Multi-scale full waveform inversion for areas with irregular surface topography in an auxiliary coordinate system
Yingming Qu 1 3 Zhenchun Li 1 Jianping Huang 1 Jinli Li 21 School of Geosciences, China University of Petroleum, Qingdao 266580, China.
2 Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences, Langfang 065000, China.
3 Corresponding author. Email: qu_geophysics@yahoo.com
Exploration Geophysics 49(1) 68-80 https://doi.org/10.1071/EG16037
Submitted: 12 March 2016 Accepted: 16 October 2016 Published: 24 November 2016
Abstract
For land exploration areas with irregular surface topography, there are many challenges and problems for full waveform inversion (FWI); for example, which type of wave equation should be used to calculate high-accuracy seismic wavefields, how to deal with diffraction of irregular surface topography, what initial velocity model should be utilised to improve the inversion accuracy and how to enhance the computational efficiency of iterative FWI. Aiming at these difficulties, we first simulate the seismic waves with the first-order acoustic wave equation in an auxiliary coordinate system, which easily describes irregular surface topography. Then, we apply this wavefield simulation frame to FWI to improve inversion quality of near-surface regions with strong elevation and velocity variation. Furthermore, to enhance the robustness and computational efficiency, a time-domain multi-scale decomposition method based on the Wiener filter and an optimised encoding strategy are introduced to the proposed inversion frame, and are critical to promoting the practical application of our method. Typical numerical tests prove that the proposed method can obtain more accurate inversion results than the traditional time-domain FWI.
Key words: auxiliary coordinate system, full waveform inversion, irregular surface topography, multi-scale decomposition, optimised encoding technology.
References
Alterman, Z., and Karal, F. C., 1968, Propagation of elastic waves in layered media by finite difference methods: Bulletin of the Seismological Society of America, 58, 367–398Appelö, D., and Petersson, N. A., 2009, A stable finite difference method for the elastic wave equation on complex geometries with free surfaces: Communications in Computational Physics, 5, 84–107
Asnaashari, A., Brossier, R., Garambois, S., Audebert, F., Thore, P., and Virieux, J., 2012, Regularized full waveform inversion including prior model information: 74th EAGE Conference and Exhibition incorporating EUROPEC, Extended Abstracts, 1–5.
Berryhill, J. R., 1979, Wave equation datuming: Geophysics, 44, 1329–1344
| Wave equation datuming:Crossref | GoogleScholarGoogle Scholar |
Berryhill, J. R., 1984, Wave equation datuming before stack: Geophysics, 49, 2064–2066
| Wave equation datuming before stack:Crossref | GoogleScholarGoogle Scholar |
Boonyasiriwat, C., Valasek, P., Routh, P., Cao, W., Schuster, G., and Macy, B., 2009, An efficient multiscale method for time-domain waveform tomography: Geophysics, 74, WCC59–WCC68
| An efficient multiscale method for time-domain waveform tomography:Crossref | GoogleScholarGoogle Scholar |
Bunks, C., Saleck, F., Zaleski, S., and Chavent, G., 1995, Multiscale seismic waveform inversion: Geophysics, 60, 1457–1473
| Multiscale seismic waveform inversion:Crossref | GoogleScholarGoogle Scholar |
Chi, B., and Dong, L., 2013, Full waveform inversion based on envelope objective function: 75th EAGE Conference and Exhibition incorporating SPE EUROPEC, Extended Abstracts, 1–5.
Choi, Y., Devault, B., and Alkhalifah, T., 2015, Application of the unwrapped phase inversion to land field data with irregular topography: 77th EAGE Conference and Exhibition incorporating SPE EUROPEC, Extended Abstracts, 2051–2055.
Collino, F., and Tsogka, C., 2001, Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media: Geophysics, 66, 294–307
| Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media:Crossref | GoogleScholarGoogle Scholar |
Denis, T., Vujasinovic, Y., and Tarantola, A., 1989, Velocity model optimization by image focusing and waveform modeling using prestack depth migration: SEG Technical Program, Expanded Abstracts, 1247–1250.
Falk, J., Tessmer, E., and Gajewski, D., 1998, Efficient finite-difference modelling of seismic waves using locally adjustable time steps: Geophysical Prospecting, 46, 603–616
| Efficient finite-difference modelling of seismic waves using locally adjustable time steps:Crossref | GoogleScholarGoogle Scholar |
Fornberg, B., 1988, The pseudospectral method: accurate representation of interfaces in elastic wave calculations: Geophysics, 53, 625–637
| The pseudospectral method: accurate representation of interfaces in elastic wave calculations:Crossref | GoogleScholarGoogle Scholar |
Guitton, A., Ayeni, G., and Gonzales, G., 2010, A preconditioning scheme for full waveform inversion: SEG Technical Program, Expanded Abstracts, 1008–1012.
Guo, Y. D., Huang, J. P., Li, Z. C., Qu, Y. M., and Hang, Y. T., 2016, Polarity encoding full waveform inversion with prior model based on blend data: 78th EAGE Conference and Exhibition incorporating EUROPEC, Extended Abstracts, 4291–4295.
