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Two-dimensional frequency-domain acoustic full-waveform inversion with rugged topography

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Abstract

We studied finite-element-method-based two-dimensional frequency-domain acoustic FWI under rugged topography conditions. The exponential attenuation boundary condition suitable for rugged topography is proposed to solve the cutoff boundary problem as well as to consider the requirement of using the same subdivision grid in joint multifrequency inversion. The proposed method introduces the attenuation factor, and by adjusting it, acoustic waves are sufficiently attenuated in the attenuation layer to minimize the cutoff boundary effect. Based on the law of exponential attenuation, expressions for computing the attenuation factor and the thickness of attenuation layers are derived for different frequencies. In multifrequency-domain FWI, the conjugate gradient method is used to solve equations in the Gauss–Newton algorithm and thus minimize the computation cost in calculating the Hessian matrix. In addition, the effect of initial model selection and frequency combination on FWI is analyzed. Examples using numerical simulations and FWI calculations are used to verify the efficiency of the proposed method.

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References

  • Brossier, R., Operto, S., and Virieus, J., 2009, Seismic imaging of complex on shore structures by 2D elastic frequency-domain full-waveform inversion: Geophysics, 74(6), WCC105–WCC118.

    Article  Google Scholar 

  • Bérenger, J. P., 1994, A perfectly matched layer for absorption of electromagnetic waves: J. Comput. Phys., 114(2), 185–200.

    Article  Google Scholar 

  • Cao, S., and Greenhalgh, S., 1998, Attenuating boundary conditions for numerical modeling of acoustic wave propagation: Geophysics, 63(1), 231–243.

    Article  Google Scholar 

  • Cerjan, C., Kosloff, D., Kosloff, R., and Reshef, M., 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics, 50(4), 705–708.

    Article  Google Scholar 

  • Chew, W. C., and Weedon, W. H., 1994, A 3D perfectly matched medium from modified maxwell’s equations with stretched coordinates: Microw. Opt. Tech. Lett., 7(13), 599–604.

    Article  Google Scholar 

  • Du, Q. Z., Li, B., and Hou, B., 2009, Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme: Applied Geopysics, 6(1), 42–49.

    Article  Google Scholar 

  • Du, Q. Z., Sun, R. Y., Qin, T., Zhu, Y. T., and Bi, L. F., 2010, A study of perfectly matched layers for joint multicomponent reverse-time migration: Applied Geophysics, 7(2), 166–173.

    Article  Google Scholar 

  • Dong, L. G., Chi, B. X., Tao, J. X., and Liu, Y. Z., 2013, Objective function behavior in acoustic full-waveform inversion: Chinese J. Geophys. (in Chinese), 56(10), 3445–3460.

    Google Scholar 

  • Fichtner, A., and Trampert, J., 2011, Resolution analysis in full waveform inversion: Geophysical Journal International, 187(3), 1604–1624.

    Article  Google Scholar 

  • Gauthier, O., Virieux, J., and Tarantola, A., 1986, Twodimensional nonlinear inversion of seismic waveforms: numerical results: Geophysics, 51(7), 1387–1403.

    Google Scholar 

  • Hicks, G. J., and Pratt, R. G., 2001, Reflection waveform Inversion Using Local Decent Methods:Estimating Attenuation and Velocity Over a Gas-Sand Deposit: Geophysics, 66(2), 598–612.

    Article  Google Scholar 

  • Hu, G. H., Jia, C. M, Xia, H. R., He, J. B., Song, L., and Shen, Z. Q., 2013, Implementation and validation of 3D acoustic full waveform inversion: Geophysical Prospecting for Petroleum, 52(4), 417–425.

    Google Scholar 

  • Komatitsch, D., and Martin, R., 2007, An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation: Geophysics, 72(5), SM155–SM167.

    Article  Google Scholar 

  • Lailly, P., 1983, The seismic inverse problem as a sequence of before stack migrations//Conference on inverse scattering: theory and applications: Society of Industrial and Applied Mathematics, Proceedings, 206–220.

    Google Scholar 

  • Long, G. H., Li, X. F., Zhang, M. G., and Zhu, T., 2009, Visco-acoustic transmission waveform inversion of velocity structure in Space-frequency domain: Acta Seismologica Sinica, 31(1), 32–41.

    Google Scholar 

  • Liu, G. F., Liu, H., Meng, X. H., and Yan, H. F., 2012, Frequency-related factors analysis in frequency domain waveform inversion: Chinese J. Geophys. (in Chinese), 55(4), 1345–1353.

    Google Scholar 

  • Malinowski, M., and Operto, S., 2008, Quantitative imaging of the Permo-Mesozoic complex and its basement by frequency domain waveform tomography of wide-aperture seismic data from the Polish Basin: Geophysical Prospecting, 56(6), 805–825.

    Article  Google Scholar 

  • Marfurt, K. J., 1984, Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations: Geophysics, 49(5), 533–549.

    Article  Google Scholar 

  • Operto, S., Ravaut, C., Improta, L., Virieux, J., Herrero, A., and Dell'Aversana, P., 2004, Quantitative imaging of complex structures from dense wide-aperture seismic data by multiscale traveltime and waveform inversions: a case study: Geophysical Prospecting, 52(6), 625–651.

    Google Scholar 

  • Plessix, R., and Perkins, C., 2010, Full waveform inversion of a deep water ocean bottom seismometer dataset: First Break, 28(1), 71–78.

    Google Scholar 

  • Pratt, R. G., and Worthington, M. H., 1990, Inverse theory applied to multi-source cross-hole tomography. Part1: Acoustic wave equation method: Geophysical Prospecting, 38(3), 287–310.

