There are only a few places on earth where you can get a 9 earthquake. Seattle is one, but CA is not., probably an 8ish is about the worst. The internet infrastructure is relatively immune to earthquakes, by weight mostly cables and UPS's and it's quite widely distributed. In spite of appearances earthquake damage can be quite localized. I lived about a dozen miles noth of Loma Prieta and suffered no damage. SF and Oakland were another 30 miles to the north.
The internet was designed to survive all kinds of damage. Larger companies usually have multiple data centers and colos so they can continue operations.
When the big one hits SF, I will probably have to walk a dozen miles to my car. Then I drive home 200 miles south, plug in to the Internet, and see what I just went through.
EDIT: I expect to survive because of tough CA building codes and decades of seismic retrofits. My homes survived two 6.5-7.0 earthquakes, because one of the first things I did after moving in was to make sure of the basics, like foundation ties and reinforced cripple walls.