How do you measure vibration?

Vibration transducers can be split basically into two types – accelerometers and geophones (or seismometers). Accelerometers have an output proportional to acceleration, and geophones have an output proportional to velocity. So how can both be used to measure vibration?
There’s a basic relationship between acceleration and velocity – the former being the rate of change, or the differential, of velocity. Therefore we can easily convert between the two by integrating an acceleration signal to yield a velocity signal. This is normally done in the time domain, using a filter (called an integrator), but it can also be done in the frequency domain by dividing an acceleration spectrum by 2πf, where f is the frequency. This effectively slopes the spectrum by -6dB/octave, so a velocity spectrum will appear to have a lot fewer high frequency components

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