If one assumes that the accumulation rate has remained constant in the upper, more recent sediments, then the age of the sediments can be calculated for any depth in the core.
In case (3), where the deepest core sections appear to be above background level, the excess Po-210 activity cannot be calculated because there is no estimate of the background level of Po-210.
It is possible to indirectly estimate the background Po-210 by measuring the Ra-226 (via Rn-222) in the sediments but this is often omitted because of the additional analytical costs.
Radium-226 in the soil exhibits the same level of radioactivity as uranium-238 from which it was originally derived, because of a natural phenomenon called secular equilibrium.
The overall result is that radium-226 is found at low and essentially unchanging levels in soils everywhere.
After several days residence time in the atmosphere, the Rn-222 naturally decays to polonium-218, a metallic radionuclide which, over a period of hours/days, falls to the earth with dust and rain.
A number of subsequent radioactive decays occur over a period of minutes and Pb-210 (half-life = 22.3 ) is produced.
Fossils are generally found in sedimentary rock not igneous rock.