2D acoustic-elastic coupled waveform inversion in the Laplace domain

ABSTRACT Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may b...

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Published in:	Geophysical Prospecting Vol. 58; no. 6; pp. 997 - 1010
Main Authors:	Bae, Ho Seuk, Shin, Changsoo, Cha, Young Ho, Choi, Yunseok, Min, Dong-Joo
Format:	Journal Article
Language:	English
Published:	Oxford, UK Blackwell Publishing Ltd 01.11.2010 Blackwell
Subjects:	Acoustic-elastic coupled media Acoustics Algorithms Applied geophysics Earth Earth sciences Earth, ocean, space Exact sciences and technology Finite-element method Geophysics Internal geophysics Inversions Laplace domain Long-wavelength Mathematical models Prospecting Two dimensional Waveform inversion Waveforms wavelength algorithms models inverse problem interfaces elastic media exploration density S-waves pressure velocity finite element analysis low frequency frequency Earth depth propagation noise waveforms direction
ISSN:	0016-8025, 1365-2478
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Abstract	ABSTRACT Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.
AbstractList	ABSTRACTAlthough waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time- and frequency-domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non-linear objective function and the unreliable low-frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace-domain waveform inversion has been proposed. The Laplace-domain waveform inversion has been known to provide a long-wavelength velocity model even for field data, which may be because it employs the zero-frequency component of the damped wavefield and a well-behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models. ABSTRACT Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.
Author	Shin, Changsoo Choi, Yunseok Cha, Young Ho Bae, Ho Seuk Min, Dong-Joo
Author_xml	– sequence: 1 givenname: Ho Seuk surname: Bae fullname: Bae, Ho Seuk organization: Department of Energy Systems Engineering, Seoul National University, Seoul 151-742, Korea – sequence: 2 givenname: Changsoo surname: Shin fullname: Shin, Changsoo email: css@model.snu.ac.kr organization: Department of Energy Systems Engineering, Seoul National University, Seoul 151-742, Korea – sequence: 3 givenname: Young Ho surname: Cha fullname: Cha, Young Ho organization: ExxonMobil Upstream Research Company, 3120 Buffalo Speedway, Houston, TX 77098, USA – sequence: 4 givenname: Yunseok surname: Choi fullname: Choi, Yunseok organization: Department of Physical Science and Engineering, King Abdullah University of Science and Technology, 4700 Thuwal, 23955-6900, Saudi Arabia – sequence: 5 givenname: Dong-Joo surname: Min fullname: Min, Dong-Joo organization: Department of Energy Systems Engineering, Seoul National University, Seoul 151-742, Korea
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References	Lee H.-Y., Lim S.-C., Min D.-J., Kwon B.-D. and Park M. 2009. 2D time-domain acoustic-elastic coupled modelling: A cell-based finite-difference method. Geosciences Journal 13, 407-414. Zienkiewicz O.C., Taylor R.L. and Zhu J.Z. 2005. The Finite Element Method: Its Basis and Fundamentals. Butterworth-Heinemann. Komatitsch D., Barnes C. and Tromp J. 2000. Wave propagation near a fluid-solid interface: A spectral-element approach. Geophysics 65, 623-631. Kolb P., Collino F. and Lailly P. 1986. Pre-stack inversion of a 1-D medium. Proceedings of the IEEE 74, 498-508. Aminzadeh F., Brac J. and Kunz T. 1997. 