Frequency-Domain Multi-Scale Early-Arrival Waveform Tomography with a Time-Domain Wavefield Modeling Engine
Tóm tắt
Early-arrival waveform tomography (EWT) is one of the most promising techniques for building near-surface velocity model. Based on finite-frequency wave equation, EWT estimates velocities by matching calculated early-arrival waveforms with the observed ones. However, the objective function of EWT can easily converge to local minimum because of the cycle-skipping phenomenon. In order to reduce the cycle-skipping problem, a hybrid-domain early-arrival waveform tomography (HEWT) is proposed in this paper. The forward modeling of HEWT is realized in the time domain where early-arrival waveforms are easier to be selected from seismic data and less memory is needed than they are in the frequency domain. The inversion is implemented in the frequency domain where multi-scale strategy is more convenient to be realized than that in the time domain. Discrete Fourier transformation (DFT) is used to transform the time-domain wavefield to the frequency-domain wavefield. Test results show that HEWT is more competitive than EWT in both accuracy and computational time.
Tài liệu tham khảo
Adamczyk, A., Malinowski, M., Górszczyk, A., 2015. Full-Waveform Inversion of Conventional Vibroseis Data Recorded along a Regional Profile from Southeast Poland. Geophysical Journal International, 203(1): 351–365. https://doi.org/10.1093/gji/ggv305
Alford, R. M., Kelly, K. R., Boore, D. M., 1974. Accuracy of Finite— Difference Modeling of the Acoustic Wave Equation. Geophysics, 39(6): 834–842. https://doi.org/10.1190/1.1440470
Berenger, J. P., 1994. A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. Journal of Computational Physics, 114(2): 185–200. https://doi.org/10.1006/jcph.1994.1159
Bian, A. F., Zou, Z. H., Zhou, H. W., et al., 2015. Evaluation of Multi-Scale Full Waveform Inversion with Marine Vertical Cable Data. Journal of Earth Science, 26(4): 481–486. https://doi.org/10.1007/s12583-015-0566-3
Boonyasiriwat, C., Valasek, P., Routh, P., et al., 2009. An Efficient Multiscale Method for Time-Domain Waveform Tomography. Geophysics, 74(6): WCC59–WCC68. https://doi.org/10.1190/1.3151869
Bunks, C., Saleck, F. M., Zaleski, S., et al., 1995. Multiscale Seismic Waveform Inversion. Geophysics, 60(5): 1457–1473. https://doi.org/10.1190/1.1443880
Crase, E., Wideman, C., Noble, M., et al., 1992. Nonlinear Elastic Waveform Inversion of Land Seismic Reflection Data. Journal of Geophysical Research, 97(B4): 4685–4703. https://doi.org/10.1029/90jb00832
Dai, Y. H., Yuan, Y., 1999. A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property. SIAM Journal on Optimization, 10(1): 177–182. https://doi.org/10.1137/s1052623497318992
Fletcher, R., Reeves, C. M., 1964. Function Minimization by Conjugate Gradients. The Computer Journal, 7(2): 149–154. https://doi.org/10.1093/comjnl/7.2.149
Hager, W. W., Zhang, H. C., 2005. A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search. SIAM Journal on Optimization, 16(1): 170–192. https://doi.org/10.1137/030601880
Hager, W. W., Zhang, H. C., 2006. A Survey of Nonlinear Conjugate Gradient Methods. Pacific Journal of Optimization, 2(1): 35–58
Hanafy, S. M., Yu, H., 2013. Early Arrival Waveform Inversion of Shallow Seismic Land Data. SEG Technical Program Expanded Abstracts 2013. Society of Exploration Geophysicists. 1738–1742. https://doi.org/10.1190/segam2013-0351.1
Hestenes, M. R., Stiefel, E., 1952. Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 49(6): 409–436. https://doi.org/10.6028/jres.049.044
Kamei, R., Pratt, R. G., 2012. Wide-Band Multifrequency Waveform Inversion in the Laplace-Fourier Domain. SEG Technical Program Expanded Abstracts 2012. Society of Exploration Geophysicists. 1–6. https://doi.org/10.1190/segam2012-1588.1
Kim, Y., Cho, H., Min, D. J., et al., 2011. Comparison of Frequency-Selection Strategies for 2D Frequency-Domain Acoustic Waveform Inversion. Pure and Applied Geophysics, 168(10): 1715–1727. https://doi.org/10.1007/s00024-010-0196-8
Komatitsch, D., Tromp, J., 2003. A Perfectly Matched Layer Absorbing Boundary Condition for the Second-Order Seismic Wave Equation. Geophysical Journal International, 154(1): 146–153. https://doi.org/10.1046/j.1365-246x.2003.01950.x
Levander, A. R., 1988. Fourth-Order Finite-Difference P-SV Seismograms. Geophysics, 53(11): 1425–1436. https://doi.org/10.1190/1.1442422
Liu, L., Ding, R. W., Liu, H. W., et al., 2015. 3D Hybrid-Domain Full Waveform Inversion on GPU. Computers & Geosciences, 83: 27–36. https://doi.org/10.13039/501100001809
Liu, Y., Li, C. C., Mou, Y. G., 1998. Finite-Difference Numerical Modeling of any even Order Accuracy. Oil Geophysical Prospecting, 33(1): 1–10 (in Chinese with English Abstract)
