Finite Difference Scheme Based on the Lebedev Grid for Seismic Wave Propagation in Fractured Media
Fractures in underground media are mostly vertical and orthogonal. Based on the assumption of long wavelengths, fractures can be considered infinitely thin planes embedded in a homogeneous medium. The fracture interface satisfies the conditions of displacement discontinuity and stress continuity, i....
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| Veröffentlicht in: | Pure and applied geophysics 2022-08, Vol.179 (8), p.2619-2636 |
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| creator | Wang, Kang Peng, Suping Lu, Yongxu Cui, Xiaoqin |
| description | Fractures in underground media are mostly vertical and orthogonal. Based on the assumption of long wavelengths, fractures can be considered infinitely thin planes embedded in a homogeneous medium. The fracture interface satisfies the conditions of displacement discontinuity and stress continuity, i.e. a linear slip boundary. The finite difference method is typically used to simulate the propagation of seismic waves at the fracture interface. In this study, a new finite difference scheme is proposed based on the velocity-stress equation, which can be used to simulate the propagation of seismic waves in vertical and orthogonal fracture media. The new finite difference scheme more closely resembles the conditions of actual vertical and orthogonal fractures. The Lebedev grid was adopted, and no interpolation was required for the calculation, which improved the accuracy. The numerical simulation of the new finite difference scheme reveals its long-term stability and accuracy. This scheme can be used for the analysis of reservoir fracture delineation. In addition, an explicit slip interface condition and the new finite difference scheme were used to comparatively model fractured media. Virtually identical results were obtained, which verifies the effectiveness of this model. Finally, based on the boundary conditions of linear slip, an improved Zoeppritz equation was established, and the effect of fracture compliance on the reflection and transmission coefficients was studied. This scheme can be used for the analysis of reservoir fracture traps. |
| doi_str_mv | 10.1007/s00024-022-03080-2 |
| format | Article |
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Based on the assumption of long wavelengths, fractures can be considered infinitely thin planes embedded in a homogeneous medium. The fracture interface satisfies the conditions of displacement discontinuity and stress continuity, i.e. a linear slip boundary. The finite difference method is typically used to simulate the propagation of seismic waves at the fracture interface. In this study, a new finite difference scheme is proposed based on the velocity-stress equation, which can be used to simulate the propagation of seismic waves in vertical and orthogonal fracture media. The new finite difference scheme more closely resembles the conditions of actual vertical and orthogonal fractures. The Lebedev grid was adopted, and no interpolation was required for the calculation, which improved the accuracy. The numerical simulation of the new finite difference scheme reveals its long-term stability and accuracy. This scheme can be used for the analysis of reservoir fracture delineation. In addition, an explicit slip interface condition and the new finite difference scheme were used to comparatively model fractured media. Virtually identical results were obtained, which verifies the effectiveness of this model. Finally, based on the boundary conditions of linear slip, an improved Zoeppritz equation was established, and the effect of fracture compliance on the reflection and transmission coefficients was studied. This scheme can be used for the analysis of reservoir fracture traps.