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Stabilized Least Squares Migration University of New Orleans ScholarWorks@UNO University of New Orleans Theses and Dissertations Dissertations and Theses Fall 12-18-2015 Stabilized Least Squares Migration Graham Ganssle [email protected] Follow this and additional works at: https://scholarworks.uno.edu/td Part of the Geophysics and Seismology Commons Recommended Citation Ganssle, Graham, "Stabilized Least Squares Migration" (2015). University of New Orleans Theses and Dissertations. 2074. https://scholarworks.uno.edu/td/2074 This Dissertation is protected by copyright and/or related rights. It has been brought to you by ScholarWorks@UNO with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Dissertation has been accepted for inclusion in University of New Orleans Theses and Dissertations by an authorized administrator of ScholarWorks@UNO. For more information, please contact [email protected]. Stabilized Least Squares Migration A Dissertation Submitted to the Graduate Faculty of the University of New Orleans In partial fulfillment of the Requirements for the degree of Doctor of Philosophy In Engineering and Applied Science Physics by Graham Ganssle B.S. University of New Orleans, 2009 M.Sc. University of New Orleans, 2011 P.G. Louisiana Board of Professional Geoscientists, 2014 December, 2015 Table of Contents Table of figures .............................................................................................. Error! Bookmark not defined. Abstract ........................................................................................................................................................ vi Intro............................................................................................................................................................... 1 Background ................................................................................................................................................... 2 Wave propagation (modeling) .................................................................................................................. 2 Wave de-propagation (migration) ............................................................................................................ 4 Iterative modeling and migration (LSM) ................................................................................................... 6 Velocity model updating (full waveform inversion) ............................................................................... 11 Iterative FWI and LSM (stabilized LSM) .................................................................................................. 12 Experiment/Methods .................................................................................................................................. 13 Modeling algorithm ................................................................................................................................ 13 Migration algorithm ................................................................................................................................ 15 FWI algorithm ......................................................................................................................................... 17 Automatic batch controller (the LSM brain) ........................................................................................... 17 Experiment .............................................................................................................................................. 18 Results ......................................................................................................................................................... 34 Modeled data (correct velocity model) .................................................................................................. 34 Conventional depth migration ................................................................................................................ 41 Conventional LSM ................................................................................................................................... 71 Stabilized LSM ......................................................................................................................................... 99 Analysis ..................................................................................................................................................... 127 Iteration comparison ............................................................................................................................ 127 Velocity Sensitivity ................................................................................................................................ 130 Reflectivity error resolution .................................................................................................................. 131 Velocity solution uniqueness ................................................................................................................ 131 Velocity error resolution ....................................................................................................................... 132 Conclusions ............................................................................................................................................... 133 Conventional LSM vs. Stabilized LSM .................................................................................................... 133 Modular algorithm - imaging resolution ............................................................................................... 134 Bibliography .............................................................................................................................................. 136 Appendix ................................................................................................................................................... 138 Vita ............................................................................................................................................................ 141 ii List of Figures Figure 1 unmigrated section (left), and migrated section (right), from Yilmaz 2001, figure 8.2-28 .............................. 5 Figure 2 Least squares migration of the Marmousi velocity model from Luo and Hale 2014, figure 1-d. .................... 9 Figure 3 Least squares migration of the Marmousi velocity model from Tan and Huang 2014, figure 14-b .............. 10 Figure 4 Conventional least squares migration workflow description from Wang 2013, figure 1. ............................. 11 Figure 5 Stabilized least squares migration workflow description. ............................................................................. 13 Figure 6 Marmousi velocity model, red is 5500 m/s, dark blue is 1500 m/s. .............................................................. 14 Figure 7 Brute stack corresponding to the Marmousi velocity model of Figure 6. ..................................................... 15 Figure 8 Depth migrated seismic section derived from the Marmousi velocity model of Figure 6. ........................... 16 Figure 9 Correct two velocity homogeneous velocity model. ..................................................................................... 20 Figure 10 Two velocity homogenous velocity model with a ten percent scalar velocity error. .................................. 21 Figure 11 Two velocity homogeneous velocity model with a ten percent stripe velocity error. ................................ 22 Figure 12 Two velocity homogeneous velocity model with a ten percent lateral velocity error. ............................... 23 Figure 13 Correct impulse response velocity model. .................................................................................................. 24 Figure 14 Impulse response velocity model with a ten percent scalar velocity error. ................................................ 25 Figure 15 Impulse response velocity model with a ten percent stripe velocity error. ................................................ 26 Figure 16 Impulse response velocity model with a ten percent lateral velocity error. ............................................... 27 Figure 17 Correct two velocity laterally heterogeneous velocity model. .................................................................... 28 Figure 18 Two velocity laterally heterogeneous velocity model with a ten percent scalar velocity error. ................. 29 Figure 19 Two velocity laterally heterogeneous velocity model with a ten percent stripe velocity error. ................. 30 Figure 20 Two velocity laterally heterogeneous velocity model with a ten percent lateral velocity error. ................ 31 Figure 21 Correct western half of the Marmousi velocity model. ............................................................................... 32 Figure 22 Western half of the Marmousi velocity model with a ten percent lateral velocity error. ........................... 33 Figure 23 Common shot gathers modeled from the two velocity homogeneous velocity model. ............................. 34 Figure 24 Brute stack of the associate CMP gathers for the two
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