Hestholm, S. O., and Ruud, B. O., 1994, 2D finite-difference elastic wave modelling including surface topography: Geophysical Prospecting, 42, 371–390
| 2D finite-difference elastic wave modelling including surface topography:Crossref | GoogleScholarGoogle Scholar |
Huang, J. P., Qu, Y. M., Li, Z. C., and Li, Q. Y., 2013, Mapping forward modeling method based on dual-variable grid: 75th EAGE Conference and Exhibition incorporating SPE EUROPEC, Extended Abstracts, 4762–4766.
Jang, U., Min, D. J., Choi, Y., and Shin, C., 2008, Frequency-domain elastic waveform inversion with irregular surface topograph: SEG Technical Program, Expanded Abstracts, 2031–2035.
Jastram, C., and Behle, A., 1992, Acoustic modeling on a vertically varying grid: Geophysical Prospecting, 40, 157–169
| Acoustic modeling on a vertically varying grid:Crossref | GoogleScholarGoogle Scholar |
Jastram, C., and Tessmer, E., 1994, Elastic modeling on a grid with vertically varying spacing: Geophysical Prospecting, 42, 357–370
| Elastic modeling on a grid with vertically varying spacing:Crossref | GoogleScholarGoogle Scholar |
Komatitsch, D., and Tromp, J., 2002, Spectral-element simulations of global seismic wave propagation - I. Validation: Geophysical Journal International, 149, 390–412
| Spectral-element simulations of global seismic wave propagation - I. Validation:Crossref | GoogleScholarGoogle Scholar |
Krebs, J. R., Anderson, J. E., Hinkley, D., Neelamani, R., Lee, S., Baumstein, A., and Lacasse, M. D., 2009, Fast full-wavefield seismic inversion using encoded sources: Geophysics, 74, WCC177–WCC188
| Fast full-wavefield seismic inversion using encoded sources:Crossref | GoogleScholarGoogle Scholar |
Levander, A., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53, 1425–1436
| Fourth-order finite-difference P-SV seismograms:Crossref | GoogleScholarGoogle Scholar |
Liseikin, V., 2010, Grid generation methods: Springer.
Liu, Y., Symes, W. W., and Li, Z., 2013, Multisource least-squares extended reverse-time migration with preconditioning guided gradient method: SEG Technical Program, Expanded Abstracts, 3709–3715.
Luo, Y., and Schuster, G. T., 1990, Wave-equation traveltime + waveform inversion: SEG Technical Program, Expanded Abstracts, 1223–1225.
Moczo, P., Bystricky, E., Kristek, J., Carcione, J., and Bouchon, M., 1997, Hybrid modelling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures: Bulletin of the Seismological Society of America, 87, 1305–1323
Pratt, R., 1990, Frequency-domain elastic modeling by finite differences: a tool for crosshole seismic imaging: Geophysics, 55, 626–632
| Frequency-domain elastic modeling by finite differences: a tool for crosshole seismic imaging:Crossref | GoogleScholarGoogle Scholar |
Pratt, R., 1999, Seismic waveform inversion in the frequency domain, part I: theory and verification in a physic scale model: Geophysics, 64, 888–901
| Seismic waveform inversion in the frequency domain, part I: theory and verification in a physic scale model:Crossref | GoogleScholarGoogle Scholar |
Pratt, R., and Shipp, R., 1999, Seismic waveform inversion in the frequency domain, part 2: fault delineation in sediments using crosshole data: Geophysics, 64, 902–914
| Seismic waveform inversion in the frequency domain, part 2: fault delineation in sediments using crosshole data:Crossref | GoogleScholarGoogle Scholar |
Pratt, R., Shin, C., and Hicks, G. J., 1998, Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion: Geophysical Journal International, 133, 341–362
| Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion:Crossref | GoogleScholarGoogle Scholar |
Qu, Y. M., Li, Z. C., Huang, J. P., Li, Q. Y., and Li, J. L., 2015, Multisource elastic full waveform inversion method for irregular surface: 2015 Workshop: Depth Model Building: Full-waveform Inversion, 32–35.
