Fracture and separation histories of stretched belemnites and other rigid-brittle inclusions in tectonites

Abstract

Apparent extension of a stretched rigid inclusion ( e R = L f, L 0−1 where L 0 and L f are original and final lengths respectively) is always less than strain-reversal extension ( e f ) calculated by sequentially closing inter-fragment gaps until the inclusion is restored to its original length. Differences between the two measures are strongly influenced by the number of fractures, n, and their timing within the total stretch history, and weakly influenced by the fracture location. Several fracture-and-separation models are established to explore these differences using Monte Carlo simulations, all normalized to e R = 0.5. When fragment and gap lengths are random and uncorrelated, e F values fall in the range 0.5 < e F < 1.0. More highly structured models yield a smaller range of possible e f values; the expected (mean) value is still much greater than 0.5 when n is small but approaches e R with increasing n and with decreasing time interval between successive fractures. Model predictions are compared with stretched belemnites in the external French Alps. Results indicate that belemnite fracturing continued throughout a substantial proportion of total stretch history, the proportion varying from locality to locality and correlating strongly with maximum stretch recorded. This probably reflects variations in stress and suggests that, if constant rheology is assumed, stretched belemnites may be used to estimate relative strain rates as well as absolute strains.