If your Mac had Tiger pre installed when you purchased it, it may not be able to run Mavericks.
Check here > OS X Mavericks: System Requirements
The next time Safari crashes, copy and paste the entire crash report in your Reply. That should reveal what the problem is.
Rarely does an upgrade fix a problem with a browser crashing because it's usually due to third party plugins of extensions.
Thank you Carolyn,
My machine is a late 2009 iMac, a replacement for another that had run Tiger. Some of the cruft I am dealing with was migrated over from that time.
Your reply, however, tells me that the problem is (probably) due to a conflict between the new version of Safari and some plug-in or extension for Safari 6.05 that I am using now. As for sending the "entire crash report" it is my ardent wish never to see one of those again. The two restore sessions already done have increased the bulk of recent Time Machine data to the point that the earliest I have is less than a month old on an external HD that is much bigger than the internal drive.)
I might be willing to risk another update/crash if I could first reduce Safari 6.05 to the plain vanilla state that should update successfully. Otherwise I will carry on until all the housekeeping is done and then update to Mavericks. ....
(Long time out while this site did maintenance) ....
I have now found lots of instructions for removing or disabling plugins or extensions. I tried simply disabling from Safari > preferences > security > (or) extensions and Safari became quite unresponsive to the point that I could not seem to reply to this post.