Attenuation of spatial aliasing in CMP domain by non-linear interpolation of seismic data along local slopes

Authors

1 Post-Doc, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran

2 Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran

3 Professor, Department of Exploration Geophysics, Curtin University of Technology, Perth, Western Australia

Abstract

Spatial aliasing is an unwanted side effect that produces artifacts during seismic data processing, imaging and interpolation. It is often caused by insufficient spatial sampling of seismic data and often happens in CMP (Common Mid-Point) gather. To tackle this artifact, several techniques have been developed in time-space domain as well as frequency domain such as frequency-wavenumber, frequency-space, and frequency-time. The main advantages of seismic interpolation in time-space domain over frequency domain are: a) frequency components of the initial signals are preserved, and b) the prior knowledge that a seismic event consists of many plane wave segments, can be used. Using the later advantage, a seismic event can be predicted by pursuing the continuity of seismic events in a trace-by-trace manner. This process, which has become popular in seismic data reconstruction and imaging within the past few years, is known as predictive painting. We use predictive painting to predict the wavefronts and two-way-travel time curves in regularly sampled CMP gathers followed by increasing the number of traces by cubic interpolation. Then, the amplitude of the interpolated trace is obtained by averaging the amplitudes of the neighbouring traces. Performance of the proposed method is demonstrated on several synthetic seismic data examples as well as a field data set.

