Canonical solutions for wave anelasticity in rocks composed of two frames Wave anelasticity solutions in composite rocks

Wave anelasticity of the fast P wave at mesoscopic scales is due to energy dissipation by conversion to slow P diffusive modes at heterogeneities much smaller than the wavelength and much larger than the pore size. We consider frames composed of two minerals and study the dissipation effects based on a generalized White plane-layered model, where the interfaces satisfy mixed boundary conditions, i.e., open, closed and partially-open pores. We consider three models to obtain the effective properties. Model 1 is based on effective mineral properties, Model 2 is a generalization of Biot theory to the case of two solids and one fluid, and Model 3 is based on a generalization of White model to the case of three layers. A particular case is that of closed pores at the interface between the layers, where no flow occurs and, consequently, there is no anelasticity and the stiffness modulus is a real quantity and does not depend on frequency. The type of boundary condition highly affects the location of the relaxation peak, which moves from high to low frequencies for decreasing interface permeability. The first two models predict similar locations of the peaks and strength (reciprocal of the quality factor). The results of Model 3 differ due to different distribution of the solid phases, since the frames are not mixed at the pore scale as in Models 1 and 2, but at a mesoscopic scale. These solutions are useful to test modeling algorithms to compute the effective P-wave modulus in more general cases.