Viscoelastic substitute models for seismic attenuation caused by squirt flow and fracture leak off
ABSTRACT
We have investigated viscoelastic substitute models for seismic attenuation caused by fluid pressure diffusion in fluid-saturated porous media. Fluid pressure diffusion may locally occur associated with fracture leak off and/or squirt flow. We use a homogenization scheme with numerical model reduction (NMR), recently established in the literature, and we derive the corresponding viscoelastic material properties that are apparent at a larger scale (i.e., the observer scale). Moreover, we find that the rheology of the resulting viscoelastic model is of the Maxwell-Zener type. Based on a series of numerical experiments, we find that this method is able to accurately and efficiently predict the overall attenuation and stiffness moduli dispersion for a range of scenarios without resolving the substructure problem explicitly. Computational homogenization, together with NMR, can be useful to simulate seismic wave propagation using a viscoelastic substitute model that accurately reproduces the energy dissipation and dispersion of a heterogeneous medium in which squirt flow and/or fracture leak-off occurs.
REFERENCES
- , 2010, Frequency and fluid effects on elastic properties of basalt: Experimental investigations: Geophysical Research Letters, 37,
L02303 , doi:10.1029/2009GL041660 .CrossrefWeb of ScienceGoogle Scholar - , 1941, General theory of three-dimensional consolidation: Journal of Applied Physics, 12,
155–164 , doi:10.1063/1.1712886 .CrossrefGoogle Scholar - , 1962, Mechanics of deformation and acoustic propagation in porous media: Journal of Applied Physics, 33,
1482–1498 , doi:10.1063/1.1728759 .CrossrefWeb of ScienceGoogle Scholar - , 2005, A model for P-wave attenuation and dispersion in a porous medium permeated by aligned fractures: Geophysical Journal International, 163,
372–384 , doi:10.1111/j.1365-246X.2005.02722.x .CrossrefWeb of ScienceGoogle Scholar - , 2010, Computational poroelasticity — A review: Geophysics, 75, no. 5,
75A229–75A243 , doi:10.1190/1.3474602 .AbstractWeb of ScienceGoogle Scholar - , 2009, P-wave dispersion and attenuation in fractured and porous reservoirs — Poroelasticity approach: Geophysical Prospecting, 57,
225–237 , doi:10.1111/j.1365-2478.2009.00785.x .CrossrefWeb of ScienceGoogle Scholar - , 2010, A simple model for squirt-flow dispersion and attenuation in fluid-saturated granular rocks: Geophysics, 75, no. 6,
N109–N120 , doi:10.1190/1.3509782 .AbstractWeb of ScienceGoogle Scholar - , 2016, Numerical identification of a viscoelastic substitute model for heterogeneous poroelastic media by a reduced order homogenization approach: Computer Methods in Applied Mechanics and Engineering, 298,
108–120 , doi:10.1016/j.cma.2015.09.024 .CrossrefWeb of ScienceGoogle Scholar - , 2019, Identification of viscoelastic properties from numerical model reduction of pressure diffusion in fluid-saturated porous rock with fractures: Computational Mechanics, 63,
49–67 , doi:10.1007/s00466-018-1584-7 .CrossrefWeb of ScienceGoogle Scholar - , 2015, Numerical homogenization of mesoscopic loss in poroelastic media: European Journal of Mechanics — A/Solids, 49,
382–395 , doi:10.1016/j.euromechsol.2014.08.011 .CrossrefWeb of ScienceGoogle Scholar - , 2010, Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review: Geophysics, 75, no. 5,
A147–A164 , doi:10.1190/1.3463417 .AbstractWeb of ScienceGoogle Scholar - , 1986, Acoustic relaxation in sedimentary rocks: Dependence on grain contacts and fluid saturation: Geophysics, 51,
757–766 , doi:10.1190/1.1442128 .AbstractWeb of ScienceGoogle Scholar - , 1977, Viscoelastic properties of fluid-saturated cracked solids: Journal of Geophysical Research, 82,
5719–5735 , doi:10.1029/JB082i036p05719 .CrossrefWeb of ScienceGoogle Scholar - , 2015, Bulk modulus dispersion and attenuation in sandstones: Geophysics, 80, no. 2,
D111–D127 , doi:10.1190/geo2014-0335.1 .AbstractWeb of ScienceGoogle Scholar - , 2014, Sensitivity of S-wave attenuation to the connectivity of fractures in fluid-saturated rocks: Geophysics, 79, no. 5,
WB15–WB24 , doi:10.1190/geo2013-0409.1 .AbstractWeb of ScienceGoogle Scholar - , 2016, A simple hydromechanical approach for simulating squirt-type flow: Geophysics, 81, no. 4,
D335–D344 , doi:10.1190/geo2015-0383.1 .AbstractWeb of ScienceGoogle Scholar - , 2011, Quasi-static finite-element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media: Journal of Geophysical Research, 116,
B01201 , doi:10.1029/2010JB007475 .CrossrefWeb of ScienceGoogle Scholar - , 2013, Do seismic waves sense fracture connectivity?: Geophysical Research Letters, 40,
692–696 , doi:10.1002/grl.50127 .CrossrefWeb of ScienceGoogle Scholar - , 2015, Laboratory-based seismic attenuation in Fontainebleau sandstone: Evidence of squirt flow: Journal of Geophysical Research, 120,
7526–7535 .Google Scholar - , 2014, Pore fluid viscosity effects on P- and S-wave anisotropy in synthetic silica-cemented sandstone with aligned fractures: Geophysical Prospecting, 62,
1238–1252 , doi:10.1111/1365-2478.12194 .CrossrefWeb of ScienceGoogle Scholar - , 2014, On attenuation of seismic waves associated with flow in fractures: Geophysical Research Letters, 41,
7515–7523 , doi:10.1002/2014GL061634 .CrossrefWeb of ScienceGoogle Scholar - , 1975, Computed seismic speeds and attenuation in rocks with partial gas saturation: Geophysics, 40,
224–232 , doi:10.1190/1.1440520 .AbstractWeb of ScienceGoogle Scholar - , 2012, Computation of dynamic seismic responses to viscous fluid of digitized three-dimensional Berea sandstones with a coupled finite-difference method: The Journal of the Acoustical Society of America, 132,
630–640 , doi:10.1121/1.4733545 .CrossrefWeb of ScienceGoogle Scholar