Keywords

Main Subjects


Bóna, A., 2011, Shot-gather time migration of planar reflectors without velocity model. Geophysics, 76(2), S93–S101, doi: 10.1190/1.3549641.
Burnett, W. and Fomel, S., 2009, 3D velocity-independent elliptically anisotropic move out correction. Geophysics, 74(5), WB129–WB136, doi: 10.1190/1.3184804.
Casasanta, L. and Fomel, S., 2011, Velocity-independent τ-p move out in a horizontally layered VTI medium. Geophysics, 76(4), U45-U57, doi: 10.1190/1.3595776.
Chen, Y., Fomel, S. and Hu, J., 2014, Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization. Geophysics, 79, V183-V193, doi: 10.1190/GEO2013-0449.1.
Chen, Y., Zhang, L. and Mo, L., 2015, Seismic data interpolation using nonlinear shaping regularization. Journal of Seismic Exploration, 24(5), 327-342, http://www.geophysical-press.com/contents_jse_vol_24_4.htm.
Claerbout, J. F., 1985, Imaging the Earth’s Interior. Blackwell Scientific Publications, Inc., http://sepwww.stanford.edu/sep/prof/iei2.
Claerbout, J. F., 1992, Earth Soundings Analysis: Processing Versus Inversion. Blackwell Scientific Publications, http://sepwww.stanford.edu/sep/prof/pvi.pdf.
Crawley, S., 2000, Seismic trace interpolation with nonstationary prediction error filters: Ph.D. thesis, Stanford University.
Fomel, S., 2002, Applications of plane-wave destruction filters. Geophysics, 67, 1946–1960, doi: 10.1190/1.1527095.
Fomel, S., 2003, Seismic reflection data interpolation with differential offset and shot continuation. Geophysics, 68, 733–744, doi: 10.1190/1.1567243.
Fomel, S., 2007, Velocity-independent time-domain seismic imaging using local event slopes: Geophysics, 72(3), S139–S147, doi: 10.1190/1.2714047.
Fomel, S., 2010, Predictive painting of 3D seismic volumes. Geophysics, 75(4), A25–A30, doi: 10.1190/1.3453847.
Fomel, S., Sava, P., Vlad, I., Liu, Y. and Bashkardin, V., 2013, Madagascar: open-source software project for multidimensional data analysis and reproducible computational experiments. Journal of Open Research Software, 1(1), p. e8, doi:  oftware.metajnl.com/articles/10.5334/jors.ag/
Gan, S., Wang, S., Chen, Y., Jin, Z. and Zhang, Y., 2015, Dealiased Seismic Data Interpolation Using Seislet Transform With Low-Frequency Constraint, IEEE Geoscience and Remote Sensing Letters, 12, 2150-2154, doi: 10.1109/LGRS.2015.2453119.
Gan, S., Chen, Y., Wang, S., Chen, X., Huang, W. and Chen, H., 2016, Compressive sensing for seismic data reconstruction using a fast projection onto convex sets algorithm based on the seislet transform. Journal of Applied Geophysics, 130, 194-208, doi: 10.1016/j.jappgeo.2016.03.033.
Gülünay, N., 2003, Seismic trace interpolation in the Fourier transform domain. Geophysics, 68, 355–369, doi: 10.1190/1.1543221.
Herrmann, F. J. and Hennenfent, G., 2008, Non-parametric seismic data recovery with curvelet frames: Geophysical Journal International, 173(1), 233–248, doi: 10.1111/j.1365-246X.2007.03698.x.
Ibrahim, A., Terenghi, P. and Sacchi, M. D. , 2015, Wavefield Reconstruction using a Stolt-Based Asymptote and Apex Shifted Hyperbolic Radon Transform: 55th Annual International Meeting, SEG, Expanded Abstracts, 3836-3841, doi: 10.1190/segam2015-5873567.1.
Karimi, P., 2015, Structure-constrained relative acoustic impedance using stratigraphic coordinates. Geophysics, 80(3), A63–A67, doi: 10.1190/GEO2014-0439.1.
Karimi, P., Fomel, S., Wood, L. and Dunlap, D., 2015, Predictive coherence: Interpretation, 3(4), SAE1–SAE7, doi: 10.1190/INT-2015-0030.1.
Khoshanavaz, M. J., Bóna, A., Urosevic, M., Dzunic, A. and Ung, K., 2016a, Oriented prestack time migration using local slopes and predictive painting in common-source domain for planar reflectors. Geophysics, 81(6), S409–S418, doi: 10.1190/GEO2016-0127.1.
Khoshanavaz, M. J., A. Bóna, and Urosevic, M., 2016b, Velocity-independent estimation of kinematic attributes in vertical transverse isotropy media using local slopes and predictive painting. Geophysics, 81(5), U73-U85, doi: 10.1190/GEO2015-0638.1.
Khoshnavaz, M. J., 2017, Oriented time-domain dip move out correction for planar reflectors in common-source domain. Geophysics, 82(6), U87-U97, doi: 10.1190/geo2016-0577.1
Leggott, R. J., Wombell, R., Conroy, G., Noss, T. and Williams, G., 2007, An efficient least-squares migration: 69th Conference and Exhibition, EAGE, Expanded Abstracts, P178, doi: 10.3997/2214-4609.201401856.
Liu, Y. and Fomel, S., 2010, OC-seislet: Seislet transform construction with differential offset continuation. Geophysics, 75(6), WB235–WB245, doi: 10.1190/1.3479554.
Liu, Y. and Fomel, S., 2011, Seismic data interpolation beyond aliasing using regularized nonstationary auto regression. Geophysics, 76(5), V69–V77, doi: 0.1190/GEO2010-0231.1.
Lu, L., 1985, Application of local slant-stack to trace interpolation: 55th Annual International Meeting, SEG, Expanded Abstracts, 560–562, doi: 10.1190/1.1892818.
Naghizadeh, M. and Sacchi, M. D. , 2007, Multistep autoregressive reconstruction of seismic records. Geophysics, 72(6), V111–V118, doi: 10.1190/1.2771685.
Naghizadeh, M. and Sacchi, M. D., 2010, Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data. Geophysics, 75(6), WB189–WB202, doi: 10.1190/1.3509468.
Porsani, M., 1999, Seismic trace interpolation using half-step prediction filters. Geophysics, 64, 1461–1467, doi: 10.1190/1.1444650.
Ronen, J., 1987, Wave-equation trace interpolation. Geophysics, 52, 973–984, doi: 10.1190/1.1442366.
Sacchi, M. D., Verschuur, D. J. and Zwartjes, P. M., 2004, Data reconstruction by generalized deconvolution: SEG, Expanded Abstracts, 23, 1989–1992, doi: 10.1190/1.1843303.
Shannon, C. E., 1948, A Mathematical Theory of Communication: Bell System Technical Journal, 27(3), 379–423, doi:10.1002/j.1538-7305.1948.tb01338.x.
Spitz, S., 1991, Seismic trace interpolation in the F-X domain. Geophysics, 56, 785–794, doi: 10.1190/1.1443096.
Stolt, R. H., 2002, Seismic data mapping and reconstruction. Geophysics, 67, 890–908, doi: 10.1190/1.1484532.
Trad, D., Ulrych, T. J. and Sacchi, M. D., 2002, Accurate interpolation with high-resolution time-variant Radon transforms. Geophysics, 67, 644–656, 10.1190/1.1468626.
Trickett, S. R., 2003, F-xy eigenimage noise suppression. Geophysics, 68, 751–759, doi: 10.1190/1.1567245.
Turner, G., 1990, Aliasing in the τ-p transform and the removal of spatially aliased coherent noise. Geophysics, 55, 1496–1503, doi: 10.1190/1.1442797.
Wang, J., Ng, M. and Perz, M., 2009, Fast high-resolution Radon transforms by greedy least-squares method. SEG, Expanded Abstracts, 28, 3128–3132, doi: 10.1190/1.3255506.
Yilmaz, O., 2001, Seismic data analysis. SEG, doi: 10.1190/1.9781560801580.
Yu, Z., Ferguson, J., McMechan, G. and Anno, P., 2007, Wavelet-Radon domain dealiasing and interpolation of seismic data. Geophysics, 72(2), V41–V49, 10.1190/1.2422797.
Zwartjes, P. M. and Sacchi, M. D. , 2007, Fourier reconstruction of nonuniformly sampled, aliased seismic data. Geophysics, 72(1), V21–V32, doi: 10.1190/1.2399442.