An inverse approach to signal correlation

A simple mathematical inverse method is used to correlate two time series D ( x ) and R ( t ), where these two signals are related to each other by the mapping function x ( t ). The mapping function describes stretching and squeezing of one signal with respect to the other. The method assumes that D ( x ) and R ( t ) are known, while x ( t ) is not. The mapping function is parameterized in terms of a sum of simple functions of unknown coefficients a i ;. These coefficients are estimated from the time series with the assumption that the best coefficients are those which maximize the coherence between R ( t ) and D x ( t ). The maximization is performed iteratively, beginning with some initial estimate of a i . The standard error in the estimates of a i and the uncertainty implied in x ( t ) is calculated. The effect of noise in the signals and sharp slope changes in the mapping function are assessed by empirical testing. Results suggest that mapping functions containing features with periods down to 6% of the signal length and as sharp as hiatuses can be recovered even if the signals contain significant noise. The method is applied to determining differential sedimentation rates from O 18 profiles measured in two cores and to measuring differential spreading rate about a mid‐ocean ridge by using marine magnetic anomalies.