Effect of Gravity on Wave Propagation

[adnan jahan]

Dear Friends,

I have started a problem, in wave propagation, I am confused in two things

If we have Cartesian coordinates OX1X2X3 with X3 is considered toward the center of Earth,

and material is considered to be of Half space,

1) I need to know the effect of gravity on wave propagation through the material

in a research paper it is given,

- (Rho)(g)(partial w/partial x) this term is given along X1 axis
and
no effect along X2 axis
and
+ (Rho)(g)(partial u/partial x) along X3 axis

can anyone please give me any hint how these effects of gravity appear in equation along these axis,

where velocity U(u,0,w)
If it is hard to understand, then I am attaching the artical,in which equation 3 is the to be considered,

Thanks

 

[adnan jahan]

AND PLEASE if any detail of granular medium, its stress strain relation is given then it will also be very supportive,