    Google Scholar 

  • Pratt, R. G., 1990, Inverse theory applied to multi-source cross-hole tomography. Part II: elastic wave-equation method, Geophysical Prospecting, 38(3), 311–330.

    Article  Google Scholar 

  • Pratt, R., Shin, C., and Hicks, G., 1998, Gauss-Newton and full newton methods in frequency-space seismic waveform inversion: Geophysical Journal International, 133(2), 341–362.

    Article  Google Scholar 

  • Pratt, R., and Sams, M., 1996, Reconciliation of crosshole seismic welocityies with well information in a layered sedimentary environment: Geophysics, 61(2), 549–560.

    Article  Google Scholar 

  • Pratt, R., 1999, Seismic waveform inversion in the frequency domain, part I: theory and verification in a physical scale model: Geophysics, 64(3), 888–901.

    Article  Google Scholar 

  • Qin, Z., Lu,. M. H., Zheng, X. D., Yao, T., Zhang, C., and Song, J. Y., 2009, The implementation of an improved NPML absorbing boundary condition in elastic wave modeling: Applied Geophysics, 6(2), 113–121.

    Article  Google Scholar 

  • Sirgue, L., Barkved, O., Dellinger, J., Albertin, U., and Kommedal, J. H., 2010, Full waveform inversion: the next leap forward in imaging at Valhall: First Break, 28(4), 65–70.

    Google Scholar 

  • Shin, C., and Cha, Y. H., 2008, Waveform inversion in the Laplace domain: Geophysical Journal International, 173(3), 922–931.

    Article  Google Scholar 

  • Shin, C., and Cha, Y. H., 2009, Waveform inversion in the Laplace-Fourier domain: Geophysical Journal International, 177(3), 1067–1079.

    Article  Google Scholar 

  • Song, J. Y., Zheng, X. D., Qin, Z., and Su, B. Y., 2011, Multi-scale seismic full waveform inversion in the frequency-domain with a multi-grid method: Applied Geophysics, 8(4), 303–310.

    Article  Google Scholar 

  • Song, R. L., Ma, J., and Wang K. S., 2005, The application of the nonsplitting perfectly matched layer in numerical modeling of wave propagation in poroelastic media: Applied Geophysics, 2(4), 216–222.

    Article  Google Scholar 

  • Song, Z. M., Williamson, P. R., and Pratt, R. G., 1995, Frequency-domain acoustic-wave modeling and inversion of crosshole data: Part II-inversion method, synthetic experiments and real-data results: Geophysics, 60(3), 796–809.

    Article  Google Scholar 

  • Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49(8), 1259–1266.

    Article  Google Scholar 

  • Tarantola, A., 1986, A strategy for nonlinear elastic inversion of seismic reflection data: Geophysics, 51(10), 1893–1903.

    Article  Google Scholar 

  • Wang, W., Han, B., and Tang, J. P., 2013, Regularization method with sparsity constraints for seismic waveform inversion: Chinese J. Geophys. (in Chinese), 56(1), 289–297.

    Google Scholar 

  • Wu, X. P., and Xu, G. M., 1999, Derivation and analysis of partial derivative matrix in resistivity 3-D inversion: Oil Geophysical Prospecting, 34(4), 363–372.

    Google Scholar 

  • Xu, S. Z., 1994, The Finite-Element Method in Geophysics: Beijing, Science Press, 261–285.

    Google Scholar 

  • Xu, K., and Wang, M. Y., 2001, Finite Element Inversion of the Coefficients of Acoustic Equation in Frequency Domain: Chinese J. Geophys. (in Chinese), 44(6), 852–864.

    Google Scholar 

  • Yang, Q. Y., Hu, G. H., and Wang, L. X., 2014, Research status and development trend of full waveform inversion: Geophysical prospecting for petroleum, 53(1), 77–83.

    Google Scholar 

  • Yuan, S. Y., Wang, S. X., Sun, W. J., Miao, L. N., and Li, Z. H., 2014, Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation: Exploration Geophysics, 45(2), 94–104.

    Article  Google Scholar 

  • Zhao, J. G., Shi, R. Q., Chen, J. Y., Pan, J. G., and Wang, H. B., 2014, An matched Z-transform perfectly matched layer absorbing boundary in the numerical modeling of viscoacoustic wave equations: Chinese J. Geophys. (in Chinese), 57(4), 1284–1291.

    Google Scholar 

  • Zhao, J. G., and Shi, R. Q., 2013, Perfectly matched layerabsorbing boundary condition for finite-element timedomain modeling of elastic wave equations: Applied Geophysics, 10(3), 323–336.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Info-physics and Geomatics Engineering, Central South University, Changsha, 410083, China

    Qian-Jiang Zhang, Long-Wei Chen, Kun Li & Dong-Dong Zhao

  2. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, 102249, China

    Shi-Kun Dai & Xing-Xing Huang

Authors
  1. Qian-Jiang Zhang
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  2. Shi-Kun Dai
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  3. Long-Wei Chen
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  4. Kun Li
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  5. Dong-Dong Zhao
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  6. Xing-Xing Huang
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Corresponding author

Correspondence to Shi-Kun Dai.

Additional information

Zhang Qian-Jiang received his M.S. (2011) in Earth Exploration and Information Technology from China University of Petroleum (Beijing). He is presently a Ph.D. candidate in Geological Resources and Geological Engineering at Central South University. His main interests are forward modeling and inversion of seismic and electromagnetic data.

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Zhang, QJ., Dai, SK., Chen, LW. et al. Two-dimensional frequency-domain acoustic full-waveform inversion with rugged topography. Appl. Geophys. 12, 378–388 (2015). https://doi.org/10.1007/s11770-015-0510-4

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  • DOI: https://doi.org/10.1007/s11770-015-0510-4

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