Liu, Y., Sen, M. K., 2009. A New Time-Space Domain High-Order Finite-Difference Method for the Acoustic Wave Equation. Journal of Computational Physics, 228(23): 8779–8806. https://doi.org/10.1016/j.jcp.2009.08.027
Luo, Y., Schuster, G. T., 1991. Wave-Equation Traveltime Inversion. Geophysics, 56(5): 645–653. https://doi.org/10.1190/1.1443081
Malinowski, M., Operto, S., Ribodetti, A., 2011. High-Resolution Seismic At tenuation Imaging from Wide-Aperture Onshore Data by Visco-Acoustic Frequency-Domain Full-Waveform Inversion. Geophysical Journal International, 186(3): 1179–1204. https://doi.org/10.1111/j.1365-246x.2011.05098.x
Mora, P., 1987. Nonlinear Two-Dimensional Elastic Inversion of Multioffset Seismic Data. Geophysics, 52(9): 1211–1228. https://doi.org/10.1190/1.1442384
Plessix, R. E., 2006. A Review of the Adjoint-State Method for Computing the Gradient of a Functional with Geophysical Applications. Geophysical Journal International, 167(2): 495–503. https://doi.org/10.1111/j.1365-246x.2006.02978.x
Polak, E., Ribiere, G., 1969. Note Sur La Convergence de Méthodes de Directions Conjuguées. Revue Française d’Informatique et de Recherche opéRationnelle Série Rouge, 3(16): 35–43. https://doi.org/10.1051/m2an/196903r100351
Powell, M. J. D., 1975. Convergence Properties of a Class of Minimization Algorithms. Nonlinear Programming, 2: 1–27. https://doi.org/10.1016/b978-0-12-468650-2.50005-5
Pratt, R. G., 1999. Seismic Waveform Inversion in the Frequency Domain, Part 1: Theory and Verification in a Physical Scale Model. Geophysics, 64(3): 888–901. https://doi.org/10.1190/1.1444597
Qi, Q., Geers, T. L., 1998. Evaluation of the Perfectly Matched Layer for Computational Acoustics. Journal of Computational Physics, 139(1): 166–183. https://doi.org/10.1006/jcph.1997.5868
Ravaut, C., Operto, S., Improta, L., et al., 2004. Multiscale Imaging of Complex Structures from Multifold Wide-Aperture Seismic Data by Frequency-Domain Full-Waveform Tomography: Application to a Thrust Belt. Geophysical Journal International, 159(3): 1032–1056. https://doi.org/10.1111/j.1365-246x.2004.02442.x
Shen, X., 2010. Near-Surface Velocity Estimation by Weighted Early-Arrival Waveform Inversion. SEG Technical Program Expanded Abstracts 2010. Society of Exploration Geophysicists. 1975–1979. https://doi.org/10.1190/1.3513230
Sheng, J., Leeds, A., Buddensiek, M., et al., 2006. Early Arrival Waveform Tomography on Near-Surface Refraction Data. Geophysics, 71(4): U47–U57. https://doi.org/10.1190/1.2210969
Shi, T. K., Zhang, J. Z., Huang, Z. L., et al., 2015. A Layer-Stripping Method for 3D Near-Surface Velocity Model Building Using Seismic First-Arrival Times. Journal of Earth Science, 26(4): 502–507. https://doi.org/10.1007/s12583-015-0569-0
Sirgue, L., Pratt, R. G., 2004. Efficient Waveform Inversion and Imaging: A Strategy for Selecting Temporal Frequencies. Geophysics, 69(1): 231–248. https://doi.org/10.1190/1.1649391
Sirgue, L., Etgen, J. T., 2008. Albertin U. 3D Frequency Domain Waveform Inversion Using Time Domain Finite Difference Methods. 70th EAGE Conference and Exhibition Incorporating SPE EUROPEC 2008. https://doi.org/10.3997/2214-4609.20147683
Song, Z. M., Williamson, P. R., 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. https://doi.org/10.1190/1.1443818
Tarantola, A., 1987. Inverse Problem Theory: Methods for Data Fitting and Parameter Estimation. Society for Industrial & Applied Mathematics, Philadelphia. 342
Virieux, J., Operto, S., 2009. An Overview of Full-Waveform Inversion in Exploration Geophysics. Geophysics, 74(6): WCC1–WCC26. https://doi.org/10.1190/1.3238367
Xu, K., McMechan, G. A., 2014. 2D Frequency-Domain Elastic Full-Waveform Inversion Using Time-Domain Modeling and a Multistep-Length Gradient Approach. Geophysics, 79(2): R41–R53. https://doi.org/10.1190/geo2013-0134.1
Yu, H., Hanafy, S. M., 2014. An Application of Multiscale Early Arrival Waveform Inversion to Shallow Seismic Data. Near Surface Geophysics, 12(4): 549–557. https://doi.org/10.3997/1873-0604.2014002
Zhang, J. Z., Huang, Y. Q., Song, L. P., et al., 2011. Fast and Accurate 3-D Ray Tracing Using Bilinear Traveltime Interpolation and the Wave Front Group Marching. Geophysical Journal International, 184(3): 1327–1340. https://doi.org/10.1111/j.1365-246x.2010.04909.x
Zhang, J. Z., Shi, T. K., Zhao, Y. S., et al., 2014. Static Corrections in Mountainous Areas Using Fresnel-Wavepath Tomography. Journal of Applied Geophysics, 111: 242–249. https://doi.org/10.13039/501100001809
Zhang, J. Z., Liu, H., Zou, Z. H., et al., 2015. Velocity Modeling and Inversion Techniques for Locating Microseismic Events in Unconventional Reservoirs. Journal of Earth Science, 26(4): 495–501. https://doi.org/10.1007/s12583-015-0565-4
Zhou, C. X., Cai, W. Y., Luo, Y., et al., 1995. Acoustic Wave-Equation Traveltime and Waveform Inversion of Crosshole Seismic Data. Geophysics, 60(3): 765–773. https://doi.org/10.1190/1.1443815