There are several techniques in earthquake engineering that are used in skyscrapers.
One is called a “tuned mass damper”, which is a heavy device that moves in a way that reduces or disrupts resonance frequency oscillations (which can be caused by winds or earthquakes and result in building’s destruction if they get too strong). For example, the Taipei 101, once the tallest building in the world, has a 660 ton steel pendulum suspended near its top.
Another technology is base isolation, such as using bearings or springs with dampers, to avoid vibration from earthquakes. The idea is to isolate the building from its substructure.
Tapering structure improves stability as well. It refers not necessarily to tapering the shape (i.e. making a pyramid), but also mass or stiffness of the building. Other techniques include elevated building foundations and steel plate shear wall systems. If you need more info, you can look up any of those technologies.
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