<p>I was studying Landau's elasticity book and I'd like to enhance my physical views on this problem:</p>
<p>&quot;A plane-parallel slab with thickness h (medium 1) lies on an elastic half-space (medium 2).
Determine the frequency as a function of the wave number for transverse waves in the slab whose direction of
oscillation is parallel to its boundaries.&quot;</p>
<p>I had no problem in solving this and I find highly dispersive transverse wave in the first slab. Is this problem modelling how we can get a Love wave from an S-wave? Is the first medium representing Earth's surface (or better, Earth's crust) and the second medium Earth's inner core? If so, why can we describe Rayleigh waves as pure surface waves whereas this is not possible for Love waves? Because if I set the thickness h to zero, I get no dispersion relation out of this problem.</p>

<geophysics><waves>
I'm a theoretical physics with no insights in Earth Science. Is this exercise dealing with Love Waves?
CoolerThanACooler
# I'm a theoretical physics with no insights in Earth Science. Is this exercise dealing with Love Waves?

(Asked by: username_0 on 2024-12-09)

I was studying Landau's elasticity book and I'd like to enhance my physical views on this problem:

"A plane-parallel slab with thickness h (medium 1) lies on an elastic half-space (medium 2).
Determine the frequency as a function of the wave number for transverse waves in the slab whose direction of
oscillation is parallel to its boundaries."

I had no problem in solving this and I find highly dispersive transverse wave in the first slab. Is this problem modelling how we can get a Love wave from an S-wave? Is the first medium representing Earth's surface (or better, Earth's crust) and the second medium Earth's inner core? If so, why can we describe Rayleigh waves as pure surface waves whereas this is not possible for Love waves? Because if I set the thickness h to zero, I get no dispersion relation out of this problem.

**Tags:** geophysics, waves


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