next up previous [pdf]

Next: About this document ... Up: Chen et al.: Deblending Previous: Acknowledgments

Bibliography

Abma, R., Q. Zhang, A. Arogunmati, and G. Beaudoin, 2012, An overview of BP's marine independent simultaneous source field trials: 82nd Annual International Meeting, SEG, Expanded Abstracts, 1404.1.

Abma, R. L., T. Manning, M. Tanis, J. Yu, and M. Foster, 2010, High quality separation of simultaneous sources by sparse inversion: 72nd Annual International Conference and Exhibition, EAGE, Extended Abstracts.

Beasley, C. J., B. Dragoset, and A. Salama, 2012, A 3d simultaneous source field test processed using alternating projections: a new active separation method: Geophysical Prospecting, 60, 591-601.

Berkhout, A. J., 2008, Changing the mindset in seismic data acquisition: The Leading Edge, 27, 924-938.

Berkhout, A. J., D. J. Verschuur, and G. Blacquière, 2012, illumination properties and imaging promises of blended, multiple-scattering seismic data: a tutorial: Geophysical Prospecting, 60, 713-732.

Canales, L., 1984, Random noise reduction: SEG expanded abstracts: 54th Annual international meeting, 525-527.

Candès, E. J., and Y. Plan, 2010, A probabilistic and ripless theory of compressed sensing: IEEE Transactions on Information Theory, 57, 7235-7254.

Chen, Y., and J. Ma, 2014, Random noise attenuation by f-x empirical mode decomposition predictive filtering: Geophysics, 79, V81-V91.

Choi, Y., and T. Alkhalifah, 2012, Application of multi-source waveform inversion to marine streamer data using the global correlation norm: Geophysical Prospecting, 60, 748-758.

Cohen, A., I. Daubechies, and J. C. Feauveau, 1992, Biorthogonal bases of compactly supported wavelets: Communications on Pure and Applied Mathematics, 45, 485-560.

Daubechies, I., M. Defrise, and C. D. Mol, 2004, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint: Communications on Pure and Applied Mathematics, 57, 1413-1457.

Daubechies, I., M. Fornasier, and I. Loris, 2008, Accelerated projected gradient method for linear inverse problems with sparsity constraints: Journal of Fourier Analysis and Applications, 14, 764-792.

Donoho, D. L., 1995, De-noising by soft-thresholding: IEEE transactions on information theory, 41, 613-627.

Donoho, D. L., and I. M. Johnstone, 1994, Ideal spatial adaptation by wavelet shrinkage: Biometrika, 81, 425-455.

Doulgeris, P., and K. Bube, 2012, Analysis of a coherency-constrained inversion for the separation of blended data: discovering the leakage subspace: 74th Annual International Conference and Exhibition, EAGE, Extended Abstracts.

Doulgeris, P., K. Bube, G. Hampson, and G. Blacquiere, 2012, Covergence analysis of a coherency-constrained inversion for the separation of blended data: Geophysical Prospecting, 60, 769-781.

Fomel, S., 2002, Application of plane-wave destruction filters: Geophysics, 67, 1946-1960.

----, 2006, Towards the seislet transform: 76th Annual International Meeting, SEG, Expanded Abstracts, 2847-2850.

----, 2007, Shaping regularization in geophysical-estimation problems: Geophysics, 72, R29-R36.

----, 2008, Nonlinear shapping regularization in geophysical inverse problems: 78th Annual International Meeting, SEG, Expanded Abstracts, 2046-2051.

Fomel, S., and Y. Liu, 2010, Seislet transform and seislet frame: Geophysics, 75, V25-V38.

Galbraith, M., and Z. Yao, 2012, Fx plus deconvolution for seismic data noise reduction: 82nd Annual International Meeting, SEG, Expanded Abstracts, 1-4.

Gao, J., X. Chen, G. Liu, and J. Ma, 2010, Irregular seismic data reconstruction based on exponentional threshold model of pocs method: Applied Geophysics, 7, 229-238.

Guitton, A., and E. Diaz, 2012, Attenuating crosstalk noise with simultaneous source full waveform inversion: Geophysical Prospecting, 60, 759-768.

Hampson, G., J. Stefani, and F. Herkenhoff, 2008, Acquisition using simultaneous sources: The Leading Edge, 27, 918-923.

Hennenfent, G., and F. Herrmann, 2006, Seismic denoising with nonunformly sampled curvelets: Computing in Science & Engineering, 8, 16-25.

Huo, S., Y. Luo, and P. G. Kelamis, 2012, Simultaneous sources separation via multidirectional vector-median filtering: Geophysics, 77, V123-V131.

Liu, Y., 2013, Noise reduction by vector median filtering: Geophysics, 78, V79-V87.

Liu, Y., and S. Fomel, 2012, Seismic data analysis using local time-frequency decomposition: Geophyscial Prospecting, 60, 1-10.

Liu, Y., S. Fomel, C. Liu, D. Wang, G. Liu, and X. Feng, 2009a, High-order seislet transform and its application of random noise attenuation: Chinese Journal of Geophysics, 52, 2142-2151.

Liu, Y., C. Liu, and D. Wang, 2009b, A 1d time-varying median filter for seismic random, spike-like noise elimination: Geophysics, 74, V17-V24.

Mahdad, A., 2012, Deblending of seismic data: TU Delft, PhD thesis.

Mahdad, A., P. Doulgeris, and G. Blacquiere, 2011, Separation of blended data by iterative estimation and subtraction of blending interference noise: Geophysics, 76, Q9-Q17.

