(Is there one?) What is the Earth's natural resonant frequency?
I will assume you are not referring to the Electromagnetic resonance, usually referred to a Schumann resonances (in which there is an abundance of available info).
If you are referring to the earth's natural mass resonant modes, I believe there are several, (which are predicted and derived mostly from geophysical and earthquake data).
Not commonly known is the fact that there is a low frequency earth resonant mode of about one every 54 minutes,... that Joseph Weber (and Robert Forward) tried to use in Gravitational wave detection using very sensitive gravimeters (long long time ago in a distant land ;))....before deciding to build the resonant (aluminum) bar detectors.