Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method
Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI b...
Ausführliche Beschreibung
Autor*in: |
Jeong, Woodon [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2015 |
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Anmerkung: |
© Springer Basel 2015 |
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Übergeordnetes Werk: |
Enthalten in: Pure and applied geophysics - Basel : Birkhäuser, 1939, 172(2015), 6 vom: 28. Jan., Seite 1491-1509 |
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Übergeordnetes Werk: |
volume:172 ; year:2015 ; number:6 ; day:28 ; month:01 ; pages:1491-1509 |
Links: |
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DOI / URN: |
10.1007/s00024-014-1020-7 |
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Katalog-ID: |
SPR000238198 |
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520 | |a Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. | ||
650 | 4 | |a Full waveform inversion |7 (dpeaa)DE-He213 | |
650 | 4 | |a objective function |7 (dpeaa)DE-He213 | |
650 | 4 | |a Student’s |7 (dpeaa)DE-He213 | |
650 | 4 | |a distribution |7 (dpeaa)DE-He213 | |
650 | 4 | |a robust waveform inversion |7 (dpeaa)DE-He213 | |
650 | 4 | |a multiparameter |7 (dpeaa)DE-He213 | |
650 | 4 | |a simultaneous source |7 (dpeaa)DE-He213 | |
700 | 1 | |a Kang, Minji |4 aut | |
700 | 1 | |a Kim, Shinwoong |4 aut | |
700 | 1 | |a Min, Dong-Joo |4 aut | |
700 | 1 | |a Kim, Won-Ki |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Pure and applied geophysics |d Basel : Birkhäuser, 1939 |g 172(2015), 6 vom: 28. Jan., Seite 1491-1509 |w (DE-627)265506743 |w (DE-600)1464028-4 |x 1420-9136 |7 nnns |
773 | 1 | 8 | |g volume:172 |g year:2015 |g number:6 |g day:28 |g month:01 |g pages:1491-1509 |
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10.1007/s00024-014-1020-7 doi (DE-627)SPR000238198 (SPR)s00024-014-1020-7-e DE-627 ger DE-627 rakwb eng Jeong, Woodon verfasserin aut Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. Full waveform inversion (dpeaa)DE-He213 objective function (dpeaa)DE-He213 Student’s (dpeaa)DE-He213 distribution (dpeaa)DE-He213 robust waveform inversion (dpeaa)DE-He213 multiparameter (dpeaa)DE-He213 simultaneous source (dpeaa)DE-He213 Kang, Minji aut Kim, Shinwoong aut Min, Dong-Joo aut Kim, Won-Ki aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 172(2015), 6 vom: 28. Jan., Seite 1491-1509 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:172 year:2015 number:6 day:28 month:01 pages:1491-1509 https://dx.doi.org/10.1007/s00024-014-1020-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 172 2015 6 28 01 1491-1509 |
spelling |
10.1007/s00024-014-1020-7 doi (DE-627)SPR000238198 (SPR)s00024-014-1020-7-e DE-627 ger DE-627 rakwb eng Jeong, Woodon verfasserin aut Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. Full waveform inversion (dpeaa)DE-He213 objective function (dpeaa)DE-He213 Student’s (dpeaa)DE-He213 distribution (dpeaa)DE-He213 robust waveform inversion (dpeaa)DE-He213 multiparameter (dpeaa)DE-He213 simultaneous source (dpeaa)DE-He213 Kang, Minji aut Kim, Shinwoong aut Min, Dong-Joo aut Kim, Won-Ki aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 172(2015), 6 vom: 28. Jan., Seite 1491-1509 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:172 year:2015 number:6 day:28 month:01 pages:1491-1509 https://dx.doi.org/10.1007/s00024-014-1020-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 172 2015 6 28 01 1491-1509 |
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10.1007/s00024-014-1020-7 doi (DE-627)SPR000238198 (SPR)s00024-014-1020-7-e DE-627 ger DE-627 rakwb eng Jeong, Woodon verfasserin aut Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. Full waveform inversion (dpeaa)DE-He213 objective function (dpeaa)DE-He213 Student’s (dpeaa)DE-He213 distribution (dpeaa)DE-He213 robust waveform inversion (dpeaa)DE-He213 multiparameter (dpeaa)DE-He213 simultaneous source (dpeaa)DE-He213 Kang, Minji aut Kim, Shinwoong aut Min, Dong-Joo aut Kim, Won-Ki aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 172(2015), 6 vom: 28. Jan., Seite 1491-1509 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:172 year:2015 number:6 day:28 month:01 pages:1491-1509 https://dx.doi.org/10.1007/s00024-014-1020-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 172 2015 6 28 01 1491-1509 |
allfieldsGer |
10.1007/s00024-014-1020-7 doi (DE-627)SPR000238198 (SPR)s00024-014-1020-7-e DE-627 ger DE-627 rakwb eng Jeong, Woodon verfasserin aut Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. Full waveform inversion (dpeaa)DE-He213 objective function (dpeaa)DE-He213 Student’s (dpeaa)DE-He213 distribution (dpeaa)DE-He213 robust waveform inversion (dpeaa)DE-He213 multiparameter (dpeaa)DE-He213 simultaneous source (dpeaa)DE-He213 Kang, Minji aut Kim, Shinwoong aut Min, Dong-Joo aut Kim, Won-Ki aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 172(2015), 6 vom: 28. Jan., Seite 1491-1509 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:172 year:2015 number:6 day:28 month:01 pages:1491-1509 https://dx.doi.org/10.1007/s00024-014-1020-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 172 2015 6 28 01 1491-1509 |
allfieldsSound |
10.1007/s00024-014-1020-7 doi (DE-627)SPR000238198 (SPR)s00024-014-1020-7-e DE-627 ger DE-627 rakwb eng Jeong, Woodon verfasserin aut Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. Full waveform inversion (dpeaa)DE-He213 objective function (dpeaa)DE-He213 Student’s (dpeaa)DE-He213 distribution (dpeaa)DE-He213 robust waveform inversion (dpeaa)DE-He213 multiparameter (dpeaa)DE-He213 simultaneous source (dpeaa)DE-He213 Kang, Minji aut Kim, Shinwoong aut Min, Dong-Joo aut Kim, Won-Ki aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 172(2015), 6 vom: 28. Jan., Seite 1491-1509 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:172 year:2015 number:6 day:28 month:01 pages:1491-1509 https://dx.doi.org/10.1007/s00024-014-1020-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 172 2015 6 28 01 1491-1509 |
