Holm، Sverre؛ Näsholm، Sven Peter (2014). "Comparison of Fractional Wave Equations for Power Law Attenuation in Ultrasound and Elastography". Ultrasound in Medicine & Biology. ج. 40 ع. 4: 695–703. arXiv:1306.6507. DOI:10.1016/j.ultrasmedbio.2013.09.033. PMID:24433745.
Sven Peter Nasholm؛ Holm، Sverre (2012). "On a Fractional Zener Elastic Wave Equation". Fractional Calculus and Applied Analysis. ج. 16. arXiv:1212.4024. DOI:10.2478/s13540-013-0003-1.
Garrett، Steven L. (2020). "Attenuation of Sound". Understanding Acoustics. Cham: Springer International Publishing. ص. 673–698. DOI:10.1007/978-3-030-44787-8_14. ISSN:1868-4513.
Szabo، Thomas L. (1995). "Causal theories and data for acoustic attenuation obeying a frequency power law". The Journal of the Acoustical Society of America. Acoustical Society of America (ASA). ج. 97 ع. 1: 14–24. DOI:10.1121/1.412332. ISSN:0001-4966.
Chen، Yangkang؛ Zhang، Guoyin؛ Gan، Shuwei؛ Zhang، Chenglin (2015). "Enhancing seismic reflections using empirical mode decomposition in the flattened domain". Journal of Applied Geophysics. ج. 119: 99–105. Bibcode:2015JAG...119...99C. DOI:10.1016/j.jappgeo.2015.05.012.
Chen، Yangkang (2016). "Dip-separated structural filtering using seislet transform and adaptive empirical mode decomposition based dip filter". Geophysical Journal International. ج. 206 ع. 1: 457–469. Bibcode:2016GeoJI.206..457C. DOI:10.1093/gji/ggw165.
Szabo، Thomas L.؛ Wu، Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. ج. 107 ع. 5: 2437–2446. Bibcode:2000ASAJ..107.2437S. DOI:10.1121/1.428630. PMID:10830366.
Szabo، Thomas L. (1994). "Time domain wave equations for lossy media obeying a frequency power law". The Journal of the Acoustical Society of America. ج. 96 ع. 1: 491–500. Bibcode:1994ASAJ...96..491S. DOI:10.1121/1.410434.
Szabo، Thomas L.؛ Wu، Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. ج. 107 ع. 5: 2437–2446. Bibcode:2000ASAJ..107.2437S. DOI:10.1121/1.428630. PMID:10830366.Szabo, Thomas L.; Wu, Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. 107 (5): 2437–2446. Bibcode:2000ASAJ..107.2437S. doi:10.1121/1.428630. PMID10830366.
Szabo، Thomas L. (1994). "Time domain wave equations for lossy media obeying a frequency power law". The Journal of the Acoustical Society of America. ج. 96 ع. 1: 491–500. Bibcode:1994ASAJ...96..491S. DOI:10.1121/1.410434.Szabo, Thomas L. (1994). "Time domain wave equations for lossy media obeying a frequency power law". The Journal of the Acoustical Society of America. 96 (1): 491–500. Bibcode:1994ASAJ...96..491S. doi:10.1121/1.410434.
Chen، W.؛ Holm، S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. ج. 115 ع. 4: 1424–1430. Bibcode:2004ASAJ..115.1424C. DOI:10.1121/1.1646399. PMID:15101619.
Carcione، J. M.؛ Cavallini، F.؛ Mainardi، F.؛ Hanyga، A. (2002). "Time-domain Modeling of Constant- Q Seismic Waves Using Fractional Derivatives". Pure and Applied Geophysics. ج. 159 ع. 7–8: 1719–1736. Bibcode:2002PApGe.159.1719C. DOI:10.1007/s00024-002-8705-z.
dAstous، F.T.؛ Foster، F.S. (1986). "Frequency dependence of ultrasound attenuation and backscatter in breast tissue". Ultrasound in Medicine & Biology. ج. 12 ع. 10: 795–808. DOI:10.1016/0301-5629(86)90077-3. PMID:3541334.
