A NEW METHOD FOR IMPROVED DATING OF LONG SPELEOTHEM RECORDS

The suggested new method for establishing of hard timescale of sediment records is based on the fact that orbital cycles have duration stable in time. So their pseudo- variations derived by evolutive spectral analysis of sediment records are in fact due only to variations of the sedimentation rate of the sediment. The ratio between the real and pseudo- duration of the orbital cycles gives the sedimentation rate deviation from the mean sedimentation rate of the dated sequence of the sediment. We use it to establish “solid” time scale of sediment records.

For this purpose we used a new method for time series analysis of unevenly sampled data. It's principles following: The time series is divided into intervals with equal time lengths T equal to the period for which we search the amplitude. The so obtained pieces are then placed one over the other. The resulting picture forms a distinct pattern when we use a period for cutting the time series into pieces, which is equal to some of the modes or harmonics of pulsation of the signal. The window is divided into ns x ns equal squares. Then the number of ‘hits’ h_i (points of the signal which lie within each square) is counted for each square i. Then we calculate the probability p_i with which the number of hits is indeed h. It is given by the formula:

(1) p_i =C_n^hi ns^-2hi(1 – ns^-2)^n-hi

where n is the number of all points in the original signal, and 1/ns² is the probability that one of the n points lies within a certain square. After finding p_i, we find the ‘total’ probability P that the set of independent events (h_i hits in the i-th square) really ‘happens’:

(2) P=Πp_i

We denote this probability to be the amplitude of the signal at the given period T for the studied time series. The so obtained periodogram we call Probability Distribution Diagram (PDD).

This method allows us to study the variations of the sedimentation rate of speleothems. Speleothem luminescence time series are a proxy index of Solar Insolation (SI), so they contain orbital variations. The evolutive spectra of speleothem records from Duhlata cave, Bulgaria has been calculated for cycles in the interval from 9000 –45000 years. Obtained variation of the pseudo- duration of the orbital cycles has been used to calculate the variation of the growth rate (sedimentation rate) of the speleothem and to establish hard time scale of the record.