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Shear‐wave splitting observations can provide insight into mantle flow, due to the link between the deformation of mantle rocks and their direction‐dependent seismic wave velocities. We identify anisotropy in the Cook Inlet segment of the Alaska subduction zone by analyzing splitting parameters of S waves from local intraslab earthquakes between 50 and 200 km depths, recorded from 2015–2017 and emphasizing stations from the Southern Alaska Lithosphere and Mantle Observation Network experiment. We classify 678 high‐quality local shear‐wave splitting observations into four regions, from northwest to southeast: (L1b) splitting measurements parallel to Pacific plate motion, (L1a) arc‐perpendicular splitting pattern, (L2) sharp transition to arc‐parallel splitting, and (L3) splitting parallel to Pacific plate motion. Forward modeling of splitting from various mantle fabrics shows that no one simple model fully explains the observed splitting patterns. An A‐type olivine fabric with fast direction dipping 45° to the northwest (300°)—aligned with the dipping slab—predicts fast directions that fit L1a observations well, but not L2. The inability of the forward model fabrics to fit all the observed splitting patterns suggests that the anisotropy variations are not due to variable ray angles, but require distinct differences in the anisotropy regime below the arc, forearc, and subducting plate.

 

Abstract An elastic map $\mathbf {T}$ T describes the strain-stress relation at a particular point $\mathbf {p}$ p in some material. A symmetry of $\mathbf {T}$ T is a rotation of the material, about  $\mathbf {p}$ p , that does not change  $\mathbf {T}$ T . We describe two ways of inferring the group $\mathcal {S} _{ \mathbf {T} }$ S T of symmetries of any elastic map $\mathbf {T}$ T ; one way is qualitative and visual, the other is quantitative. In the first method, we associate to each $\mathbf {T}$ T its “monoclinic distance function” "Equation missing" on the unit sphere. The function "Equation missing" is invariant under all of the symmetries of  $\mathbf {T}$ T , so the group $\mathcal {S} _{ \mathbf {T} }$ S T is seen, approximately, in a contour plot of "Equation missing" . The second method is harder to summarize, but it complements the first by providing an algorithm to compute the symmetry group $\mathcal {S} _{ \mathbf {T} }$ S T . In addition to $\mathcal {S} _{ \mathbf {T} }$ S T , the algorithm gives a quantitative description of the overall approximate symmetry of  $\mathbf {T}$ T . Mathematica codes are provided for implementing both the visual and the quantitative approaches. 

The elastic map, or generalized Hooke’s Law, associates stress with strain in an elastic material. A symmetry of the elastic map is a reorientation of the material that does not change the map. We treat the topic of elastic symmetry conceptually and pictorially. The elastic map is assumed to be linear, and we study it using standard notions from linear algebra—not tensor algebra. We depict strain and stress using the “beachballs” familiar to seismologists. The elastic map, whose inputs and outputs are strains and stresses, is in turn depicted using beachballs. We are able to infer the symmetries for most elastic maps, sometimes just by inspection of their beachball depictions. Many of our results will be familiar, but our versions are simpler and more transparent than their counterparts in the literature.