</description><identifier>ISSN: 0033-4553</identifier><identifier>EISSN: 1420-9136</identifier><identifier>DOI: 10.1007/s00024-022-03080-2</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Accuracy ; Boundary conditions ; Coefficients ; Crack propagation ; Earth and Environmental Science ; Earth Sciences ; Finite difference method ; Fractures ; Geophysics/Geodesy ; Interpolation ; Mathematical models ; Numerical simulations ; P-waves ; Propagation ; Reservoirs ; Seismic propagation ; Seismic stability ; Seismic wave propagation ; Seismic waves ; Simulation ; Slip ; Stability analysis ; Stress propagation ; Wave propagation ; Wavelengths</subject><ispartof>Pure and applied geophysics, 2022-08, Vol.179 (8), p.2619-2636</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a342t-3492998e09a614582d7458135c5af4de049e30c12e8ceee9df01b7064042258a3</citedby><cites>FETCH-LOGICAL-a342t-3492998e09a614582d7458135c5af4de049e30c12e8ceee9df01b7064042258a3</cites><orcidid>0000-0003-4772-3073</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00024-022-03080-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00024-022-03080-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Wang, Kang</creatorcontrib><creatorcontrib>Peng, Suping</creatorcontrib><creatorcontrib>Lu, Yongxu</creatorcontrib><creatorcontrib>Cui, Xiaoqin</creatorcontrib><title>Finite Difference Scheme Based on the Lebedev Grid for Seismic Wave Propagation in Fractured Media</title><title>Pure and applied geophysics</title><addtitle>Pure Appl. Geophys</addtitle><description>Fractures in underground media are mostly vertical and orthogonal. Based on the assumption of long wavelengths, fractures can be considered infinitely thin planes embedded in a homogeneous medium. The fracture interface satisfies the conditions of displacement discontinuity and stress continuity, i.e. a linear slip boundary. The finite difference method is typically used to simulate the propagation of seismic waves at the fracture interface. In this study, a new finite difference scheme is proposed based on the velocity-stress equation, which can be used to simulate the propagation of seismic waves in vertical and orthogonal fracture media. The new finite difference scheme more closely resembles the conditions of actual vertical and orthogonal fractures. The Lebedev grid was adopted, and no interpolation was required for the calculation, which improved the accuracy. The numerical simulation of the new finite difference scheme reveals its long-term stability and accuracy. This scheme can be used for the analysis of reservoir fracture delineation. In addition, an explicit slip interface condition and the new finite difference scheme were used to comparatively model fractured media. Virtually identical results were obtained, which verifies the effectiveness of this model. Finally, based on the boundary conditions of linear slip, an improved Zoeppritz equation was established, and the effect of fracture compliance on the reflection and transmission coefficients was studied. This scheme can be used for the analysis of reservoir fracture traps.</description><subject>Accuracy</subject><subject>Boundary conditions</subject><subject>Coefficients</subject><subject>Crack propagation</subject><subject>Earth and Environmental Science</subject><subject>Earth Sciences</subject><subject>Finite difference method</subject><subject>Fractures</subject><subject>Geophysics/Geodesy</subject><subject>Interpolation</subject><subject>Mathematical models</subject><subject>Numerical simulations</subject><subject>P-waves</subject><subject>Propagation</subject><subject>Reservoirs</subject><subject>Seismic propagation</subject><subject>Seismic stability</subject><subject>Seismic wave propagation</subject><subject>Seismic waves</subject><subject>Simulation</subject><subject>Slip</subject><subject>Stability analysis</subject><subject>Stress propagation</subject><subject>Wave propagation</subject><subject>Wavelengths</subject><issn>0033-4553</issn><issn>1420-9136</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1LAzEQQIMoWKt_wFPAc3Ty1d0ctdoqVBSqeAxpdrZNsbs12Rb890ZX8OZl5vLeDDxCzjlccoDiKgGAUAyEYCChBCYOyIArAcxwOTokAwApmdJaHpOTlNYAvCi0GZDFJDShQ3ob6hojNh7p3K9wg_TGJaxo29BuhXSGC6xwT6cxVLRuI51jSJvg6ZvbI32O7dYtXRcyHRo6ic53u5jtR6yCOyVHtXtPePa7h-R1cvcyvmezp-nD-HrGnFSiY1IZYUyJYNyIK12KqsiTS-21q1WFoAxK8Fxg6RHRVDXwRQEjBUoIXTo5JBf93W1sP3aYOrtud7HJL60ouCw1FIpnSvSUj21KEWu7jWHj4qflYL9b2r6lzS3tT0srsiR7KWW4WWL8O_2P9QUcw3Tk</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Wang, Kang</creator><creator>Peng, Suping</creator><creator>Lu, Yongxu</creator><creator>Cui, Xiaoqin</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TG</scope><scope>7UA</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABUWG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>C1K</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F1W</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>H96</scope><scope>HCIFZ</scope><scope>KL.