The past environment is often reconstructed by measuring a given proxy (e.g. δ¹⁸O) in an environmental archive, i.e. a species which gradually accumulates mass and records the current environment during this mass formation (e.g. corals, shells, trees, etc...). When such an environmental proxy is measured, its values are known as a function of distance. However, to relate the data to environmental variations, the date associated with each measurement, i.e. the time base, should be known. This is not straightforward solved, since species usually do not grow at constant rates. In this paper, we investigate this problem for annually resolved archives, which exhibit a certain periodicity. Such signals are often found in clams or corals. Due to variations in accretion rate the data along the distance axis have a disturbed periodic profile. A method is developed to extract information about the accretion rate, such that the original (periodic) signal as function of time can be recovered. Simultaneously the exact shape of the periodic signal is estimated. The final methodology is quasi-independent of choices made by the investigator. Every step in the procedure is described in detail and finally, the method is exemplified on a real world example.