How old is the Earth by the Annual observations? (tree rings, ice cores etc...)
The longest record of annual cycles (Devil's Hole calcite data)stretches back 500,000 years. But that does not represent the age of the earth, merely the minimum age of the earth. That calcite data is consistent with uranium-series dating. The uranium-series dating is used on ancient rocks to give dates of close to 4 billion years old. Argon radiometric dating has produced dating consistent with known historical lava flows and the eruption of Mt Vesuvius. The same technique has dated ancient rocks at close to 4 billion years old.
The logical conclusion is that the earth is at least 4 billion years old.