The actual, countable annual layers in ice cores can be counted back to 20,000 years after which the ice has compacted so much it becomes difficult to distinguish them. However the ice cores themselves are steeper still by miles. But just for the sake of proof, you already have 14,000 years of ice that existed before the people who misinterpret the Bible say the universe existed.
http://www.encyclopedia.com/doc/1G2-3409400161.html
Here's another non-linearity article, it's quite thought provoking.
Ice Cores and the Age of the Earth by Larry Vardiman, Ph.D.