none 10.1190/geo2020-0956.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 133897366 5981 2025121211214303200 10.1190 2025-12-12T16:21:50Z 2022-01-19T11:17:50Z 18 Geophysics 0016-8033 1942-2156 05 01 2022 87 3 Phase-amplitude-based polarized direct envelope inversion in the time-frequency domain Yong Hu China University of Mining and Technology 1 , School of Resources and Geosciences, Xuzhou 221116, China. jluhuyong@sina.com http://orcid.org/0000-0001-7910-9188 Ru-Shan Wu University of California 2 , Department of Earth and Planetary Sciences, Santa Cruz, California 95064, USA. rwu@ucsc.edu . http://orcid.org/0000-0001-9188-4953 Xingguo Huang Jilin University 3 , College of Instrumentation and Electrical Engineering, Changchun 130026, China. xingguohuang@jlu.edu.cn (corresponding author) http://orcid.org/0000-0001-9719-6297 Yun Long Jilin University 3 , College of Instrumentation and Electrical Engineering, Changchun 130026, China. longy@jlu.edu.cn . http://orcid.org/0000-0001-8051-755X Yongzhong Xu China University of Mining and Technology 1 , School of Resources and Geosciences, Xuzhou 221116, China. xuyongzhong2004@126.com . Li-Guo Han Jilin University 4 , College of Geo-Exploration Science and Technology, Changchun 130026, China. hanlg@jlu.edu.cn ABSTRACT Large-scale geologic structures with strong contrasts present difficulties for seismic imaging and inversion. Previously, direct envelope inversion (DEI) with ultralow frequency has been proposed to retrieve strong-contrast velocity models. However, the envelope signals lose the instantaneous phase of the original wavefield, resulting in erroneous seismic inversion results. To solve this problem, the instantaneous phase of the wavefield is encoded into envelopes for DEI. In this way, a polarized envelope is created to contain both abundant low frequencies and the instantaneous phase information of the original seismic waveform. Furthermore, to improve the resolution of deep regions underneath the strong reflections, we propose a phase-amplitude-based polarized direct envelope inversion (PA-PDEI) misfit in the time-frequency domain that uses an amplitude factor to emphasize the phase information. This makes it possible to adjust the amplitude influence and boost the low-amplitude seismic signals for deep targets. Tests on a model with a salt body and on field data show that combining the PA-PDEI with the phase-amplitude-based full-waveform inversion (PA-FWI) make it possible to reliably reconstruct velocity models, especially for deep regions, despite large and strong perturbations. 02 25 2022 05 01 2022 01 19 2022 R245 R260 The Natural Science Foundation of Jiangsu Province BK20200644 National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809 42104116 China Postdoctoral Science Foundation http://dx.doi.org/10.13039/501100002858 2021M703580 1 10.1190/crossmark-policy library.seg.org true 2021-01-13 2021-12-02 2021-12-07 2022-02-25 The Natural Science Foundation of Jiangsu Province BK20200644 National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809 42104116 China Postdoctoral Science Foundation http://dx.doi.org/10.13039/501100002858 2021M703580 10.1190/geo2020-0956.1 https://pubs.geoscienceworld.org/geophysics/article/87/3/R245/612192/Phase-amplitude-based-polarized-direct-envelope https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/87/3/R245/5603782/geo-2020-0956.1.pdf https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/87/3/R245/5603782/geo-2020-0956.1.pdf https://pubs.geoscienceworld.org/geophysics/article/87/3/r245/612192/phase-amplitude-based-polarized-direct-envelope 0956-540X Geophysical Journal International Alkhalifah 200 363 2014 10.1093/gji/ggu379 Scattering-angle based filtering of the waveform inversion gradients 0016-8033 Geophysics Alkhalifah 81 6 R417 2016 10.1190/geo2015-0650.1 Multiscattering inversion for low-model wavenumbers 0016-8033 Geophysics Anagaw 79 5 R165 2014 10.1190/geo2013-0263.1 Comparison of multifrequency selection strategies for simultaneous-source full-waveform inversion 0016-8025 Geophysical Prospecting Bednar 55 465 2007 10.1111/j.1365-2478.2007.00618.x Comparison of waveform inversion — Part 2: Phase approach Journal of Earth Science Bian 22 241 2011 10.1007/s12583-011-0177-6 Layer-stripping full waveform inversion with damped seismic reflection data 0956-540X Geophysical Journal International Bozdağ 185 845 2011 10.1111/j.1365-246X.2011.04970.x Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements 0016-8033 Geophysics Bunks 60 1457 1995 10.1190/1.1443880 Multiscale seismic waveform inversion 0956-540X Geophysical Journal International Chen 220 235 2020 10.1093/gji/ggz442 Reflection waveform inversion based on full-band seismic data reconstruction for salt structure inversion 0016-8025 Geophysical Prospecting Chen 66 1258 2018 10.1111/1365-2478.12624 Reflection multi-scale envelope inversion 0926-9851 Journal of Applied Geophysics Chen 153 113 2018 10.1016/j.jappgeo.2018.04.008 Multi-scale signed envelope inversion 0926-9851 Journal of Applied Geophysics Chi 109 36 2014 10.1016/j.jappgeo.2014.07.010 Full waveform inversion method using envelope objective function without low frequency data 0016-8033 Geophysics Choi 80 5 R251 2015 10.1190/geo2014-0498.1 Unwrapped phase inversion with an exponential damping SIAM Journal on Imaging Sciences Esser 11 376 2018 10.1137/17M111328X Total variation regularization strategies in full-waveform inversion 0956-540X Geophysical Journal International Fichtner 175 665 2008 10.1111/j.1365-246X.2008.03923.x Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain 0926-9851 Journal of Applied Geophysics Hu 139 195 2017 10.1016/j.jappgeo.2017.02.017 Adaptive multi-step full waveform inversion based on waveform mode decomposition 10.1190/segam2020-3425157.1 Hu Y. 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