorem misc longitudinal wave propagation misc inhomogeneous continuum misc Physics One-Way Wave Equation Derived from Impedance Theorem
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topic_title	QC1-999 One-Way Wave Equation Derived from Impedance Theorem one-way wave equation 1st order wave equation two-way wave equation 2nd order wave equation impedance theorem longitudinal wave propagation inhomogeneous continuum
topic	misc QC1-999 misc one-way wave equation misc 1st order wave equation misc two-way wave equation misc 2nd order wave equation misc impedance theorem misc longitudinal wave propagation misc inhomogeneous continuum misc Physics
topic_unstemmed	misc QC1-999 misc one-way wave equation misc 1st order wave equation misc two-way wave equation misc 2nd order wave equation misc impedance theorem misc longitudinal wave propagation misc inhomogeneous continuum misc Physics
topic_browse	misc QC1-999 misc one-way wave equation misc 1st order wave equation misc two-way wave equation misc 2nd order wave equation misc impedance theorem misc longitudinal wave propagation misc inhomogeneous continuum misc Physics
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	One-Way Wave Equation Derived from Impedance Theorem
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title_full	One-Way Wave Equation Derived from Impedance Theorem
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title_sort	one-way wave equation derived from impedance theorem
callnumber	QC1-999
title_auth	One-Way Wave Equation Derived from Impedance Theorem
abstract	The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived.
abstractGer	The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived.
abstract_unstemmed	The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived.
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title_short	One-Way Wave Equation Derived from Impedance Theorem
url	https://doi.org/10.3390/acoustics2010012 https://doaj.org/article/59fdb2674eff496899f02651cfec92ca https://www.mdpi.com/2624-599X/2/1/12 https://doaj.org/toc/2624-599X
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