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Enthalten in Pure and applied geophysics 172(2015), 6 vom: 28. Jan., Seite 1491-1509 volume:172 year:2015 number:6 day:28 month:01 pages:1491-1509 |
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Enthalten in Pure and applied geophysics 172(2015), 6 vom: 28. Jan., Seite 1491-1509 volume:172 year:2015 number:6 day:28 month:01 pages:1491-1509 |
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Full waveform inversion objective function Student’s distribution robust waveform inversion multiparameter simultaneous source |
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Jeong, Woodon @@aut@@ Kang, Minji @@aut@@ Kim, Shinwoong @@aut@@ Min, Dong-Joo @@aut@@ Kim, Won-Ki @@aut@@ |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR000238198</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327142144.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00024-014-1020-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR000238198</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00024-014-1020-7-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jeong, Woodon</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Basel 2015</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Full waveform inversion</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">objective function</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Student’s</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">distribution</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">robust waveform inversion</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">multiparameter</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">simultaneous source</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kang, Minji</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kim, Shinwoong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Min, Dong-Joo</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kim, Won-Ki</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Pure and applied geophysics</subfield><subfield code="d">Basel : Birkhäuser, 1939</subfield><subfield code="g">172(2015), 6 vom: 28. 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|
author |
Jeong, Woodon |
spellingShingle |
Jeong, Woodon misc Full waveform inversion misc objective function misc Student’s misc distribution misc robust waveform inversion misc multiparameter misc simultaneous source Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method |
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1420-9136 |
topic_title |
Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method Full waveform inversion (dpeaa)DE-He213 objective function (dpeaa)DE-He213 Student’s (dpeaa)DE-He213 distribution (dpeaa)DE-He213 robust waveform inversion (dpeaa)DE-He213 multiparameter (dpeaa)DE-He213 simultaneous source (dpeaa)DE-He213 |
topic |
misc Full waveform inversion misc objective function misc Student’s misc distribution misc robust waveform inversion misc multiparameter misc simultaneous source |
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misc Full waveform inversion misc objective function misc Student’s misc distribution misc robust waveform inversion misc multiparameter misc simultaneous source |
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misc Full waveform inversion misc objective function misc Student’s misc distribution misc robust waveform inversion misc multiparameter misc simultaneous source |
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Elektronische Aufsätze Aufsätze Elektronische Ressource |
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Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method |
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(DE-627)SPR000238198 (SPR)s00024-014-1020-7-e |
title_full |
Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method |
author_sort |
Jeong, Woodon |
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Pure and applied geophysics |
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1491 |
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Jeong, Woodon Kang, Minji Kim, Shinwoong Min, Dong-Joo Kim, Won-Ki |
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172 |
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Elektronische Aufsätze |
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Jeong, Woodon |
doi_str_mv |
10.1007/s00024-014-1020-7 |
title_sort |
full waveform inversion using student’s t distribution: a numerical study for elastic waveform inversion and simultaneous-source method |
title_auth |
Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method |
abstract |
Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. © Springer Basel 2015 |
abstractGer |
Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. © Springer Basel 2015 |
abstract_unstemmed |
Abstract Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l1-norm-based objective functions. However, the l1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l2-norm and l1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l2-norm is sensitive to noise, whereas the l1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l1- and l2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l1- and l2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution. © Springer Basel 2015 |
collection_details |
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container_issue |
6 |
title_short |
Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method |
url |
https://dx.doi.org/10.1007/s00024-014-1020-7 |
remote_bool |
true |
author2 |
Kang, Minji Kim, Shinwoong Min, Dong-Joo Kim, Won-Ki |
author2Str |
Kang, Minji Kim, Shinwoong Min, Dong-Joo Kim, Won-Ki |
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265506743 |
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hochschulschrift_bool |
false |
doi_str |
10.1007/s00024-014-1020-7 |
up_date |
2024-07-03T14:51:01.621Z |
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score |
7.400275 |