When the relative acceleration of water with respect to the soil skeleton is not significant compared with the motion of the soil skeleton itself, the variable w can be eliminated by dropping the acceleration terms associated with w as we can see in the basic assumption.
For most problems in earthquake response analysis, this approximation is sufficiently accurate. The above equation system (1-7) can now be reduced by eliminating w between (2) and (3) to the equations 1.a, 1.b and 1.c