Such catastrophes would have to do a better job of isolating people than they've been doing so far. Humanity is remarkably similar from a genetic perspective when taken as a species. I don't think your theory stands much chance unless you're willing to go interplanetary or inter-stellar. On planet earth we are remarkably mobile, to the point where if we lose all shipping ability and even knowledge of other civilizations that we'll likely re-discover all this from first principles within at most a few thousand years.
I was thinking "catastrophe" as in a wipe out the dinosaurs asteroid hit or a global pandemic that takes out 95% of the population (think Ebola)or an EMP event that results civilization collapse, etc. So if Silicon Valley residents are the only survivors (god help us :-)and there is a higher IQ density there than other locations and if IQ is really significantly genetic, then the average IQ of humans has increased and can be maintained in the population. Other pockets of survivors would have an IQ density similar to that present in the general population existing before the catastrophe and based on our hypothetical case, lower than that in Silicon Valley. It is the geographic isolation and geographic concentration of a particular genetic trait that makes this type of selection possible.
Nothing. I was just using an example of which I had some familiarity. In the context of this hypothetical thread, it is interesting to note that there is apparently some scientific data suggesting that Asians have a slightly higher IQ than other races. Not being an expert I can't readily provide the references. The other reason for using Silicon Valley as an example is that the theoretical we are discussing requires a survivor population that has a higher IQ density than the average population. The larger the sampling the closer the IQ density approaches average. Although I guess the argument would still hold for a city or country. I was just thinking that the difference in IQ density between Silicon Vally and California as a whole might be 20 points while the difference between China and the US might be 2 points.