They mean that there's a preferred lineation to the individual grains. Consider cutting a sphere out of something similar to this: http://minerva.union.edu/hol

They mean that there's a preferred lineation to the individual grains. Consider cutting a sphere out of something similar to this: http://minerva.union.edu/hollochk/c_physicalgeology/images/Lineation1.jpg http://minerva.union.edu/hollochk/c_physicalgeology/images/L... You can imagine making a sphere by packing together a bunch of small needles. Not all of them need to be oriented the same way, but they can align under the right conditions. Because the needles are small in comparison to the size of the sphere, that alignment can change depending on where you are in the sphere. In this case, they're hypothesizing that the "needles" are basically oriented differently at the outside of the sphere than near the center. More specifically, that they're oriented north-south at the outside of Earth's inner core and "east-west" near the center of Earth's inner core. This is based on the observation that there's a strong anisotropy to the seismic velocities in the innermost parts of the Earth's core. The easiest way to explain any sort of seismic anisotropy this is through alignment of mineral grains (In many minerals sound travels faster along one axis of the crystal structure than along the other). However, this is one of the first times anyone's been able to clearly resolve differences in aniostropy with depth into the inner core.