Chen، W.؛ Holm، S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. ج. 115 ع. 4: 1424–1430. Bibcode:2004ASAJ..115.1424C. DOI:10.1121/1.1646399. PMID:15101619.Chen, W.; Holm, S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. 115 (4): 1424–1430. Bibcode:2004ASAJ..115.1424C. doi:10.1121/1.1646399. PMID15101619.
Holm، Sverre؛ Näsholm، Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. ج. 130 ع. 4: 2195–2202. Bibcode:2011ASAJ..130.2195H. DOI:10.1121/1.3631626. PMID:21973374.
Waters، K.R.؛ Mobley، J.؛ Miller، J.G. (2005). "Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion". IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ج. 52 ع. 5: 822–823. DOI:10.1109/TUFFC.2005.1503968. PMID:16048183.
Nachman، Adrian I.؛ Smith، James F.؛ Waag، Robert C. (1990). "An equation for acoustic propagation in inhomogeneous media with relaxation losses". The Journal of the Acoustical Society of America. ج. 88 ع. 3: 1584–1595. Bibcode:1990ASAJ...88.1584N. DOI:10.1121/1.400317.
Caputo، M.؛ Mainardi، F. (1971). "A new dissipation model based on memory mechanism". Pure and Applied Geophysics Pageoph. ج. 91 ع. 1: 134–147. Bibcode:1971PApGe..91..134C. DOI:10.1007/BF00879562.
Holm، Sverre؛ Näsholm، Sven Peter (2014). "Comparison of Fractional Wave Equations for Power Law Attenuation in Ultrasound and Elastography". Ultrasound in Medicine & Biology. ج. 40 ع. 4: 695–703. arXiv:1306.6507. DOI:10.1016/j.ultrasmedbio.2013.09.033. PMID:24433745.
Holm، Sverre؛ Näsholm، Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. ج. 130 ع. 4: 2195–2202. Bibcode:2011ASAJ..130.2195H. DOI:10.1121/1.3631626. PMID:21973374.Holm, Sverre; Näsholm, Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. 130 (4): 2195–2202. Bibcode:2011ASAJ..130.2195H. doi:10.1121/1.3631626. PMID21973374.
Nachman، Adrian I.؛ Smith، James F.؛ Waag، Robert C. (1990). "An equation for acoustic propagation in inhomogeneous media with relaxation losses". The Journal of the Acoustical Society of America. ج. 88 ع. 3: 1584–1595. Bibcode:1990ASAJ...88.1584N. DOI:10.1121/1.400317.Nachman, Adrian I.; Smith, James F.; Waag, Robert C. (1990). "An equation for acoustic propagation in inhomogeneous media with relaxation losses". The Journal of the Acoustical Society of America. 88 (3): 1584–1595. Bibcode:1990ASAJ...88.1584N. doi:10.1121/1.400317.
Näsholm، Sven Peter؛ Holm، Sverre (2011). "Linking multiple relaxation, power-law attenuation, and fractional wave equations". The Journal of the Acoustical Society of America. ج. 130 ع. 5: 3038–3045. Bibcode:2011ASAJ..130.3038N. DOI:10.1121/1.3641457. PMID:22087931.
Sven Peter Nasholm؛ Holm، Sverre (2012). "On a Fractional Zener Elastic Wave Equation". Fractional Calculus and Applied Analysis. ج. 16. arXiv:1212.4024. DOI:10.2478/s13540-013-0003-1.
Chen، Yangkang؛ Zhang، Guoyin؛ Gan، Shuwei؛ Zhang، Chenglin (2015). "Enhancing seismic reflections using empirical mode decomposition in the flattened domain". Journal of Applied Geophysics. ج. 119: 99–105. Bibcode:2015JAG...119...99C. DOI:10.1016/j.jappgeo.2015.05.012.
Chen، Yangkang (2016). "Dip-separated structural filtering using seislet transform and adaptive empirical mode decomposition based dip filter". Geophysical Journal International. ج. 206 ع. 1: 457–469. Bibcode:2016GeoJI.206..457C. DOI:10.1093/gji/ggw165.
Szabo، Thomas L.؛ Wu، Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. ج. 107 ع. 5: 2437–2446. Bibcode:2000ASAJ..107.2437S. DOI:10.1121/1.428630. PMID:10830366.