</scope><scope>L.G</scope><scope>L7M</scope><scope>M2P</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PYCSY</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0003-4772-3073</orcidid></search><sort><creationdate>20220801</creationdate><title>Finite Difference Scheme Based on the Lebedev Grid for Seismic Wave Propagation in Fractured Media</title><author>Wang, Kang ; Peng, Suping ; Lu, Yongxu ; Cui, Xiaoqin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a342t-3492998e09a614582d7458135c5af4de049e30c12e8ceee9df01b7064042258a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Accuracy</topic><topic>Boundary conditions</topic><topic>Coefficients</topic><topic>Crack propagation</topic><topic>Earth and Environmental Science</topic><topic>Earth Sciences</topic><topic>Finite difference method</topic><topic>Fractures</topic><topic>Geophysics/Geodesy</topic><topic>Interpolation</topic><topic>Mathematical models</topic><topic>Numerical simulations</topic><topic>P-waves</topic><topic>Propagation</topic><topic>Reservoirs</topic><topic>Seismic propagation</topic><topic>Seismic stability</topic><topic>Seismic wave propagation</topic><topic>Seismic waves</topic><topic>Simulation</topic><topic>Slip</topic><topic>Stability analysis</topic><topic>Stress propagation</topic><topic>Wave propagation</topic><topic>Wavelengths</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Kang</creatorcontrib><creatorcontrib>Peng, Suping</creatorcontrib><creatorcontrib>Lu, Yongxu</creatorcontrib><creatorcontrib>Cui, Xiaoqin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Water Resources Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>SciTech Premium Collection</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Pure and applied geophysics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Kang</au><au>Peng, Suping</au><au>Lu, Yongxu</au><au>Cui, Xiaoqin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Finite Difference Scheme Based on the Lebedev Grid for Seismic Wave Propagation in Fractured Media</atitle><jtitle>Pure and applied geophysics</jtitle><stitle>Pure Appl. Geophys</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>179</volume><issue>8</issue><spage>2619</spage><epage>2636</epage><pages>2619-2636</pages><issn>0033-4553</issn><eissn>1420-9136</eissn><abstract>Fractures in underground media are mostly vertical and orthogonal. Based on the assumption of long wavelengths, fractures can be considered infinitely thin planes embedded in a homogeneous medium. The fracture interface satisfies the conditions of displacement discontinuity and stress continuity, i.e. a linear slip boundary. The finite difference method is typically used to simulate the propagation of seismic waves at the fracture interface. In this study, a new finite difference scheme is proposed based on the velocity-stress equation, which can be used to simulate the propagation of seismic waves in vertical and orthogonal fracture media. The new finite difference scheme more closely resembles the conditions of actual vertical and orthogonal fractures. The Lebedev grid was adopted, and no interpolation was required for the calculation, which improved the accuracy. The numerical simulation of the new finite difference scheme reveals its long-term stability and accuracy. This scheme can be used for the analysis of reservoir fracture delineation. In addition, an explicit slip interface condition and the new finite difference scheme were used to comparatively model fractured media. Virtually identical results were obtained, which verifies the effectiveness of this model. Finally, based on the boundary conditions of linear slip, an improved Zoeppritz equation was established, and the effect of fracture compliance on the reflection and transmission coefficients was studied. This scheme can be used for the analysis of reservoir fracture traps.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00024-022-03080-2</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0003-4772-3073</orcidid></addata></record> |
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| subjects | Accuracy Boundary conditions Coefficients Crack propagation Earth and Environmental Science Earth Sciences Finite difference method Fractures Geophysics/Geodesy Interpolation Mathematical models Numerical simulations P-waves Propagation Reservoirs Seismic propagation Seismic stability Seismic wave propagation Seismic waves Simulation Slip Stability analysis Stress propagation Wave propagation Wavelengths |
| title | Finite Difference Scheme Based on the Lebedev Grid for Seismic Wave Propagation in Fractured Media |
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