Question: Modify the wave equation (12.4b) to include the effect of gravity. Assume that the medium is homogeneous and the gravitational field is constant. By comparing

Modify the wave equation (12.4b) to include the effect of gravity. Assume that the medium is homogeneous and the gravitational field is constant. By comparing the orders of magnitude of the terms in the wave equation, verify that the gravitational terms can be ignored for high-enough frequency elastodynamic modes: ω » g/C_L,T. For wave speeds ∼ 3 kms⁻¹, this gives ω/(2π) » 0.0005Hz. Seismic waves are mostly in this regime.

a p- a1 = (K + = ) K+V(VE) + V .

a p- a1 = (K + = ) K+V(VE) + V . (12.4b)

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