Szabo، Thomas L. (1994). "Time domain wave equations for lossy media obeying a frequency power law". The Journal of the Acoustical Society of America. ج. 96 ع. 1: 491–500. Bibcode:1994ASAJ...96..491S. DOI:10.1121/1.410434.
Szabo، Thomas L.؛ Wu، Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. ج. 107 ع. 5: 2437–2446. Bibcode:2000ASAJ..107.2437S. DOI:10.1121/1.428630. PMID:10830366.Szabo, Thomas L.; Wu, Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. 107 (5): 2437–2446. Bibcode:2000ASAJ..107.2437S. doi:10.1121/1.428630. PMID10830366.
Szabo، Thomas L. (1994). "Time domain wave equations for lossy media obeying a frequency power law". The Journal of the Acoustical Society of America. ج. 96 ع. 1: 491–500. Bibcode:1994ASAJ...96..491S. DOI:10.1121/1.410434.Szabo, Thomas L. (1994). "Time domain wave equations for lossy media obeying a frequency power law". The Journal of the Acoustical Society of America. 96 (1): 491–500. Bibcode:1994ASAJ...96..491S. doi:10.1121/1.410434.
Chen، W.؛ Holm، S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. ج. 115 ع. 4: 1424–1430. Bibcode:2004ASAJ..115.1424C. DOI:10.1121/1.1646399. PMID:15101619.
Carcione، J. M.؛ Cavallini، F.؛ Mainardi، F.؛ Hanyga، A. (2002). "Time-domain Modeling of Constant- Q Seismic Waves Using Fractional Derivatives". Pure and Applied Geophysics. ج. 159 ع. 7–8: 1719–1736. Bibcode:2002PApGe.159.1719C. DOI:10.1007/s00024-002-8705-z.
Chen، W.؛ Holm، S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. ج. 115 ع. 4: 1424–1430. Bibcode:2004ASAJ..115.1424C. DOI:10.1121/1.1646399. PMID:15101619.Chen, W.; Holm, S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. 115 (4): 1424–1430. Bibcode:2004ASAJ..115.1424C. doi:10.1121/1.1646399. PMID15101619.
Holm، Sverre؛ Näsholm، Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. ج. 130 ع. 4: 2195–2202. Bibcode:2011ASAJ..130.2195H. DOI:10.1121/1.3631626. PMID:21973374.
Nachman، Adrian I.؛ Smith، James F.؛ Waag، Robert C. (1990). "An equation for acoustic propagation in inhomogeneous media with relaxation losses". The Journal of the Acoustical Society of America. ج. 88 ع. 3: 1584–1595. Bibcode:1990ASAJ...88.1584N. DOI:10.1121/1.400317.
Caputo، M.؛ Mainardi، F. (1971). "A new dissipation model based on memory mechanism". Pure and Applied Geophysics Pageoph. ج. 91 ع. 1: 134–147. Bibcode:1971PApGe..91..134C. DOI:10.1007/BF00879562.
Holm، Sverre؛ Näsholm، Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. ج. 130 ع. 4: 2195–2202. Bibcode:2011ASAJ..130.2195H. DOI:10.1121/1.3631626. PMID:21973374.Holm, Sverre; Näsholm, Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. 130 (4): 2195–2202. Bibcode:2011ASAJ..130.2195H. doi:10.1121/1.3631626. PMID21973374.
Nachman، Adrian I.؛ Smith، James F.؛ Waag، Robert C. (1990). "An equation for acoustic propagation in inhomogeneous media with relaxation losses". The Journal of the Acoustical Society of America. ج. 88 ع. 3: 1584–1595. Bibcode:1990ASAJ...88.1584N. DOI:10.1121/1.400317.Nachman, Adrian I.; Smith, James F.; Waag, Robert C. (1990). "An equation for acoustic propagation in inhomogeneous media with relaxation losses". The Journal of the Acoustical Society of America. 88 (3): 1584–1595. Bibcode:1990ASAJ...88.1584N. doi:10.1121/1.400317.
Näsholm، Sven Peter؛ Holm، Sverre (2011). "Linking multiple relaxation, power-law attenuation, and fractional wave equations". The Journal of the Acoustical Society of America. ج. 130 ع. 5: 3038–3045. Bibcode:2011ASAJ..130.3038N. DOI:10.1121/1.3641457. PMID:22087931.
