I suppose I should verify the understanding of anisotropy I gleaned over the first week for you ladies and gentlemen.
The basics: often, we idealize a fluid as isotropic, meaning that it has the same properties in all directions. It follows that within each broad category of seismic wave, p-waves and s-waves (compressional, longitudinal waves which have amplitudes along a stress, and shear, transverse waves which have amplitudes orthogonal to a stress), waves travel at the same speed no matter their directions.
However, many earth materials, such as olivine, don't exhibit this. They have orientations which propagate waves faster or slower due to the "stiffness" along their directions, computed by the bulk and shear moduli. For an analogy, imagine how fast a taut Slinkie carries a compression verses a loose one, how quickly a tense rope carries a disturbance, or how the speed of sound is greater in brass than air. Often, the spacing in the medium's structure is lesser in the fast directions and greater in the slow directions. (Generally, waves travel faster under greater pressure, but that's a finer point I won't elaborate upon here for the sake of simplicity.) The equations say so, and you can't lie using Greek letters. (Believe me, I've tried.)
What are some geological processes that can cause anisotrophy? In the crust, metamorphic foliation is sometimes at fault--when stresses cause materials in a rock to line up along a direction, so the rock doesn't have equant properties in that direction. In addition, microcracks in sedimentary rocks slow waves attempting to cross this spacing. In the upper mantle, where the mineral olivine is prevalent, the molecular structure of olivine facilitates the transmission of stress similarly.
How do we measure it seismically? When an s-wave enters an anisotropic medium, it splits into two perpendicular polarizations dependent on the medium's anisotropy. One polarization, "stiffer" than the other, races ahead. You can then note the polarizations of incoming s-waves and their spacings in time to estimate the anisotropic orientation(s) and thickness of the medium. Hence, we specifically examine the properties of incoming s-waves.
That should do the subject justice for now. I'll return to preparation for a brief presentation later today.
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