INVERSION OF STABLE ISOTOPE SIGNALS IN TOOTH ENAMEL: RECOVERING THE PRIMARY ISOTOPE TIME-SERIES

Within the last several years, workers have sought to gain seasonal information from stable isotopes by analyzing series of samples along the growth axes of teeth. These intra-tooth isotope profiles directly record seasonal information about diet and environment because tooth enamel forms progressively from crown towards root on a time-scale of weeks to months. However, the tooth enamel signal is time-averaged and damped, partially because of the protracted period of time over which a volume of developing enamel accumulates mineral. Therefore a high-amplitude pattern of isotopic variation in an animal will be recorded as a lower amplitude pattern of isotopic variation in tooth enamel. This poses significant problems for meaningful interpretation of intra-tooth isotope profiles. To this end, we have explored the use of inversion methods that allow for detailed reconstruction of input signals based on the measured enamel signal and knowledge of the enamel maturation parameters for teeth. The tooth enamel problem is posed as a linear system Am=d, where A is a matrix that uses maturation parameters and sampling geometry information to relate the input vector m (the primary isotope time-series) to the measured isotope vector d. MATLAB codes have been written that calculate A using maturation parameters and sampling geometry as inputs. Additional codes have been developed that solve for a family of input series m that predict d within sampling and isotope uncertainty. These methods allow for the reconstruction of meaningful input signals.