Müller، Tobias M.؛ Gurevich، Boris؛ Lebedev، Maxim (سبتمبر 2010). "Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review". Geophysics. ج. 75 ع. 5: 75A147–75A164. Bibcode:2010Geop...75A.147M. DOI:10.1190/1.3463417.
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Szabo، Thomas L.؛ Wu، Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. ج. 107 ع. 5: 2437–2446. Bibcode:2000ASAJ..107.2437S. DOI:10.1121/1.428630. PMID:10830366.
Szabo، Thomas L.؛ Wu، Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. ج. 107 ع. 5: 2437–2446. Bibcode:2000ASAJ..107.2437S. DOI:10.1121/1.428630. PMID:10830366.Szabo, Thomas L.; Wu, Junru (2000). "A model for longitudinal and shear wave propagation in viscoelastic media". The Journal of the Acoustical Society of America. 107 (5): 2437–2446. Bibcode:2000ASAJ..107.2437S. doi:10.1121/1.428630. PMID10830366.
Chen، W.؛ Holm، S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. ج. 115 ع. 4: 1424–1430. Bibcode:2004ASAJ..115.1424C. DOI:10.1121/1.1646399. PMID:15101619.
dAstous، F.T.؛ Foster، F.S. (1986). "Frequency dependence of ultrasound attenuation and backscatter in breast tissue". Ultrasound in Medicine & Biology. ج. 12 ع. 10: 795–808. DOI:10.1016/0301-5629(86)90077-3. PMID:3541334.
Chen، W.؛ Holm، S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. ج. 115 ع. 4: 1424–1430. Bibcode:2004ASAJ..115.1424C. DOI:10.1121/1.1646399. PMID:15101619.Chen, W.; Holm, S. (2004). "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency". The Journal of the Acoustical Society of America. 115 (4): 1424–1430. Bibcode:2004ASAJ..115.1424C. doi:10.1121/1.1646399. PMID15101619.
Holm، Sverre؛ Näsholm، Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. ج. 130 ع. 4: 2195–2202. Bibcode:2011ASAJ..130.2195H. DOI:10.1121/1.3631626. PMID:21973374.
Waters، K.R.؛ Mobley، J.؛ Miller، J.G. (2005). "Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion". IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ج. 52 ع. 5: 822–823. DOI:10.1109/TUFFC.2005.1503968. PMID:16048183.
Holm، Sverre؛ Näsholm، Sven Peter (2014). "Comparison of Fractional Wave Equations for Power Law Attenuation in Ultrasound and Elastography". Ultrasound in Medicine & Biology. ج. 40 ع. 4: 695–703. arXiv:1306.6507. DOI:10.1016/j.ultrasmedbio.2013.09.033. PMID:24433745.
Holm، Sverre؛ Näsholm، Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. ج. 130 ع. 4: 2195–2202. Bibcode:2011ASAJ..130.2195H. DOI:10.1121/1.3631626. PMID:21973374.Holm, Sverre; Näsholm, Sven Peter (2011). "A causal and fractional all-frequency wave equation for lossy media". The Journal of the Acoustical Society of America. 130 (4): 2195–2202. Bibcode:2011ASAJ..130.2195H. doi:10.1121/1.3631626. PMID21973374.
Näsholm، Sven Peter؛ Holm، Sverre (2011). "Linking multiple relaxation, power-law attenuation, and fractional wave equations". The Journal of the Acoustical Society of America. ج. 130 ع. 5: 3038–3045. Bibcode:2011ASAJ..130.3038N. DOI:10.1121/1.3641457. PMID:22087931.
Garrett، Steven L. (2020). "Attenuation of Sound". Understanding Acoustics. Cham: Springer International Publishing. ص. 673–698. DOI:10.1007/978-3-030-44787-8_14. ISSN:1868-4513.
Szabo، Thomas L. (1995). "Causal theories and data for acoustic attenuation obeying a frequency power law". The Journal of the Acoustical Society of America. Acoustical Society of America (ASA). ج. 97 ع. 1: 14–24. DOI:10.1121/1.412332. ISSN:0001-4966.