Abstract
Advanced seismic imaging and inversion are dependent on a velocity model that is sufficiently accurate to render reliable and meaningful results. For that reason, methods for extracting such velocity models from seismic data are always in high demand and are topics of active investigation. Velocity models can be obtained from both the time and depth domains. Relying on the former, time migration is an inexpensive, quick and robust process. In spite of its limitations, especially in the case of complex geologies, time migration can, in many instances (e.g. simple to moderate geological structures), produce image results compatible to the those required for the project at hand. An accurate time-velocity model can be of great use in the construction of an initial depth-velocity model, from which a high-quality depth image can be produced. Based on available explicit and analytical expressions that relate the kinematic attributes (namely, traveltimes and local slopes) of local events in the recording (demigration) and migrated domains, we revisit tomographic methodologies for velocity-model building, with a specific focus on the time domain, and on those that makes use of local slopes, as well as traveltimes, as key attributes for imaging. We also adopt the strategy of estimating local inclinations in the time-migrated domain (where we have less noise and better focus) and use demigration to estimate those inclinations in the recording domain. On the theoretical side, the main contributions of this work are twofold: 1) we base the velocity model estimation on kinematic migration/demigration techniques that are nonlinear (and therefore more accurate than simplistic linear approaches) and 2) the corresponding Fréchet derivatives take into account that the velocity model is laterally heterogeneous. In addition to providing the comprehensive mathematical algorithms involved, three proof-of-concept numerical examples are demonstrated, which confirm the potential of our methodology.
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References
Adler F., Baina R., Soudani M.A., Cardon P. and Richard J.-B., 2008. Nonlinear 3d tomographic least-squares inversion of residual moveout in kirchhoff prestack-depth-migration common-image gathers. Geophysics, 73, VE13–VE23.
Aster R.C., Borchers B. and Thurber C.H., 2013. Parameter Estimation and Inverse Problems. 2nd Edition. Academic Press, Waltham, MA.
Bakker P., 2002. Image Structure Analysis for Seismic Interpretation. Ph.D. Thesis. Delft Techncial University, Delft, The Netherlands.
Barros T., Ferrari R., Krummenauer R. and Lopes R., 2015. Differential evolution-based optimization procedure for automatic estimation of the common-reflection surface traveltime parameters. Geophysics, 80, WD189–WD200.
Bartels R.H., Beatty J.C. and Barsky B.A., 1987. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann Publishers, Burlington, MA.
Bauer A., Schwarz B. and Gajewski D., 2009. Enhancement of prestack diffraction data and attributes using a traveltime decomposition approach. Stud. Geophys. Geod., 60, 471–486.
Baykulov M. and Gajewski D., 2009. Prestack seismic data enhancement with partial common-reflection-surface (CRS) stack. Geophysics, 74, V49–V58.
Bergler S., Hubral P., Marchetti P., Cristini A. and Cardone G., 2002. 3D common-reflection-surface stack and kinematic wavefield attributes. The Leading Edge, 21, 1010–1015.
Berkovitch A., Belfer I. and Landa E., 2008. Multifocusing as a method of improving subsurface imaging. The Leading Edge, 27, 250–256.
Berkovitch A., Belfer I., Hassin Y. and Landa E., 2009. Diffraction imaging by multifocusing. Geophysics, 74, WCA75–WCA81.
Bigun J. and Granlund G.H., 1987. Optimal orientation detection of linear symmetry. In: Proceedings of the IEEE First International Conference on Computer Vision. Computer Society Press of the IEEE, 433–438.
Billette F. and Lambaré G., 1998. Velocity macro-model estimation from seismic reflection data by stereotomography Geophys. J. Int., 135, 671–690.
Bloot R., Coimbra T.A., Faccipieri J.H. and Tygel M., 2018. Common-reflection-surface method in weakly anisotropic vertical transverse isotropic media. Geophysics, 83, C99–C113.
Bóna A., 2011. Shot-gather time migration of planar reflectors without velocity model. Geophysics, 76, S93–S101.
Bonomi E., Cristini M., Theis D. and Marchetti P., 2009. 3D CRS analysis: a data-driven optimization for the simultaneous estimate of the eight parameters. SEG Technical Program Expanded Abstracts 2009, 3284–3291, DOI: https://doi.org/10.1190/1.3255542.
