warning system

I don't quite understand the last part about the computer, but grammatically it's acceptable.
What is actually meant in the if clause, of course, is Even if we had had the ..., but the substitution of had for had had does not obscure the real meaning.

CJ

New2grammarEven if we had the earthquake detection system in place, we still wouldn't have gotten more than a second or two warning because the waves got here at the same time the computer was processing.

It says the computer that processes seismic signals would still be processing the data when the earthquake waves hit the city because of the s

New2grammarWould it be better to use "would have gotten" and "would still be" in place of the bolded?

You have to realize that there is no "better" in this case. Both are grammatical and possible. Each means something different. You have to choose the one that tells the truth about the situation.
The question is like saying this:
Which is correct?

Wow. I didn't know you would interpret it that way.

CalifJimThe question is like saying this:

Which is correct? I saw a dog. or I saw a cat.

No. It's purely hypothetical. It's said by a seismic authority at a news conference regarding today's earthquake in LA.
She said the original but since the system is not yet operation

New2grammarNo. It's purely hypothetical.

If so, you need the "would"s. It seems to me, from what you've said, that the speaker who made the original statement was not as precise as he or she could have been.
CJ

New2grammarIt's purely hypothetical.

In that case you need the would's. It sounds like the original speaker was being less precise than he or she could have been.
CJ