How do I secure this post to the structure to protect against seismic damage?
It looks like the posts are toe nailed into the beams, that's pretty common in older construction, it wouldn't pass for new construction in most locales.  

I couldn't say whether slapping on some fittings is the right way to make your home more structurally sound in case of an earthquake.  This answer is just to point you to some of the fittings I've seen and used, maybe this will help you research this further.  

I have had good luck with Simpson Strongtie, they make joist hangers and many other structural fittings.  They have a good web site and good phone support.  Simpson Strongtie  

Some of their post caps have to be installed before the post is set, but this one can be added after the fact:  



However those will only work if the post is standard 6x6 dimensions (not actually 6"x6").  These could be used with any size posts / beams:  

 


They make holddowns for the bottom of the post too:  



but I really don't know if it's wise to anchor into those post bases.  Again, just showing you some fittings, not suggesting you should just go out and install these without further research (contractor, inspector, engineer, etc.)