Chauris H., Noble M.S., Lambaré G. and Podvin P., 2002a. Migration velocity analysis from locally coherent events in 2-d laterally heterogeneous media, part I: Theoretical aspects. Geophysics, 67, 1202–1212.
Chauris H., Noble M.S., Lambaré G. and Podvin P., 2002b. Migration velocity analysis from locally coherent events in 2-d laterally heterogeneous media, part II: Applications on synthetic and real data. Geophysics, 67, 1213–1224.
Coimbra T.A., de Figueiredo J.J.S., Schleicher J., Novais A. and Costa J.C., 2013. Migration velocity analysis using residual diffraction moveout in the poststack depth domain. Geophysics, 78, S125–S135.
Coimbra T.A., Faccipieri J.H., Rueda D.S. and Tygel M., 2016a. Common-reflection-point time migration. Stud. Geophys. Geod., 60, 500–530.
Coimbra T.A., Novais A. and Schleicher J., 2016b. Offset-continuation stacking: Theory and proof of concept. Geophysics, 81, V387–V401.
Cooke D., Bóna A. and Hansen B., 2009. Simultaneous time imaging, velocity estimation, and multiple suppression using local event slopes. Geophysics, 74, WCA65–WCA73.
Dell S. and Gajewski D., 2011. Common-reflection-surface-based workflow for diffraction imaging. Geophysics, 76, S187–S195.
Dell S., Gajewski D. and Tygel M., 2014. Image-ray tomography. Geophys. Prospect., 62, 413–426.
Dix C.H., 1955. Seismic velocities from surface measurements. Geophysics, 20, 68–86.
Douma H. and de Hoop M.V., 2006. Leading-order seismic imaging using curvelets. SEG Technical Program Expanded Abstracts 2006, 2411–2415, DOI: https://doi.org/10.1190/1.2370019.
Faccipieri J.H., Serrano D.R., Gelius L.J. and Tygel M., 2013. Recovering diffractions in CRS stacked sections. First Break, 31, 27–31.
Faccipieri J.H., Coimbra T.A., Gelius L.J. and Tygel M., 2016. Stacking apertures and estimation strategies for reflection and diffraction enhancement. Geophysics, 81, V271–V282.
Fomel S., 2002. Applications of plane-wave destruction filters. Geophysics, 67, 1946–1960.
Fomel S., 2007a. Velocity-independent time-domain seismic imaging using local event slopes. Geophysics, 72, S139–S147.
Fomel S., 2007b. Local seismic attributes. Geophysics, 72, A29–A33.
Fomel S. and Kazinnik R., 2012. Non-hyperbolic common reflection surface. Geophys. Prospect., 61, 21–27.
Garabito G., Cruz J.C.R. and Solner W., 2017. Finite-offset common reflection surface stack using global optimisation for parameter estimation: a land data example. Geophys. Prospect., 65, 1123–1137.
Gelius L.-J. and Tygel M., 2015. Migration-velocity building in time and depth from 3D (2D) Common-Reflection-Surface (CRS) stacking — theoretical framework. Stud. Geophys. Geod., 59, 253–282.
Gjøystdal H. and Ursin B., 1981. Inversion of reflection times in three dimensions. Geophysics, 46, 972–983.
Guillaume P., Audebert F., Berthet P., David B., Herrenschmidt A. and Zhang X., 2001. 3D finite-offset tomographic inversion of CRP-scan data, with or without anisotropy. SEG Technical Program Expanded Abstracts 2001, 718–721, DOI: https://doi.org/10.1190/1.1816731.
Guillaume P., Lambaré G., Leblanc O., Mitouard P., Moigne J.L., Montel J.-P., Prescott T., Siliqi R., Vidal N., Zhang X. and Zimine S., 2008. Kinematic invariants: an efficient and flexible approach for velocity model building. SEG Technical Program Expanded Abstracts 2008, 3687–3692, DOI: https://doi.org/10.1190/1.3064100.
Guillaume P., Reinier M., Lambaré G., Cavalié A., Adamsen M.I. and Bruun B.M., 2013. Dip constrained non-linear slope tomography: an application to shallow channels characterization. SEG Global Meeting Abstracts, 1587–159, DOI: https://doi.org/10.1190/sbgf2013-325.
