Is a seismic gravity perturbation a gravitational wave? Powerful enough earthquakes generate gravity perturbations that propagate at $c$ and can be detected by sensitive enough seismographers. See, e.g., this news in Nature:

In the latest paper, Vallée and his colleagues report many more observations of gravity signals immediately after the Tohoku quake. The signal was most apparent at monitoring stations between about 1,000 and 2,000 kilometres from the quake’s epicentre. At that distance, the fast-as-light signals had enough time to arrive and be clearly recorded before the seismic waves swamped them.

There isn't any fundamental difference between signals/pulses and waves (which can be described as a sequence of pulses). So, if spacetime can be pictured as a sort of a medium and gravitational waves as perturbations that propagate through it, these seismographic measurements would appear to constitute observations of gravitational waves.
But almost no one is referring to them as such, so this understanding should be mistaken. Why? Is the description above taking the mechanical wave analogy too far? Is this gravitational pulse an example of a change in the "quasistatic gravitational field" (see, e.g., this question)? If so, how exactly?
 A: 
how is the propagation of this change in gravity (from that point in the crust to the detectors) not a gravitational pulse? 

Let us take two negative charged masses $a$ and $b$ at a distance $r$, , assume they are "fastened" lightly. If we move $a$  towards $b$, reducing $r$ , the field will change and $b$ will move due to repulsion. In classical electromagnetism there will be some radiation due to the changing fields, but the main mover is is  the repulsion, not an effect of radiation. The repulsive forces are bound to be transmitted  by the velocity of light.
Gravitational fields are attractive. In a solid as the mantle of the earth, the system is stable. If a motion changes the field distribution, like a seismic event, the relative attractive fields will change and the change in the field will go as the velocity of light. In gravitation also there are gravitational waves generated in a more complex manner than electromagnetism, there should be asymmetric mass distributions, but due to the very small values of the gravitational constant these waves will be very very faint. As with the electron example above, the main input comes from the changing forces due to the changing field .
If we go to the quantum mechanical level, the repulsive force between electrons is with virtual photons, and assuming quantization of gravity, it will be virtual gravitons which will be responsible for the attractive effect. Electromagnetic waves are emergent from zillions of real photons, and one expects that gravitational waves will be emerging from zillions of real gravitons.
Thus the effect seen is gravitational and has to depend on the velocity of light, but it is not a gravitational wave.
A: This is not gravitational radiation. This is just changes in gravity measured by gravimeters due to the changing distribution of rock. As rock moves then from a Newtonian perspective this changes the Newtonian gravitational force locally.
Advanced physics though could be used. Sensitive atomic clocks placed around the world could pick up the buckling or rock. As the mass distribution changes the relative clock rates of atomic clocks would change. Gravitational radiation is also plausible, where some years back I calculated how gravitational radiation could be detected in a nuclear burst. With an earthquake the treatment would be difficult. but it is not impossible that measurable gravitation waves could be detected with LIGO or some other interferometer.
A: As you point out, these detected wavelike gravitational phenomena are in some senses similar to the "traditional" gravitational waves detected by LIGO, and in other senses different. So whether or not they count as "real" gravitational waves is essentially just a question of exactly where you draw the boundary of your definition. The physics community tends to universally formalize definitions for concepts much less often than the math community does, so different physicists might answer this question in different ways.
Nevertheless, I personally would argue that these aren't "real" graviational waves, because I think that they're sort of qualitatively less interesting. Although I haven't thought about this very carefully, I think that a rough heuristic for a useful place to draw the boundary is "Would these waves still exist if the speed of light/gravity were infinite?". For "traditional" gravity waves like from black hole mergers, I believe that the answer is no, because they display some periodic aspects that don't simply reflect the periodicity of the sources. But for these seismic waves, the answer is yes, because they would still appear (very slightly sooner) with the same qualitative behavior in a hypothetical non-relativistic universe perfectly described by Newtonian gravity with no delay. So that makes then in some sense "less interesting" (and certainly not a useful experimental validation of GR).
I'm sure that there are some more subtle edge cases where this heuristic remains ambiguous, though.
