Frequency-wavenumber implementation for P- and S-wave separation from multi-component seismic data
Zhiyuan Li 1 4 Xiaona Ma 1 2 Chao Fu 3 Bingluo Gu 1 2 Guanghe Liang 11 Institute of Geology and Geophysics, Chinese Academy of Sciences, No. 19, Beitucheng Western Road, Chaoyang District, Beijing 100029, China.
2 College of Earth Sciences, University of Chinese Academy of Sciences, No. 19A, Yuquan Road, Beijing 100049, China.
3 Shenhua Geological Exploration Co. Ltd, No. 22, West Riverside Road, Dongcheng District, Beijing 100011, China.
4 Corresponding author. Email: lizhiyuan@mail.iggcas.ac.cn
Exploration Geophysics 47(1) 32-43 https://doi.org/10.1071/EG14047
Submitted: 5 May 2014 Accepted: 4 February 2015 Published: 13 March 2015
Abstract
In this paper, we present a frequency-wavenumber domain scheme to separate P- and S-waves from multi-component seismic data at the free surface. Based on the relationship between the P- and S-wave separated elastic equation, and the divergence and curl operators, we modify the equation to make it applicable to surface seismic data. In the modified equation, the P-wavenumber is chosen to reject the P-waves, and the S-wavenumber is chosen to eliminate the S-waves. The changes in the P-S amplitude ratio caused by the wavenumber choice are corrected. For the free surface condition, an up-going wavefield separation filter is introduced into the modified equation, which can remove the free surface effects from the surface seismic data. In the case of a free surface exhibiting lateral heterogeneity, the seismic data are first transformed into the frequency domain using the fast Fourier transform (FFT), and then are transformed into the wavenumber domain using the discrete Fourier transform (DFT). In the second transform using the DFT, the modified equation is used to separate the P- and S-waves. Numerical tests on synthetic data for three models demonstrate the good performance and accuracy of the scheme.
Key words: divergence and curl, frequency-wavenumber domain, multi-component seismic data, P- and S-wave separation.
References
Aki, K., and Richards, P. G., 2002, Quantitative seismology: University Science Books.Al-anboori, A., van der Baan, M., and Kendall, J. M., 2005, Approximate separation of pure-mode and converted waves in 3-C reflection seismics by τ-p transform: Geophysics, 70, V81–V86
| Approximate separation of pure-mode and converted waves in 3-C reflection seismics by τ-p transform:Crossref | GoogleScholarGoogle Scholar |
Dankbaar, J. W. M., 1985, Separation of P-and S-waves: Geophysical Prospecting, 33, 970–986
| Separation of P-and S-waves:Crossref | GoogleScholarGoogle Scholar |
Dellinger, J., and Etgen, J., 1990, Wave-field separation in two-dimensional anisotropic media: Geophysics, 55, 914–919
| Wave-field separation in two-dimensional anisotropic media:Crossref | GoogleScholarGoogle Scholar |
Greenhalgh, S. A., Mason, I. M., Lucas, E., Pant, D., and Eames, R. T., 1990, Controlled direction reception filtering of P-and S-waves in τ-p space: Geophysical Journal International, 100, 221–234
| Controlled direction reception filtering of P-and S-waves in τ-p space:Crossref | GoogleScholarGoogle Scholar |
Guevara, S. E., and Cary, P. W., 1999, Wavefield separation in the presence of statics: application to synthetic and real data: CREWES Research Report, Vol. 11, 1–20.
Huang, Y. J., and Zhu, G. M., 2009, Elastic reverse-time migration of VSP transmitted PS waves, in Z. Liu, and Y. Sun, eds., Proceedings of the Beijing 2009 International Geophysical Conference and Exposition: SEG, 233.
Ilan, A., and Loewenthal, D., 1976, Instability of finite difference schemes due to boundary conditions in elastic media: Geophysical Prospecting, 24, 431–453
| Instability of finite difference schemes due to boundary conditions in elastic media:Crossref | GoogleScholarGoogle Scholar |
Li, X. Y., and Crampin, S., 1993, Linear-transform techniques for processing shear-wave anisotropy in four-component seismic data: Geophysics, 58, 240–256
| Linear-transform techniques for processing shear-wave anisotropy in four-component seismic data:Crossref | GoogleScholarGoogle Scholar |
Li, Z. Y., Liang, G. H., and Gu, B. L., 2013, Improved method of separating P- and S-waves using divergence and curl: Chinese Journal of Geophysics, 56, 2012–2022
| Improved method of separating P- and S-waves using divergence and curl:Crossref | GoogleScholarGoogle Scholar |
Lu, J., Wang, Y., and Yao, C., 2012, Separating P- and S-waves in an affine coordinate system: Journal of Geophysics and Engineering, 9, 12–18
| Separating P- and S-waves in an affine coordinate system:Crossref | GoogleScholarGoogle Scholar |
Ma, D. T., and Zhu, G. M., 2003, P- and S-wave separated elastic wave equation numerical modeling: Oil and Geophysical Prospecting, 38, 482–486
Paffenholz, J., McLain, B., Zaske, J., and Keliher, P. J., 2002, Subsalt multiple attenuation and imaging: observations from the Sigsbee2B synthetic dataset: 72nd Annual International Meeting, SEG, Expanded Abstracts, 2122–2125.
Robertsson, J. O., and Curtis, A., 2002, Wavefield separation using densely deployed three-component single-sensor groups in land surface-seismic recordings: Geophysics, 67, 1624–1633
| Wavefield separation using densely deployed three-component single-sensor groups in land surface-seismic recordings:Crossref | GoogleScholarGoogle Scholar |
Sun, R., Chow, J., and Chen, K. J., 2001, Phase correction in separating P- and S-waves in elastic data: Geophysics, 66, 1515–1518
| Phase correction in separating P- and S-waves in elastic data:Crossref | GoogleScholarGoogle Scholar |
Sun, R., McMechan, G. A., and Chuang, H. H., 2011, Amplitude balancing in separating P-and S-waves in 2D and 3D elastic seismic data: Geophysics, 76, S103–S113
| Amplitude balancing in separating P-and S-waves in 2D and 3D elastic seismic data:Crossref | GoogleScholarGoogle Scholar |
van der Baan, M., 2006, PP/PS wavefield separation by independent component analysis: Geophysical Journal International, 166, 339–348
| PP/PS wavefield separation by independent component analysis:Crossref | GoogleScholarGoogle Scholar |
Wang, Y., and Singh, S. C., 2003, Separation of P- and S-wavefields from wide-angle multicomponent OBC data for a basalt model: Geophysical Prospecting, 51, 233–245
| Separation of P- and S-wavefields from wide-angle multicomponent OBC data for a basalt model:Crossref | GoogleScholarGoogle Scholar |
Wang, Y., Singh, S. C., and Barton, P. J., 2002, Separation of P- and SV-wavefields from multi-component seismic data in the τ-p domain: Geophysical Journal International, 151, 663–672
| Separation of P- and SV-wavefields from multi-component seismic data in the τ-p domain:Crossref | GoogleScholarGoogle Scholar |
Yao, D. Z., Zhou, X. X., and Zhong, B. S., 1993, Method for separating out P-wave or S-wave in VSP data, and its application: Oil and Geophysical Prospecting, 28, 623–628