This represents a major misunderstanding of what a gravitational wave is. The effect presented is simply the semi-static gravitational field at earth due to the earth, moon and sun. It is predicted by Newtonian gravity. There is no 'wave' that propagated, it's the instant positions of the 3 bodies that change over 1 day (and over 1 year also).
It does not show that the change moved at the speed of light, which gravitational waves do. Nothing in Newton's equations talk about the speed of light. The GR equations for 3 bodies moving like the earth-sun-moon can only be solved approximately, and in this case it'd be through a post-Newtonian approximation. The pseudo-static term(s) would be the same but possibly some GR correction - and if it is (And I'm not sure if the strongest term correction might not be something like the term for the perihelion of mercury, or something else, in any case extremely small and not measurable in their g measurement). But that's not even a grav wave. The grav waves would be even smaller probably - you'd have to compute the rate of change of the quadrupole moment of the configuration, and do some other calculations. The simpler problem of just the grav radiation of the earth-sun rotation around each other gives a resultant power dissipated that translates in the orbit of the earth loosing altitude ('altitude' above the sun) of the size of 1 proton per day. That g change they measured in your graph is about 10 to the minus 7 g's. It isn't even dissipative, as the bodies keep doing the same thing over and over, in your approximation. If you don't see that dissipation you are not seeing the gravitational waves.
There is probably many other ways to see that what you're discussing, what the graphic measured, is not a gravitational wave, but rather a very slow change in a static gravity field, the one produced by the 3 bodies.
Grav waves produce something different than just a change in gravity in one direction, they do it in 2 directions at once, an asymmetrical squeezing of a circle first in one axis and then in the other, like squeezing a balloon in one direction, making it bulge in the other.
Like Nathaniel said, it's like comparing a (semi) static electric field (say produced by rubbing a couple rags together) and moving them around some, with light.
Note: yes, even changing static fields can not produce a change in what's observed at a distance faster than the speed of light, but that doesn't come in at all in your graphic, too small a differential effect for it to see it.
Best Answer
This is the data recorded from the first black hole merger:
The figure is from this paper by the LIGO collaboration. A PDF of the paper is available here.
The detectable signal lasted around 0.1 of a second, but the black holes were orbiting each other so fast that they completed about ten orbits during that time. Basically each oscillation in the data is one orbit.
The data immediately gives the rate of decay of the orbit as the black holes merge and the amplitude with which the gravitational waves are emitted, plus lots of other information hidden away in the detail. This is easily enough to confirm that this was a black hole merger and to measure the masses of the black holes involved.
Each pair of black holes only merge once, so this was the first and last signal detected from that particular pair of black holes. However the universe is a big place and there are lots of black hole binaries in it, so we expect black hole mergers to take place regularly. LIGO has already detected three mergers. The first (shown above) on 14th September 2015, then a second possible detection (at low confidence) in October 2015 and then a third firm detection on 26th December 2015.
LIGO took a pause to upgrade its sensitivity, but is now working again. As a rough estimate we expect it to detect a merger around one a month, that is roughly once a month a black hole binary will merge somewhere in the region of the universe that lies within LIGO's detection limits.
We don't know in advance where an when a merger will occur, so it's just a matter of waiting until one happens near enough to be detected.