3-D Salt and Overthrust Models. SEG. Gauthier O., Virieux J. and Tarantola A. 1986. Two-dimensional nonlinear inversion of seismic waveforms: Numerical results. Geophysics 51, 1387-1403. Pratt R.G., Shin C. and Hicks G.J. 1998. Gauss-Newton and full Newton method in frequency domain seismic waveform inversion. Geophysical Journal International 133, 341-362. Shin C., Pyun S. and Bednar J.B. 2007. Comparison of waveform inversion, part 1: Conventional wavefield vs logarithmic wavefield. Geophysical Prospecting 55, 449-464. Komatitsch D., Tsuboi S. and Tromp J. 2005. The spectral-element method in seismology. Geophysical Monography Series 157, 205-227. Mora P. 1987. Nonlinear two-dimensional elastic inversion of multioffset seismic data. Geophysics 52, 1211-1228. Shin C. and Ha W. 2008. A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains. Geophysics 73, VE119-VE133. Zhang J. 2004. Wave propagation across fluid-solid interfaces: A grid method approach: Geophysical Journal International 159, 240-252. Shin C. and Min D.-J. 2006. Waveform inversion using a logarithmic wavefield. Geophysics 71, R31-R42. Pyun S., Shin C. and Bednar J.B. 2007. Comparison of waveform inversion, part 2: Amplitude approach. Geophysical Prospecting 55, 477-485. Ewing W.M., Jardetzky W.S. and Press F. 1957. Elastic Waves in Layered Media. McGraw-Hill. Shin C., Yoon K., Marfurt K.J., Park K., Yang D., Lim H.Y. et al . 2001. Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion. Geophysics 66, 1856-1863. Tarantola A. 1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics 49, 1259-1266. Ha T., Chung W. and Shin C. 2009. Waveform inversion using a back-propagation algorithm and a Huber function norm. Geophysics 74, R15-R24. Shin C. and Cha Y.H. 2008. Waveform inversion in the Laplace domain. Geophysical Journal International 173, 922-931. Choi Y., Min D.-J. and Shin C. 2008. Two-dimensional waveform inversion of multi-component data in acoustic-elastic coupled media. Geophysics 56, 863-881. 2006; 71 2009; 13 2009; 74 2004; 159 1986; 51 1987; 52 1986; 74 2000 1984; 49 2005; 157 2000; 65 1997 2008; 56 1983 2005 1998; 133 2001; 66 2008; 73 2007; 55 1957 2008; 173 e_1_2_7_6_1 Zienkiewicz O.C. (e_1_2_7_23_1) 2005 e_1_2_7_5_1 e_1_2_7_4_1 Lailly P. (e_1_2_7_11_1) 1983 e_1_2_7_9_1 e_1_2_7_8_1 e_1_2_7_7_1 e_1_2_7_19_1 e_1_2_7_18_1 e_1_2_7_17_1 e_1_2_7_16_1 Choi Y. (e_1_2_7_3_1) 2008; 56 e_1_2_7_15_1 e_1_2_7_14_1 e_1_2_7_13_1 e_1_2_7_12_1 e_1_2_7_22_1 Aminzadeh F. (e_1_2_7_2_1) 1997 e_1_2_7_10_1 e_1_2_7_21_1 e_1_2_7_20_1
References_xml	– reference: Gauthier O., Virieux J. and Tarantola A. 1986. Two-dimensional nonlinear inversion of seismic waveforms: Numerical results. Geophysics 51, 1387-1403. – reference: Komatitsch D., Barnes C. and Tromp J. 2000. Wave propagation near a fluid-solid interface: A spectral-element approach. Geophysics 65, 623-631. – reference: Komatitsch D., Tsuboi S. and Tromp J. 2005. The spectral-element method in seismology. Geophysical Monography Series 157, 205-227. – reference: Pyun S., Shin C. and Bednar J.B. 2007. Comparison of waveform inversion, part 2: Amplitude approach. Geophysical Prospecting 55, 477-485. – reference: Shin C., Yoon K., Marfurt K.J., Park K., Yang D., Lim H.Y. et al . 2001. Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion. Geophysics 66, 1856-1863. – reference: Aminzadeh F., Brac J. and Kunz T. 1997. 3-D Salt and Overthrust Models. SEG. – reference: Shin C. and Cha Y.H. 2008. Waveform inversion in the Laplace domain. Geophysical Journal International 173, 922-931. – reference: Shin C. and Min D.