Hertweck T., Schleicher J. and Mann J., 2007. Data stacking beyond CMP. The Leading Edge, 26, 818–827.
Hoecht G., Ricarte P., Bergler S. and Landa E., 2009. Operator-oriented CRS interpolation. Geophys. Prospect., 57, 957–979.
Hubral P., 1999. Special issue: Macro model independent seismic imaging. J. Appl. Geophys., 42, 137–138.
Hubral P. and Krey T., 1980. Interval Velocities from Seismic Reflection Time Measurements. Society of Exploration Geophysicists, Tulsa, USA.
Iversen E., 2004. The isochron ray in seismic modeling and imaging. Geophysics, 69, 1053–1070.
Iversen E. and Gjøystdal H., 1996. Event-oriented velocity estimation based on prestack data in time or depth domain. Geophys. Prospect., 44, 643–686.
Iversen E., Tygel M., Ursin B. and Hoop M.V., 2012. Kinematic time migration and demigration of reflections in pre-stack seismic data. Geophys. J. Int., 189, 1635–1666.
Jäger R., Mann J., Höcht G. and Hubral P., 2001. Common-reflection-surface stack: Image and attributes. Geophysics, 66, 97–109.
Khoshnavaz M.J., 2017. Oriented time-domain dip moveout correction for planar reflectors in common-source domain. Geophysics, 82, U87–U97.
Khoshnavaz M.J., Bóna A., Dzunic A., Ung K. and Urosevic M., 2016a. Oriented prestack time migration using local slopes and predictive painting in the common-source domain for planar reflectors. Geophysics, 81, S409–S418.
Khoshnavaz M.J., Bóna A. and Urosevic M., 2016b. Velocity-independent estimation of kinematic attributes in vertical transverse isotropy media using local slopes and predictive painting. Geophysics, 81, U73–U85.
Kleyn A.H., 1977. On the migration of reflection time contour maps. Geophys. Prospect., 25, 125–140.
Klokov A. and Fomel S., 2012. Separation and imaging of seismic diffractions using migrated dip-angle gathers. Geophysics, 77, S131–S143.
Knutsson H., 1989. Representing local structure using tensors. In: Pietikainen M. and Ron̈ing J. (Eds), Proceedings of the 6th Scandinavian Conference on Image Analysis. International Association for Pattern Recognition, 244–251.
Lambaré G., Deladerrière N., Traonmilin Y., Touré J.P., Moigne J.L. and Herrmann P., 2009. Nonlinear tomography for time imaging. Extended Abstract. 71st EAGE Conference and Exhibition Incorporating SPE EUROPEC 2009. EAGE Publications BV, DOI: https://doi.org/10.3997/2214-4609.201400386.
Landa E., 2007. Beyond Conventional Seismic Imaging. EAGE, The Hague, The Netherlands.
Landa E., Gurevich B., Keydar S. and Trachtman P., 1999. Application of multifocusing method for subsurface imaging. J. Appl. Geophys., 42, 283–300.
Landa E., Keydar S. and Moser T.J., 2010. Multifocusing revisited — inhomogeneous media and curved interfaces. Geophys. Prospect., 58, 925–938.
Messud J., Lambaré G., Guillaume P. and Rohel C., 2015. Non-linear slope tomography for orthorhombic pre-stack time imaging. Extended Abstract. 77th EAGE Conference and Exhibition 2015. EAGE Publications BV, DOI: https://doi.org/10.3997/2214-4609.201412575.
Minato S., Tsuji T., Matsuoka T., Nishizaka N. and Ikeda M., 2012. Global optimisation by simulated annealing for common reflection surface stacking and its application to low-fold marine data in southwest japan. Explor. Geophys., 43, 59–69.
Neidell N.S. and Taner M.T., 1971. Semblance and other coherency measures for multichannel data. Geophysics, 36, 482–497.
Perroud M., Hubral P. and Höcht G., 1999. Common-reflection-point stacking in laterally inhomogeneous media. Geophys. Prospect., 47, 1–24.
Rad P.B., Schwarz B., Gajewski D. and Vanelle C., 2018. Common-reflection-surface-based prestack diffraction separation and imaging. Geophysics, 83, S47–S55.
Randen T., Monsen E., Signer C., Abrahamsen A., Hansen J.O., Sæter T. and Schlaf J., 2000. Three-dimensional texture attributes for seismic data analysis. SEG Technical Program Expanded Abstracts 2000, 668–671, DOI: https://doi.org/10.1190/1.1816155.
