How sensitive are typical seismometers?
The table below gives you a nice summary snapshot up to 2015.


  


Reference:  Kamp, P.J., 2016. Towards an Ultra Sensitive Seismic Accelerometer (Master's thesis, University of Twente).

Sercel accelerometer, the top one in the table, is widely used in Oil and Gas industry, for example, to monitor induced seismicity. Below is an excerpt from the article: "A high-sensitivity MEMS-based accelerometer", by J. Laine and D. Mougenot (2014), The Leading Edge, 33(11).

1 g is about ~10 m/s^2 (9.80665) so 1 ng ~ 10^-8  m/s^2. For the Sercel then 360 ng mentioned in the paper (three times the rms noise level) = 3.6 ^10-6 m/s^2.

Correct me if I am wrong.