Wave processes in saturated porous elastically deformed media

The symmetric form of poroelasticity dynamic equations in terms of velocities, stresses and pressure

“…In [4,5], the existence of four types of sound oscillations is revealed: two transverse (their properties are the same as those in an isotropic medium) and two longitudinal. In the isotropic case, a di erence of the linearized system of equations (1) from well-known equations of the FrenkelBiot type [6,7], is described by the three elastic constants [4,5].…”

“…In the isotropic case, a di erence of the linearized system of equations (1) from well-known equations of the FrenkelBiot type [6,7], is described by the three elastic constants [4,5]. These elastic parameters in a one-to-one manner are expressed by the three velocities (c t , cp , cp ) of elastic oscillations [8], [9], [10]:…”

A 2D kernel determination problem in a visco‐elastic porous medium with a weakly horizontally inhomogeneity

“…Equations () to () describe the propagation of elastic SH (transverse) waves in a porous medium with memory in the two‐dimensional case (in terms of time and spatial variables). We note that the direct and inverse dynamical problems for these equations for k ( x , t )=0 were studied in previous works 22,23 . This formulation of the inverse problem without taking into account the dependence of the kernel K on x and the derivative with respect to x on Σ 1 is equal to zero was considered in Durdiev and Rahmonov 13 .…”

“…A nonlinear mathematical model was constructed in Dorovsky 21 that combines the equations of the continuum theory of filtration. The question of the existence of a solution of this type requires studying the system of equations of porous media in a reversible approximation, that is, in the absence of dissipative processes 21,22 …”

“…Assuming that there is inter component friction, we rewrite the system of equations of movement in an inhomogeneous isotropic viscoelastic‐porous medium. Moreover, we assume that the coefficients depend only on z and that the displacement velocity vectors are represented in the form Then, for nonzero components of the displacement velocity vector from the equation of movement, we obtain (see Dorovsky et al 22 ) …”