MS_effective_medium
MS_effective_medium - generate elastic constants from various effective medium theories.
Generate elastic constants for the effective medium parameters based on various theories, identified by the string 'theory'. Subsequent required arguments depend on the theory invoked.
Currently available theories:
Tandon and Weng, 84 (tandon or t&w) Spheroids
(Isotropic host matrix with unidirectionally aligned isotropic spheroid inclusions)
[Ceff,rh]=MS_effective_medium('t&w',vpm,vsm,rhm,vpi,vsi,rhi,del,f) or Input parameters: vpm,vsm,rhm : isotropic parameters of the matrix (km/s, kg/m3) del : aspect ratio of spheroids: del < 1 = smarties del = 1 = spheres del > 1 = cigars f : volume fractions of inclusions vpi, vsi, rhi : isotropic parameters of the inclusions
[Ceff,rh]=MS_effective_medium('t&w',Cm,rhm,Ci,rhi,del,f) or Input parameters: Cm,rh : elasticity and density of the matrix (GPa, kg/m3) del : aspect ratio of spheroids: del < 1 = smarties del = 1 = spheres del > 1 = cigars f : volume fractions of inclusions Ci, rhi : isotropic parameters of the inclusions
Output parameters: Ceff : Elastic constants (GPa) (symmetry in X1 direction) rh : aggregate density (kg/m3)
Hudson, 1980, 1981 (hudson or crack) Cracks
[Ceff,rh]=MS_effective_medium('hudson',vpm,vsm,rhm,vpc,vsc,rhc,ar,cd) or Input parameters: vpm,vsm,rhm : isotropic parameters of the matrix (km/s, kg/m3) ar : aspect ratio of cracks cd : crack density vpc, vsc, rhc : isotropic parameters of the fill material
[Ceff,rh]=MS_effective_medium('hudson',Cm,rhm,Ci,rhi,ar,cd) or Input parameters: Cm,rh : elasticity and density of the matrix (GPa, kg/m3) ar : aspect ratio of cracks cd : crack density Cc, rhc : isotropic parameters of the fill material
Output parameters: Ceff : Elastic constants (GPa) (symmetry in X1 direction) rh : aggregate density (kg/m3)
Backus, 1962 (backus) stack of thin horizontal layers
[Ceff,rh]=MS_effective_medium('backus',thickness,vp,vs,rh) or Input parameters: thickness : layer thicknesses (vector) vp,vs,rh : isotropic parameters of the layers (km/s, kg/m3) (vector)
Output parameters: Ceff : Elastic constants (GPa) (symmetry in X1 direction) rh : aggregate density (kg/m3)
[Ceff,rh]=MS_effective_medium('backus',thickness,C,rh) or Input parameters: thickness : layer thicknesses (vector) C : elasticity of the layers (GPa) (6x6xn tensor) rh : density of the layers (GPa, kg/m3) (vector)
Output parameters: Ceff : Elastic constants (GPa) (symmetry in X3 direction) rh : aggregate density (kg/m3)
References
Tandon, GP and Weng, GJ. The Effect of Aspect Ratio of Inclusions on the Elastic Properties of Unidirectionally Aligned Composites. Polymer Composites, 5, pp 327-333, 1984.
Hudson, J. A., Overall properties of a cracked solid, Math. Proc. Camb. Phil. Soc., 88, pp 371-384. 1980
Hudson, J. A., Wave speeds and attenuation of elastic waves in material containing cracks, Geophys. J. R. Astr. Soc., 64, pp 133-150. 1981
Crampin, S. Effective anisotropic elastic constants for wave propagation through cracked solids. Geophys. J. R. Astr. Soc., 76, pp 135-145, 1984
Backus, G. E., Long-Wave Elastic Anisotropy Produced by Horizontal Layering. J. Geophys. Res., pp 4427-4440
See also: MS_elasticDB