none 10.1190/1.2192912 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 21815845 5981 2025121113411633500 10.1190 2025-12-11T18:41:26Z 2006-06-09T19:13:16Z 346 Geophysics 1942-2156 0016-8033 2006 01 01 2006 71 3 Yanghua Wang 1Imperial College London, Centre for Reservoir Geophysics, Department of Earth Science and Engineering, London SW7 2BP, United Kingdom. E-mail: yanghua.wang@imperial.ac.uk. Abstract A principal limitation on seismic resolution is the earth attenuation, or Q-effect, including the energy dissipation of high-frequency wave components and the velocity dispersion that distorts seismic wavelets. An inverse Q-filtering procedure attempts to remove the Q-effect to produce high-resolution seismic data, but some existing methods either reduce the S/N ratio, which limits spatial resolution, or generate an illusory high-resolution wavelet that contains no more subsurface information than the original low-resolution data. In this paper, seismic inverse Q-filtering is implemented in a stabilized manner to produce high-quality data in terms of resolution and S/N ratio. Stabilization is applied to only the amplitude compensation operator of a full inverse Q-filter because its phase operator is unconditionally stable, but the scheme neither amplifies nor suppresses high frequencies at late times where the data contain mostly ambient noise. The latter property makes the process invertible, differentiating from some conventional stabilized inverse schemes that tend to suppress high frequencies at late times. The stabilized inverse Q-filter works for a general earth Q-model, variable with depth or traveltime, and is more accurate than a layered approach, which involves an approximation to the amplitude operator. Because the earth Q-model can now be defined accurately, instead of a constant-Q layered structure, the accuracy of the inverse Q-filter is much higher than for a layered approach, even when implemented in the Gabor transform domain. For the stabilization factor, an empirical relation is proposed to link it to a user-specified gain limit, as in an explicit gain-controlling scheme. Synthetic and real data exam-ples demonstrate that the stabilized inverse Q-filter corrects the wavelet distortion in terms of shape and timing, compensates for energy loss without boosting ambient noise, and produces desirable seismic images with high resolution and high S/N ratio. 2006 01 01 2006 06 02 2006 V51 V60 10.1190/1.2192912 https://pubs.geoscienceworld.org/geophysics/article/71/3/V51/274678/Inverse-Q-filter-for-seismic-resolution https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/71/3/V51/3214519/gsgpy_71_3_V51.pdf https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/71/3/V51/3214519/gsgpy_71_3_V51.pdf http://geophysics.geoscienceworld.org/cgi/doi/10.1190/1.2192912 Bulletin of the Seismological Society of America Bano 86 1179 1996 10.1785/BSSA0860041179 Q-phase compensation of seismic records in the frequency domain Proceedings of IEEE Bastiaans 68 538 1980 10.1109/PROC.1980.11686 Gabor's expansion of a signal into Gaussian elementary signals Ben-Menahem 1981 10.1007/978-1-4612-5856-8 Seismic waves and sources Imaging of acoustic energy by wavefield extrapolation Berkhout 1982 Seismic migration Geophysics Bickel 50 1426 1985 10.1190/1.1442011 Plane-wave Q deconvolution Feichtinger 1998 Gabor analysis and algorithms — Theory and applications Journal of Geophysical Research Futterman 67 5279 1962 10.1029/JZ067i013p05279 Dispersive body waves Journal of the Institute of Electrical Engineers Gabor 93 429 1946 Theory of communication Hale 209–231 1981 Q and adaptive prediction error filters Hale 133–158 1982 Q-adaptive deconvolution Geophysics Hargreaves 56 519 1991 10.1190/1.1443067 Inverse Q filtering by Fourier transform Geophysics Irving 68 960 2003 10.1190/1.1581068 Removal of wavelet dispersion from GPR data Journal of Geophysical Research Kjartansson 84 4737 1979 10.1029/JB084iB09p04737 Constant Q wave propagation and attenuation Kolsky 1953 Stress waves in solids Philosophical Magazine Kolsky 1 693 1956 10.1080/14786435608238144 The propagation of stress pulses in viscoelastic solids Mason 1958 Physical acoustics and properties of solids Geophysics Robinson 44 1345 1979 10.1190/1.1441011 A technique for the continuous representation of dispersion in seismic data Geophysics Robinson 47 1106 1982 10.1190/1.1441374 Time-variable dispersion processing through the use of phased sinc functions Geophysical Journal of the Royal Astronomical Society Strick 13 197 1967 10.1111/j.1365-246X.1967.tb02154.x The determination of Q, dynamic viscosity and transient creep curves from wave propagation measurements Geophysics Trorey 27 766 1962 10.1190/1.1439098 Theoretical seismograms with frequency and depth dependent absorption Geophysics Varela 58 1167 1993 10.1190/1.1443500 Modeling of attenuation and dispersion Journal of Seismic Exploration Wang 8 133 1999 Random noise attenuation using forward-backward linear prediction Geophysics Hale 67 657 2002 10.1190/1.1468627 A stable and efficient approach to inverse Q-filtering Geophysics Hale 68 337 2003 10.1190/1.1543219 Quantifying the effectiveness of stabilized inverse Q-filtering Geophysical Research Letters Hale 31 L17606 2004 Q analysis on reflection seismic data Journal of Geophysical Engineering Wang 1 187 2004 10.1088/1742-2132/1/3/003 Modified Kolsky model for seismic attenuation and dispersion Geophysical Research Letters Wang 31 L21608 2004 10.1029/2004GL020525 Seismic migration with inverse Q-filtering