Shi, Y. M., Zhao, W. Z., and Cao, H., 2007, Nonlinear process control of wave-equation inversion and its application in the detection of gas: Geophysics, 72, R9–R18
| Nonlinear process control of wave-equation inversion and its application in the detection of gas:Crossref | GoogleScholarGoogle Scholar |
Shin, C., and Cha, Y. H., 2008, Waveform inversion in the Laplace domain: Geophysical Journal International, 173, 922–931
| Waveform inversion in the Laplace domain:Crossref | GoogleScholarGoogle Scholar |
Shin, C., and Cha, Y. H., 2009, Waveform inversion in the Laplace–Fourier domain: Geophysical Journal International, 177, 1067–1079
| Waveform inversion in the Laplace–Fourier domain:Crossref | GoogleScholarGoogle Scholar |
Shin, J., Kim, Y., Shin, C., and Calandra, H., 2013, Laplace-domain full waveform inversion using irregular finite elements for complex foothill environments: Journal of Applied Geophysics, 96, 67–76
| Laplace-domain full waveform inversion using irregular finite elements for complex foothill environments:Crossref | GoogleScholarGoogle Scholar |
Sirgue, L., and Pratt, R. G., 2004, Efficient waveform inversion and imaging: a strategy for selecting temporal frequencies: Geophysics, 69, 231–248
| Efficient waveform inversion and imaging: a strategy for selecting temporal frequencies:Crossref | GoogleScholarGoogle Scholar |
Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, 1259–1266
| Inversion of seismic reflection data in the acoustic approximation:Crossref | GoogleScholarGoogle Scholar |
Tarantola, A., 1986, A strategy for nonlinear elastic inversion of seismic reflection data: Geophysics, 51, 1893–1903
| A strategy for nonlinear elastic inversion of seismic reflection data:Crossref | GoogleScholarGoogle Scholar |
Tessmer, E., 2000, Seismic finite-difference modeling with spatially varying time steps: Geophysics, 65, 1290–1293
| Seismic finite-difference modeling with spatially varying time steps:Crossref | GoogleScholarGoogle Scholar |
Tessmer, E., and Kosloff, D., 1994, 3D elastic modelling with surface topography by a Chebychev spectral method: Geophysics, 59, 464–473
| 3D elastic modelling with surface topography by a Chebychev spectral method:Crossref | GoogleScholarGoogle Scholar |
Tessmer, E., Kosloff, D., and Behle, A., 1992, Elastic wave propagation simulation in the presence of surface topography: Geophysical Journal International, 108, 621–632
| Elastic wave propagation simulation in the presence of surface topography:Crossref | GoogleScholarGoogle Scholar |
Thompson, J., Soni, B., and Weatherill, N., 1999, Handbook of grid generation: CRC Press.
Virieux, J., 1984, SH-wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 49, 1933–1942
| SH-wave propagation in heterogeneous media: velocity-stress finite-difference method:Crossref | GoogleScholarGoogle Scholar |
Virieux, J., 1986, P-SV-wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 51, 889–901
| P-SV-wave propagation in heterogeneous media: velocity-stress finite-difference method:Crossref | GoogleScholarGoogle Scholar |
Virieux, J., and Operto, S., 2009, An overview of full-waveform inversion in exploration geophysics: Geophysics, 74, WCC1–WCC26
| An overview of full-waveform inversion in exploration geophysics:Crossref | GoogleScholarGoogle Scholar |
Wang, B. L., and Goo, J. H., 2010, Fast full inversion of multi-shot seismic data: SEG Technical Program, Expanded Abstracts, 1055–1058.
Wang, Y., and Rao, Y., 2009, Reflection seismic waveform tomography: Journal of Geophysical Research, 114, 1–12
| Reflection seismic waveform tomography:Crossref | GoogleScholarGoogle Scholar |
Wiggins, J. W., 1984, Kirchhoff integral extrapolation and migration of nonplanar data: Geophysics, 49, 1239–1248
| Kirchhoff integral extrapolation and migration of nonplanar data:Crossref | GoogleScholarGoogle Scholar |
Yoon, K., Shin, C., and Marfurt, K. J., 2003, Waveform inversion using time-windowed back propagation: SEG Technical Program, Expanded Abstracts, 690–693.
Yoon, K., Suh, S., Cai, J., and Wang, B., 2012, Improvements in time domain FWI and its applications: SEG Technical Program, Expanded Abstracts, 1–5.
Zhang, W., and Chen, X., 2006, Traction image method for irregular free surface boundaries in finite difference seismic wave simulation: Geophysical Journal International, 167, 337–353
| Traction image method for irregular free surface boundaries in finite difference seismic wave simulation:Crossref | GoogleScholarGoogle Scholar |
Zhang, Z. G., Lin, Y., and Huang, L., 2011, Full waveform inversion in the time domain with an energy weighted gradient: SEG Technical Program, Expanded Abstracts, 2772–2776.
Zhang, D. L., Zhan, G., and Dai, W., 2012a, Multisource full waveform inversion with topography using ghost extrapolation: International Geophysical Conference and Oil and Gas Exhibition, 1–4.
Zhang, W., Shen, Y., and Zhao, L., 2012b, Three-dimensional anisotropic seismic wave modelling in spherical coordinates by a collocated-grid finite-difference method: Geophysical Journal International, 188, 1359–1381
| Three-dimensional anisotropic seismic wave modelling in spherical coordinates by a collocated-grid finite-difference method:Crossref | GoogleScholarGoogle Scholar |
Zhang, Z. G., Huang, L., and Lin, Y., 2012c, A wave-energy-based precondition approach to full-waveform inversion in the time domain: SEG Technical Program, Expanded Abstracts, 1–5.