Riabinkin 1957. Fundamentals of resolving power of controlled directional reception (CDR) of seismic waves. In: Gardner G.H.F. and Lu L. (Eds), Slant-Stack Processing, 14, 36–60, Society of Exploration Geophysicists, Tulsa, USA.
Rieber F., 1936. Visual presentation of elastic wave patterns under various structural conditions. Geophysics, 1, 196–218.
Shah P.M., 1973. Use of wavefront curvature to relate seismic data with subsurface parameters. Geophysics, 38, 812–825.
Söllner W. and Andersen E., 2005. Kinematic time migration and demigration in a 3D visualization system. J. Seism. Explor., 14, 255–270.
Söllner W., Andersen E. and Lima J., 2004. Fast time-to-depth mapping by first-order ray transformation in a 3-D visualization system. SEG Technical Program Expanded Abstracts 2004, 1081–1084, DOI: https://doi.org/10.1190/1.1851071.
Spinner M. and Mann J., 2006. True-amplitude based Kirchhoff time migration for AVO/AVA analysis. Geophysics, 15, 133–152.
Stolk C.C., de Hoop M.V. and Symes W.W., 2009. Kinematics of shot-geophone migration. Geophysics, 74, WCA19–WCA34.
Stovas A. and Fomel S., 2015. Mapping of moveout attributes using local slopes. Geophys. Prospect., 64, 31–37.
Sword C.H., 1986. Tomographic determination of interval velocities from picked reflection seismic data. SEG Technical Program Expanded Abstracts 1986, 657–660, DOI: https://doi.org/10.1190/1.1892933.
Tygel M. and Santos L.T., 2007. Quadratic normal moveouts of symmetric reflections in elastic media: A quick tutorial. Stud. Geophys. Geod., 51, 185–206.
Ursin P., 1982. Quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces Geophysics, 47, 1012–1021.
van de Weijer J., van Vliet L., Verbeek P. and van Ginkel R., 2001. Curvature estimation in oriented patterns using curvilinear models applied to gradient vector fields. IEEE Trans. Pattern Anal. Mach. Intell., 23, 1035–1042.
Vanelle C., Abakumov I. and Gajewski D., 2018. Wavefront attributes in anisotropic media. Geophys. J. Int., 214, 430–443.
Walda J. and Gajewski D., 2017. Determination of wavefront attributes by differential evolution in the presence of conflicting dips. Geophysics, 82, V229–V239.
Waldeland A.U., Coimbra T.A., Faccipieri J.H., Solberg A.H.S. and Gelius L.J., 2019. Fast estimation of prestack common reflection surface parameters. Geophys. Prospect., 67, 1163–1183.
Whitcombe D.N., Murray E.H., Aubin L.A.S. and Carroll R.J., 1994. The application of 3-D depth migration to the development of an alaskan offshore oil field. Geophysics, 59, 1551–1560.
Yuan S., Wang S., Luo C. and Wang T., 2018. Inversion-based 3-D seismic denoising for exploring spatial edges and spatio-temporal signal redundancy. IEEE Geosci. Remote Sens. Lett., 15, 1682–1686.
Yuan S., Su Y., Wang T., Wang J. and Wang S., 2019. Geosteering phase attributes: A new detector for the discontinuities of seismic images. IEEE Geosci. Remote Sens. Lett., 16, 145–149.
Zhang Y., Bergler S., Tygel M. and Hubral P., 2002. Model-independent travel-time attributes for 2-D, finite-offset multicoverage reflections. Pure Appl. Geophys., 159, 1601–1616.
Acknowledgments
The authors acknowledge support from the Norwegian Research Council through the Petro-Maks 2 project (NFR/234019). We thank Lundin Norway AS for making the 3D field dataset available for this study. We also grateful to NORSAR for providing the software for the synthetic data generation.
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Zhao, H., Waldeland, A.U., Serrano, D.R. et al. Time-migration velocity estimation using Fréchet derivatives based on nonlinear kinematic migration/demigration solvers. Stud Geophys Geod 64, 26–75 (2020). https://doi.org/10.1007/s11200-019-1172-0
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DOI: https://doi.org/10.1007/s11200-019-1172-0