Correlation of Time Series: An Inverse Approach with Applications in Geology and Geophysics: ABSTRACT
Douglas G. Martinson · AAPG Bulletin · 1982
A simple mathematical inverse method has been developed to correlate two time series Y1(x1) and Y2(x2), where these two signals are related to each other by a mapping function x1(x2). The mapping function describes differences between the two signals and is parameterized in terms of a sum of simple functions of unknown coefficients, ai. These coefficients are estimated from the time series with the assumption that the best coefficients are those which minimize the difference between Y1[x1(x2)] and Y2(x2). The standard analytic errors in the estimates of ai and thus the uncertainty in x1(x2), have been calculated and are negligible. The method has been applied to the correlation of stratigraphic records, well logs, seismic records, and magnetic anomalies. In all cases, high resolution correlations have been attained and continuous mapping functions recovered. The mapping functions in the first three of these applications reveal the continuous change in relative sedimentation rate histories or thickness of strata between the two profiles being correlated. In the magnetic anomaly application, it reveals asymmetries in the spreading rates at the particular spreading center. Uniqueness of the correlations (at any particular level of resolution) is estimated statistically and analytically.