How does one explain this pattern generated by earthquake waving driving a pendulum? How to explain this pattern generated by earthquake wave driving a pendulum?  Specially, there are three groups of curves that look categorically different:
1) The group of curves outside the olive-shaped envelope
2) The group of intertwined curves at the center
3) The group of curves inside the envelope but outside (2).

 A: It's difficult to say for certain because so many designs are possible. However, this might shine some additional light on the question. Based on historical seismograph tracings and possible arc paths of the pendulum when set in motion by a person, I would speculate that only the inner rose pattern (the iris and pupil of the eye) was created by the quake. I believe the sclera and upper/lower lid portions of the eye were likely preexisting. 
https://www.bgs.ac.uk/discoveringGeology/hazards/earthquakes/History_of_instruments.html
A: This seems to be some new kind of seismogram to me. Looks like I am right. Robbed directly from wiki,

The principle can be shown by an early special purpose seismometer. This consisted of a large stationary pendulum, with a stylus on the bottom. As the earth starts to move, the heavy mass of the pendulum has the inertia to stay still in the non-earth frame of reference. The result is that the stylus scratches a pattern corresponding with the Earth's movement.

So, I'll start in the some sorted order.

The group of curves outside the olive-shaped envelope

I think this is the starting point of the shock. The analogy is something like this: The pendulum is still in motion with the last past earth's frame and it has not synced itself again. So, when it does - the pattern starts to change. During the tremors, the pattern is disturbed a lot. One more thing to notice (your image doesn't show the scale): They have used a very small pendulum (a sand tracing one) for the design (sensitivity maybe) and allowed to move on sand (looks like some muddy colloid so that it shouldn't be affected so much by friction, $\mu$ is very low)
The smooth ellipses were originally formed before the earthquake. How I tell this? We know the pattern for a pendulum. Don't we? It has started from the top of the pattern, curves somewhere near the middle, then the ellipse continues to incline about an angle (which is due to the earth's motion).

The group of curves inside the envelope but outside (2)

As the quake starts to show up, the pendulum notes down every fractional increase of the it's magnitude. And so, the inclination of the ellipses totally curve out (perpendicularly) thereby forming new ellipses at right angles to the previous ones. Now you might ask me a question...
Why are the perpendicular ellipses confined to a small region and do not spread out?
As you can see in the image, each and every fringe in the larger ellipses are equidistant (somewhat) from each other. As the magnitude increases, the fringes begin to compress which could be noticed in the small ellipses. This shows that the quakes weren't too smooth. As the pendulum starts the ellipse, the quake forces it to wiggle in the exactly opposite direction. For this reason, 

The group of intertwined curves at the center

This is very very simple than the others. The earthquake has increased to its utmost magnitude. Now, the ground has shaken in every direction which has confused the pendulum to oscillate everywhere. Luckily, it has also made a rose by its random twist & twirl...
A: The link in the question explains how it was formed.
The outer concentric elipses were formed before the earthquake by someone just setting it in motion.
The inner elipses were formed by the earthquake itself, these gradually approaching circles over time to overwrite the earlier elipses, finally coming to rest at the centre.
The second position of rest suggests there was natural resettlement of the ground after the earthquake, and this gave rise to the strange rose pattern overwriting the earlier pattern.
