Fortunately, there is a lot that can be done to mitigate the
effects of earthquakes. Some expensive technology has been
developed, but there also exist many practical and inexpensive
measures that can be taken. Some simple methods are illustrated
here, and some references to other information is included below.
(a) shows a coil of plastic tubing used as a cushion and to provide better balance for a round-bottomed vessel, preventing the vessel from tipping over.
(b) shows a filament (such as fishing line) used to anchor the vessel to the mounting surface and prevent tipping.
(c) shows the use of a bag of sand used to weight the vessel and center its point of balance, preventing tipping.
(d) shows the use of a specially prepared armature to hold the vessel and prevent it from tipping. (Point of contact with object can be cushioned - with a plastic coating, for example.)
(e) shows the vessel placed in a substrate which has been shaped or hollowed out to fit the base of the vessel.
(f) shows the use of a gum, clay, or wax to add support for the vessel from the sides and prevent tipping.
It is also possible to brace or secure shelving to reduce the chances of damage due to tipping.
For storage areas, it makes sense to cover or close shelf openings. This can be accomplished with doors, metal rods or panels, elastic cords, or nets - my preferred method. Barriers of elastic and even metal will flex and bend in an earthquake and may allow objects to drop through the gaps this produces. Hard surfaces are also dangerous if the objects are bounced against them. Nets allow visibility of shelf contents and are a soft barrier that shouldn't damage artifacts or specimens.