# Seismic Wave modelling: Elastic Wave or Acoustic Wave?

I am modelling a seismic wave equation using FEM. In the few papers that I read, I understand the following: (Kindly correct me if you disagree)

• A shear (secondary wave - no change of volume) is more important to model than the compression (primary wave - no rotation) as it brings more devastation than the latter.

• The elastic wave equation is a better representative of a seismic wave than the acoustic wave equation because simulating it, we propagate both 'p' and 's' waves in the mesh instead of just 'p' which we get from simulating acoustic equation. (p - primary; s- secondary)

• The elastic wave equation also known as Navier's equation of elastodynamics can be multiplied by curl operator to give the Shear wave equation, or it can be multiplied by divergence operator to give the acoustic wave equation. Both shear and acoustic wave equations are very similar except for the expressions for their speed. This expression is what differentiates both the equations and is responsible for the shape that they take. I say this because I found both expressions to be exactly same except that the acoustic wave also uses Lame's parameter $\lambda$ in addition to shear modulus $\mu$ and mass density $\rho$.

My main concern is to know which waves are propagating in my mesh if I am simulating the elastodynamic or elastic wave equation. Is it both 'p' and 's'?

Thank you!

• Yes, its both P & S. Having said that I am not sure if the separation is useful as far as teaching students is concerned. In any case the FE implementation is rather straightforward. Take a look at geology.wisc.edu/~stali/defmod (I am the author) Aug 9 '16 at 13:02
• It is possible to simulate just a P wave or just an S wave, for example in a waveguide with periodic boundary conditions. However, once such a wave impinges on any physical boundary or an obstacle, the other type of wave will be generated immediately. Aug 9 '16 at 14:15
• @DanielRch So that means, when my 'p' and 's' waves generated from a source are hitting a physical boundary, they are automatically generating surface waves like love and rayleigh waves? Correct?
– CRG
Aug 9 '16 at 17:14
• @stali thank you! I was wondering what is free field BC? If I give a dirichlet BC of zero on a boundary, the wave reflects back. Another option maybe to create a sponge layer ot Absorbing BC to absorb/ damp the hitting waves. But what if I define the physical boundary and do not provide any Dirichlet condition to it? Is that a free boundary which can simulate the ground surface where I want to observe the displacement in Paraview? What I am asking is what BC, if any, should we provide to the ground surface where we want to visualize the effect of incoming wave? Thanks a lot.
– CRG
Aug 9 '16 at 17:23
• Love and Rayleigh waves are neither P waves nor S waves, and yes, they are also usually generated when an elastic wave hits a boundary. Aug 9 '16 at 17:23