On the construction of geomagnetic timescales from non-prejudicial treatment of magnetic anomaly data from multiple ridges

When marine magnetic-anomaly data are used to construct geomagnetic polarity timescales, the usual assumption of a smooth spreading-rate function at one seafloor spreading ridge forces much more erratic rate functions at other ridges. To eliminate this problem, we propose a formalism for the timescale problem that penalizes non-smooth spreading behaviour equally for all ridges. Specifically, we establish a non-linear Lagrange multiplier optimization problem for finding the timescale that (1) agrees with known chron ages and with anomaly-interval distance data from multiple ridges and (2) allows the rate functions for each ridge to be as nearly constant as possible, according to a cumulative penalty function. The method is applied to a synthetic data set reconstructed from the timescale and rate functions for seven ridges, derived by Cande & Kent (1992) under the assumption of smooth spreading in the South Atlantic. We find that only modest changes in the timescale (less than 5 per cent for each reversal) are needed if no one ridge is singled out for the preferential assumption of smoothness. Future implementation of this non-prejudicial treatment of spreading-rate data from multiple ridges to large anomaly-distance data sets should lead to the next incremental improvement to the pre-Quaternary geomagnetic polarity timescale, as well as allow a more accurate assessment of global and local changes in seafloor spreading rates over time.