Newton’s third law and seismic boundary conditions in poroelasticity.

Abstract

It is known that the application of Newton’s third law of motion on porous‐porous welded contact implies that the total force exerted on the interface by one side is balanced by an equal and opposite force exerted on the interface by the other side. Here it is shown that Newton’s third law of motion also amounts to the continuity of the solid and the fluid phasic forces of the two sides at the interface as well as the equalization of the solid and fluid phasic forces on each side. That is, at the interface all forces are equal to one another, and that holds true irrespective of the alignment of the pores at the interface. That, in turn, also suggests that the velocity field associated with the total mass of poro‐continuum is continuous at the interface. In conjunction with the requirement that the total energy must be conserved these yield the continuity of a weighted difference of solid and fluid velocities at the interface. Here, the weight factor is the product of the reciprocal density of the poro‐continuum and the difference of the reciprocal densities of the two phases. The boundary conditions thus constructed uphold Newton’s third law of motion.