Seismic analysis and random vibration

Not my primary field, but we do some vibration testing for auto parts.

If you know the actual PSD, then testing to that configuration will give predictive results for the conditions expected.

Testing at single point only gives the outcomes for that specific frequency.

Even if you test at 10 points per octave across the total expected frequency range, then you will still have three issues to deal with.

Firstly you would have to scale the response at each frequency for relative expected magnitude in any expected seismic event. The second is that there may be responses where frequency harmonics are not linear in an additive context. The final concern is that you still have not tested the complete frequency response, but only the response at the sample frequencies. (There could be an undetected destructive harmonic.)

Aside: We've observed filaments inside auto bulbs behaving in wonderful ways at some very specific frequencies.

There is also another analysis that uses a single square wave input to determine system responses, since the square wave consists of additive multiple harmonic sine waves. (I believe that is what has been used for oil exploration where explosive detonations are used as the input signal.)

In summary, if you know the actual PSD and have the equipment to model it, then use that method.

If the item fails, then resort to single frequency searches to find the destructive harmonic so that you can address the issue.