Stretched exponential relaxation of viscous remanence and magnetic dating of erratic boulders

Viscous remanence continuously increases with the duration of reorientation of rocks, and the remanence gets partially overprinted in rocks parallel to the Earth's magnetic field. This overprinted viscous remanence is unblocked at a certain temperature that enables the estimation of the time required for the rock to acquire the magnetism, by assuming the exponential law of Néel's single-domain theory. However, previous results of dating the rocks by the exponential law have shown older ages than radiometric or cosmogenic exposure ages. Néel's exponential decay law is applicable to a system whose magnetic grains have an identical relaxation time. However, in real systems, the expected behavior is not usually observed because relaxation times vary for individual grains. Moreover, the variation of viscous remanence with the logarithmic law for a distribution of relaxation times is predicted to be concave downward. Here we found that the stretched exponential law, exp{−(t/τ)^{1 − n}} with 0 ≤ n < 1, explains previously published data on viscous decay. The observed stretched exponential relaxation can be interpreted in terms of the global relaxation of a system containing many relaxing species, each of which decays exponentially in time with a specific fixed relaxation rate. Using this law, we derived an extended time-temperature relationship of magnetite involving the Néel's exponential decay law with n = 0 and a system containing many relaxing times with variable n. The extended time-temperature relationship shows that the age of a coral tsunami boulder with high anomalous unblocking temperatures can be fitted with an assigned radiometric age.