----, 2012, Iterative method for the separation of blended seismic data: discussion on the algorithmic aspects: Geophysical Prospecting, 60, 782-801.

Mallat, S. G., 2009, A wavelet tour of signal processing: The sparse way: Academic Press.

Mitchell, S., C. Ray, E. Marc, D. Hays, and K. Craft, 2010, Fairfieldnodal's excellent nodal adventure: 80th Annual International Meeting, SEG, Expanded Abstracts, 3740-3745.

Moore, I., B. Dragoset, T. Ommundsen, D. Wilson, C. Ward, and D. Eke, 2008, Simultaneous source separation using dithered sources: 78th Annual International Meeting, SEG, Expanded Abstracts, 2806-2809.

Naghizadeh, M., and M. D. Sacchi, 2010, Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data: Geophysics, 75, WB189-WB202.

Plessix, R.-E., G. Baeten, J. W. de Maag, F. ten Kroode, and Z. Rujie, 2012, Full waveform inversion and distance separated simultaneous sweeping: a study with a land seismic data set: Geophysical Prospecting, 60, 733-747.

Sacchi, M. D., and H. Kuehl, 2000, Fx arma filters: 70th Annual International Meeting, SEG, Expanded Abstracts, 2092-2095.

Sweldens, W., 1995, Lifting scheme: A new philosophy in biorthogonal wavelet constructions: Wavelet applications in signal and image processing iii: Proceedings of SPIE 2569, 68-79.

van Borselen, R., R. Baardman, T. Martin, B. Goswami, and E. Fromyr, 2012, An inversion approach to separating sources in marine simultaneous shooting acquision-application to a gulf of mexico data set: Geophysical Prospecting, 60, 640-647.

Wang, D., C. Liu, Y. Liu, and G. Liu, 2008, Application of wavelet transform based on lifting scheme and percentiles soft-threshold to elimination of seismic random noise: Progress in Geophysics (in Chinese), 23, 1124-1130.

Wapenaar, K., J. van der Neut, and J. Thorbecke, 2012, Deblending by direct inversion: Geophysics, 77, A9-A12.

Xue, Z., Y. Chen, S. Fomel, and J. Sun, 2014, Imaging incomplete data and simultaneous-source data using least-squares reverse-time migration with shaping regularization: 84th Annual International Meeting, SEG, Expanded Abstracts, submitted.

Yang, P., J. Gao, and W. Chen, 2012, Improved pocs interpolation using a percentage thresholding strategy and excessively zero-padded fft: 82nd Annual International Meeting, SEG, Expanded Abstracts, 1-6.

----, 2013, On analysis-based two-step interpolation methods for randomly sampled seismic data: Computers & Geosciences, 51, 449-461.

Appendix A

Review of seislet transform

Fomel (2006) and Fomel and Liu (2010) proposed a digital wavelet-like transform, which is defined with the help of the wavelet-lifting scheme (Sweldens, 1995) combined with local plane-wave destruction. The wavelet-lifting utilizes predictability of even traces from odd traces of 2-D seismic data and finds a difference $ \mathbf{r}$ between them, which can be expressed as:

$\displaystyle \mathbf{r}=\mathbf{o}-\mathbf{P\left[e\right]},$ (19)

where $ \mathbf{P}$ is the prediction operator. A coarse approximation $ \mathbf{c}$ of the data can be achieved by updating the even component:

$\displaystyle \mathbf{c}=\mathbf{e}+\mathbf{U\left[r\right]},$ (20)

where $ \mathbf{U}$ is the updating operator.

The digital wavelet transform can be inverted by reversing the lifting-scheme operations as follows:

$\displaystyle \mathbf{e}=\mathbf{c}-\mathbf{U\left[r\right]},$ (21)

$\displaystyle \mathbf{o}=\mathbf{r}+\mathbf{P\left[e\right]}.$ (22)

The foward transform starts with the finest scale (the original sampling) and goes to the coarsest scale. The inverse transfrom starts with the coarsest scale and goes back to the finest scale. At the start of forward transform, $ \mathbf{e}$ and $ \mathbf{o}$ corresponds to the even and odd traces of the data domain. At the start of the inverse transform, $ \mathbf{c}$ and $ \mathbf{r}$ will have just one trace of the coarsest scale of the seislet domain.

The above prediction and update operators can be defined, for example, as follows:

$\displaystyle \mathbf{P}\left[\mathbf{e}\right]_k=\left(\mathbf{P}^{(+)}_k\left[\mathbf{e}_{k-1}\right]+\mathbf{P}^{(-)}_k\left[\mathbf{e}_k\right]\right)/2,$ (23)

and

$\displaystyle \mathbf{U}\left[\mathbf{r}\right]_k=\left(\mathbf{P}^{(+)}_k\left[\mathbf{r}_{k-1}\right]+\mathbf{P}^{(-)}_k\left[\mathbf{r}_k\right]\right)/4,$ (24)

where $ \mathbf{P}^{(+)}_k$ and $ \mathbf{P}^{(-)}_k$ are operators that predict a trace from its left and right neighbors, correspondingly, by shifting seismic events according to their local slopes. This scheme is analogous to CDF biorthogonal wavelets (Cohen et al., 1992). The predictions need to operate at different scales, which means different separation distances between traces. Taken through different scales, equations A-1-A-6 provide a simple definition for the 2D seislet transform. More accurate versions are based on other schemes for the digital wavelet transform (Liu et al., 2009a).


next up previous [pdf]

Next: About this document ... Up: Chen et al.: Deblending Previous: Acknowledgments

2014-08-20