Existence of a second island of stability of predictor–corrector schemes for calculating synthetic seismograms
SUMMARY As the first step towards a general analysis of the stability of optimally accurate predictor–corrector (P–C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P–C schemes for a 1‐D homogeneous case. Letting Δt be the time step, h be...
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| Veröffentlicht in: | Geophysical journal international 2012-01, Vol.188 (1), p.253-262 |
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| container_title | Geophysical journal international |
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| creator | Geller, Robert J. Mizutani, Hiromitsu Hirabayashi, Nobuyasu |
| description | SUMMARY
As the first step towards a general analysis of the stability of optimally accurate predictor–corrector (P–C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P–C schemes for a 1‐D homogeneous case. Letting Δt be the time step, h be the spatial grid interval, β be the velocity of seismic wave propagation and be the dimensionless Courant parameter, we find that each scheme has the following stability properties: stability for , instability for , stability for and instability for , where . We refer to the region as the second island of stability. The values of , and are scheme‐dependent. The existence of a second island of stability in a numerical scheme for solving the wave equation has not, to our knowledge, been previously reported. |
| doi_str_mv | 10.1111/j.1365-246X.2011.05251.x |
| format | Article |
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As the first step towards a general analysis of the stability of optimally accurate predictor–corrector (P–C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P–C schemes for a 1‐D homogeneous case. Letting Δt be the time step, h be the spatial grid interval, β be the velocity of seismic wave propagation and be the dimensionless Courant parameter, we find that each scheme has the following stability properties: stability for , instability for , stability for and instability for , where . We refer to the region as the second island of stability. The values of , and are scheme‐dependent. The existence of a second island of stability in a numerical scheme for solving the wave equation has not, to our knowledge, been previously reported.</description><identifier>ISSN: 0956-540X</identifier><identifier>EISSN: 1365-246X</identifier><identifier>DOI: 10.1111/j.1365-246X.2011.05251.x</identifier><language>eng</language><publisher>Oxford, UK: Blackwell Publishing Ltd</publisher><subject>Computational seismology ; Equations of motion ; Instability ; Islands ; Numerical approximations and analysis ; Numerical solutions ; Predictor-corrector methods ; Seismograms ; Stability ; Wave propagation</subject><ispartof>Geophysical journal international, 2012-01, Vol.188 (1), p.253-262</ispartof><rights>2011 The Authors Geophysical Journal International © 2011 RAS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a3861-9f21f8a498766e80c4cc662de898f7fd027add873e87db33885209c8b259eeeb3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1111%2Fj.1365-246X.2011.05251.x$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1111%2Fj.1365-246X.2011.05251.x$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Geller, Robert J.</creatorcontrib><creatorcontrib>Mizutani, Hiromitsu</creatorcontrib><creatorcontrib>Hirabayashi, Nobuyasu</creatorcontrib><title>Existence of a second island of stability of predictor–corrector schemes for calculating synthetic seismograms</title><title>Geophysical journal international</title><description>SUMMARY
As the first step towards a general analysis of the stability of optimally accurate predictor–corrector (P–C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P–C schemes for a 1‐D homogeneous case. Letting Δt be the time step, h be the spatial grid interval, β be the velocity of seismic wave propagation and be the dimensionless Courant parameter, we find that each scheme has the following stability properties: stability for , instability for , stability for and instability for , where . We refer to the region as the second island of stability. The values of , and are scheme‐dependent. The existence of a second island of stability in a numerical scheme for solving the wave equation has not, to our knowledge, been previously reported.</description><subject>Computational seismology</subject><subject>Equations of motion</subject><subject>Instability</subject><subject>Islands</subject><subject>Numerical approximations and analysis</subject><subject>Numerical solutions</subject><subject>Predictor-corrector methods</subject><subject>Seismograms</subject><subject>Stability</subject><subject>Wave propagation</subject><issn>0956-540X</issn><issn>1365-246X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNo9kE1OwzAQhS0EEqVwhyzZJNiO7TgLFqgqpagSG5C6sxxn0rrKT7FT0ey4AzfkJDgUMZt5M_P0pPkQighOSKi7XUJSwWPKxDqhmJAEc8pJcjxDk__DOZrgnIuYM7y-RFfe7zAmjDA5Qfv50foeWgNRV0U68mC6toysr3VoYeV7Xdja9sM47B2U1vSd-_78Mp1zMOrImy004KMqaKNrc6h1b9tN5Ie230JvTUi1vuk2Tjf-Gl1UuvZw89en6O1x_jp7ilcvi-XsYRXrVAoS5xUlldQsl5kQILFhxghBS5C5rLKqxDTTZSmzFGRWFmkqJac4N7KgPAeAIp2i21Pu3nXvB_C9aqw3UIe_oDt4RTDBUjLGabDen6wftoZB7Z1ttBuCQ42E1U6NINUIUo2E1S9hdVSL5-Wo0h-LrXVq</recordid><startdate>201201</startdate><enddate>201201</enddate><creator>Geller, Robert J.</creator><creator>Mizutani, Hiromitsu</creator><creator>Hirabayashi, Nobuyasu</creator><general>Blackwell Publishing Ltd</general><scope>7SM</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>201201</creationdate><title>Existence of a second island of stability of predictor–corrector schemes for calculating synthetic seismograms</title><author>Geller, Robert J. ; Mizutani, Hiromitsu ; Hirabayashi, Nobuyasu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a3861-9f21f8a498766e80c4cc662de898f7fd027add873e87db33885209c8b259eeeb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Computational seismology</topic><topic>Equations of motion</topic><topic>Instability</topic><topic>Islands</topic><topic>Numerical approximations and analysis</topic><topic>Numerical solutions</topic><topic>Predictor-corrector methods</topic><topic>Seismograms</topic><topic>Stability</topic><topic>Wave propagation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Geller, Robert J.</creatorcontrib><creatorcontrib>Mizutani, Hiromitsu</creatorcontrib><creatorcontrib>Hirabayashi, Nobuyasu</creatorcontrib><collection>Earthquake Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Geophysical journal international</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Geller, Robert J.</au><au>Mizutani, Hiromitsu</au><au>Hirabayashi, Nobuyasu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of a second island of stability of predictor–corrector schemes for calculating synthetic seismograms</atitle><jtitle>Geophysical journal international</jtitle><date>2012-01</date><risdate>2012</risdate><volume>188</volume><issue>1</issue><spage>253</spage><epage>262</epage><pages>253-262</pages><issn>0956-540X</issn><eissn>1365-246X</eissn><abstract>SUMMARY
As the first step towards a general analysis of the stability of optimally accurate predictor–corrector (P–C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P–C schemes for a 1‐D homogeneous case. Letting Δt be the time step, h be the spatial grid interval, β be the velocity of seismic wave propagation and be the dimensionless Courant parameter, we find that each scheme has the following stability properties: stability for , instability for , stability for and instability for , where . We refer to the region as the second island of stability. The values of , and are scheme‐dependent. The existence of a second island of stability in a numerical scheme for solving the wave equation has not, to our knowledge, been previously reported.</abstract><cop>Oxford, UK</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1111/j.1365-246X.2011.05251.x</doi><tpages>10</tpages></addata></record> |
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| language | eng |
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| source | Oxford Journals Open Access Collection; Wiley Online Library All Journals |
| subjects | Computational seismology Equations of motion Instability Islands Numerical approximations and analysis Numerical solutions Predictor-corrector methods Seismograms Stability Wave propagation |
| title | Existence of a second island of stability of predictor–corrector schemes for calculating synthetic seismograms |
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