Maybe a kind of low-pass system would allow it to react to slower change and ignore the higher amplitude, higher frequency of the tremors， though.
(Did I do that right?)
However, the earths crust deforms a few cm due to tidal forces. Which weekens local gravity. Aparently you can measure tides in a trees sap so detecting them on a small scale is probably possible. (My google fo is failing to find that one though.)