Formation of shatter cones by symmetric fracture bifurcation: Phenomenological modeling and validation

Abstract

Several models of shatter cone formation require a heterogeneity at the cone apex of high impedance mismatch to the surrounding bulk rock. This heterogeneity is the source of spherically expanding waves that interact with the planar shock front or the following release wave. While these models are capable of explaining the overall conical shape of shatter cones, they are not capable of explaining the subcone structure and the diverging and branching striations that characterize the surface of shatter cones and lead to the so-called horse-tailing effect. Here, we use the hierarchical arrangement of subcone ridges of shatter cone surfaces as key for understanding their formation. Tracing a single subcone ridge from its apex downward reveals that each ridge branches after some distance into two symmetrically equivalent subcone ridges. This pattern is repeated to form new branches. We propose that subcone ridges represent convex-curved fracture surfaces and their intersection corresponds to the bifurcation axis. The characteristic diverging striations are interpreted as the intersection lineations delimiting each subcone. Multiple symmetric crack branching is the result of rapid fracture propagation that may approach the Raleigh wave speed. We present a phenomenological model that fully constructs the shatter cone geometry to any order. The overall cone geometry including apex angle of the enveloping cone and the degree of concavity (horse-tailing) is largely governed by the convexity of the subcone ridges. Straight cones of various apical angles, constant slope, and constant bifurcation angles form if the subcone convexity is low (30°). Increasing subcone convexity leads to a stronger horse-tailing effect and the bifurcation angles increase with increasing distance from the enveloping cone apex. The model predicts possible triples of enveloping cone angle, bifurcation angle, and subcone angle. Measurements of these quantities on four shatter cones from different impact structures and lithologies agree well with model predictions.