-J. 2006. Waveform inversion using a logarithmic wavefield. Geophysics 71, R31-R42. – reference: Mora P. 1987. Nonlinear two-dimensional elastic inversion of multioffset seismic data. Geophysics 52, 1211-1228. – reference: Ewing W.M., Jardetzky W.S. and Press F. 1957. Elastic Waves in Layered Media. McGraw-Hill. – reference: Ha T., Chung W. and Shin C. 2009. Waveform inversion using a back-propagation algorithm and a Huber function norm. Geophysics 74, R15-R24. – reference: Tarantola A. 1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics 49, 1259-1266. – reference: Choi Y., Min D.-J. and Shin C. 2008. Two-dimensional waveform inversion of multi-component data in acoustic-elastic coupled media. Geophysics 56, 863-881. – reference: Kolb P., Collino F. and Lailly P. 1986. Pre-stack inversion of a 1-D medium. Proceedings of the IEEE 74, 498-508. – reference: Shin C., Pyun S. and Bednar J.B. 2007. Comparison of waveform inversion, part 1: Conventional wavefield vs logarithmic wavefield. Geophysical Prospecting 55, 449-464. – reference: Zienkiewicz O.C., Taylor R.L. and Zhu J.Z. 2005. The Finite Element Method: Its Basis and Fundamentals. Butterworth-Heinemann. – reference: Pratt R.G., Shin C. and Hicks G.J. 1998. Gauss-Newton and full Newton method in frequency domain seismic waveform inversion. Geophysical Journal International 133, 341-362. – reference: Shin C. and Ha W. 2008. A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains. Geophysics 73, VE119-VE133. – reference: Zhang J. 2004. Wave propagation across fluid-solid interfaces: A grid method approach: Geophysical Journal International 159, 240-252. – reference: Lee H.-Y., Lim S.-C., Min D.-J., Kwon B.-D. and Park M. 2009. 2D time-domain acoustic-elastic coupled modelling: A cell-based finite-difference method. Geosciences Journal 13, 407-414. – start-page: 2201 year: 2000 end-page: 2204 – volume: 65 start-page: 623 year: 2000 end-page: 631 article-title: Wave propagation near a fluid‐solid interface: A spectral‐element approach publication-title: Geophysics – volume: 66 start-page: 1856 year: 2001 end-page: 1863 article-title: Efficient calculation of a partial‐derivative wavefield using reciprocity for seismic imaging and inversion publication-title: Geophysics – year: 1957 – volume: 74 start-page: 498 year: 1986 end-page: 508 article-title: Pre‐stack inversion of a 1‐D medium publication-title: Proceedings of the IEEE – volume: 71 start-page: R31 year: 2006 end-page: R42 article-title: Waveform inversion using a logarithmic wavefield publication-title: Geophysics – volume: 13 start-page: 407 year: 2009 end-page: 414 article-title: 2D time‐domain acoustic‐elastic coupled modelling: A cell‐based finite‐difference method publication-title: Geosciences Journal – year: 2005 – volume: 56 start-page: 863 year: 2008 end-page: 881 article-title: Two‐dimensional waveform inversion of multi‐component data in acoustic‐elastic coupled media publication-title: Geophysics – volume: 73 start-page: VE119 year: 2008 end-page: VE133 article-title: A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains publication-title: Geophysics – year: 1997 – start-page: 206 year: 1983 end-page: 220 – volume: 173 start-page: 922 year: 2008 end-page: 931 article-title: Waveform inversion in the Laplace domain publication-title: Geophysical Journal International – volume: 52 start-page: 1211 year: 1987 end-page: 1228 article-title: Nonlinear two‐dimensional elastic inversion of multioffset seismic data publication-title: Geophysics – volume: 49 start-page: 1259 year: 1984 end-page: 1266 