The attenuation and dispersion of seismic wave will occur when seismic wave propagates in patchy-saturated media and is influenced by fluid patch distribution and size.The patch characteristics in turn can be influenced by capillary forces mainly.The effect of capillarity on wave attenuation in patchy-saturated rocks is not fully understood.In view of such a situation,the authors make use of the concept of patch membrane stiffness as a macroscopic expression of capillarity,incorporate the capillary forces into spherical patchy saturation model by changing a pressure discontinuity at patch interfaces,get a new model and compare the variation of wave attenuation and dispersion before and after the consideration of the capillarity based on the new model.It is suggested that considering capillarity will increase seismic velocity and decrease the dispersion and attenuation coefficient.The authors applied this capillary-extended spherical patchy saturation model to interpret velocity-saturation and attenuation-saturation relations.A comparison with the original model shows that the new model can fit the velocity-saturation and attenuation-saturation experimental relation trend well,which suggests that capillary-extended spherical patchy saturation model can have important implications for interpreting velocity-saturation and attenuation-saturation relations in patchy-saturated rocks.
[1] Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range[J].The Journal of the Acoustical Society of America,1956a,28(2):179-191.
[2] Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher-frequency range[J].The Journal of the Acoustical Society of America,1956b,28(2):168-178.
[3] Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482-1498.
[4] Berryman J G,Wang H F.Double-porosity modeling in elastic wave propagation for reservoir characterization[J].Proc. SPIE 3453,Mathematical Methods in Geophysical Imaging,1998:58-69.
[5] Dutta N C,Ode H.Seismic reflections from a gas-water contact[J].Geophysics,1983,48(2):148-162.
[6] Batzle M,Hofmann R,Han D H,et al.Fluids and frequency dependent seismic velocity of rocks[J].The Leading Edge,2001,20(2):168-171.
[7] White J E,Mikhayloya N G,Lyakhovitskiy F M.Low-frequency seismic waves in fluid-saturated layered rocks. Izvestija[J].Physics of the Solid Earth,1975a,52(11):654-659.
[8] White J E.Computed seismic speeds and attenuation in rocks with partial gas saturation[J].Geophysics,1975b,40(2):224-232.
[9] Dutta N C,Odé H.Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-Part I:Biot theory[J].Geophysics,1979a,44(11):1777-1788.
[10] Dutta N C,Odé H.Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-Part II:Results[J].Geophysics,1979b,44(11):1789-1805.
[11] Vogelaar B,Smeulders D.Extension of White's layered model to the full frequency range[J].Geophysical Prospecting,2007,55:685-695.
[12] 刘炯,马坚伟,杨慧珠.周期成层Patchy模型中纵波的频散和衰减研究[J].地球物理学报,2009,52(11):2879-2885.
[13] 刘炯,马坚伟,杨慧珠.White球状Patchy模型中纵波传播研究[J].地球物理学报,2010,52(4):954-962.
[14] Carcione J,Helle H,Pham N.White's model for wave propagation in partially saturated rocks:Comparison with poroelastic numerical experiments[J].Geophysics,2003,68(4):1389-1398.
[15] Carcione J,Picotti S.P-wave seismic attenuation by slow-wave diffusion:Effects of inhomogeneous rock properties[J].Geophysics,2006,71(3):O1-O8.
[16] 邓继新,王尚旭,杜伟.介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例[J].地球物理学报,2012,55(8):2716-2727.
[17] Tserkovnyak Y,Johnson D L.Capillary forces in the acoustics of patchy-saturated porous media[J].The Journal of the Acoustical Society of America,2003,114(5):2596-2606.
[18] Moerig R,Waite W,Boyd O,et al.Seismicattenuation in artificial glass cracks:Physical and physicochemical effects of fluids[J].Geophysical Research Letters,1996,23(16):2053-2056.
[19] Averbakh V,Bredikhin V,Lebedev A,et al.Acoustic spectroscopy of fluid saturation effects in carbonate rock[J].Acoustical Physics,2010,56(5):794-806.
[20] Knight R,Dvorkin J,Nur A.Acoustic signatures of partial saturation[J].Geophysics,1998,63(1):132-138.
[21] Rubino J,Holliger K.Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks[J].Geophysical Journal International,2012,188(3):1088-1102.
[22] Nagy P B,Blaho G.Experimental measurements of surface stiffness on water-saturated porous solids[J].The Journal of the Acoustical Society of America,1994,95(2):828-835.
[23] Mavko G,Mukerji T,Dvorkin J.The rock physics handbook:Tools for seismic analysis in porous media[M].Cambridge University Press,1998.
[24] Johnson D L.Theory of frequency dependent acoustics in patchy saturated porous media[J].Journal of the Acoustical Society of America,2001,110(2):682-694.
[25] Lopes S,Lebedev M,Müller T M,et al.Forced imbibition into a limestone:Measuring P-wave velocity and water saturation dependence on injection rate[J].Geophysical Prospecting,2014,62(5):1126-1142.