article-title: Inversion of seismic reflection data in the acoustic approximation publication-title: Geophysics – volume: 133 start-page: 341 year: 1998 end-page: 362 article-title: Gauss‐Newton and full Newton method in frequency domain seismic waveform inversion publication-title: Geophysical Journal International – volume: 55 start-page: 449 year: 2007 end-page: 464 article-title: Comparison of waveform inversion, part 1: Conventional wavefield vs logarithmic wavefield publication-title: Geophysical Prospecting – volume: 51 start-page: 1387 year: 1986 end-page: 1403 article-title: Two‐dimensional nonlinear inversion of seismic waveforms: Numerical results publication-title: Geophysics – volume: 157 start-page: 205 year: 2005 end-page: 227 article-title: The spectral‐element method in seismology publication-title: Geophysical Monography Series – volume: 55 start-page: 477 year: 2007 end-page: 485 article-title: Comparison of waveform inversion, part 2: Amplitude approach publication-title: Geophysical Prospecting – volume: 74 start-page: R15 year: 2009 end-page: R24 article-title: Waveform inversion using a back‐propagation algorithm and a Huber function norm publication-title: Geophysics – volume: 159 start-page: 240 year: 2004 end-page: 252 article-title: Wave propagation across fluid‐solid interfaces: A grid method approach publication-title: Geophysical Journal International – ident: e_1_2_7_20_1 doi: 10.1190/1.1487129 – ident: e_1_2_7_7_1 doi: 10.1190/1.1815890 – volume: 56 start-page: 863 year: 2008 ident: e_1_2_7_3_1 article-title: Two‐dimensional waveform inversion of multi‐component data in acoustic‐elastic coupled media publication-title: Geophysics – ident: e_1_2_7_19_1 doi: 10.1111/j.1365-2478.2007.00617.x – ident: e_1_2_7_4_1 doi: 10.1063/1.3060203 – ident: e_1_2_7_6_1 doi: 10.1190/1.3112572 – ident: e_1_2_7_8_1 doi: 10.1109/PROC.1986.13490 – ident: e_1_2_7_15_1 doi: 10.1111/j.1365-2478.2007.00619.x – ident: e_1_2_7_21_1 doi: 10.1190/1.1441754 – ident: e_1_2_7_10_1 doi: 10.1029/157GM13 – ident: e_1_2_7_18_1 doi: 10.1190/1.2194523 – start-page: 206 volume-title: Conference on Inverse Scattering: Theory and Application year: 1983 ident: e_1_2_7_11_1 – ident: e_1_2_7_13_1 doi: 10.1190/1.1442384 – ident: e_1_2_7_9_1 doi: 10.1190/1.1444758 – ident: e_1_2_7_16_1 doi: 10.1111/j.1365-246X.2008.03768.x – volume-title: The Finite Element Method: Its Basis and Fundamentals year: 2005 ident: e_1_2_7_23_1 – ident: e_1_2_7_22_1 doi: 10.1111/j.1365-246X.2004.02372.x – ident: e_1_2_7_12_1 doi: 10.1007/s12303-009-0037-x – ident: e_1_2_7_17_1 doi: 10.1190/1.2953978 – volume-title: 3‐D Salt and Overthrust Models year: 1997 ident: e_1_2_7_2_1 – ident: e_1_2_7_5_1 doi: 10.1190/1.1442188 – ident: e_1_2_7_14_1 doi: 10.1046/j.1365-246X.1998.00498.x
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Snippet	ABSTRACT Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the... Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and... ABSTRACTAlthough waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the...
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SubjectTerms	Acoustic-elastic coupled media Acoustics Algorithms Applied geophysics Earth Earth sciences Earth, ocean, space Exact sciences and technology Finite-element method Geophysics Internal geophysics Inversions Laplace domain Long-wavelength Mathematical models Prospecting Two dimensional Waveform inversion Waveforms
Title	2D acoustic-elastic coupled waveform inversion in the Laplace domain
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