Formation of shatter cones by symmetric fracture bifurcation: Phenomenological modeling and validation
Formation of shatter cones by symmetric fracture bifurcation: Phenomenological modeling and validation
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DOI：
10.1111/maps.12677
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发表时间：
2016-08-01
影响因子：
2.2
通讯作者：
Wilk, Jakob
中科院分区：
文献类型：
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作者：
Kenkmann, Thomas;Hergarten, Stefan;Wilk, Jakob
几种破碎锥地层模型要求锥尖处存在非均质性，且与周围围岩存在高阻抗失配。这种非均质性是与平面激波前缘或随后的释放波相互作用的球形膨胀波的来源。虽然这些模型能够解释破碎锥的整体圆锥形状，但它们无法解释子锥结构以及破碎锥表面的发散和分支条纹，这些条纹导致了所谓的马尾效应。在这里，我们使用破碎锥表面的子锥脊的分层排列作为理解它们形成的关键。从其顶端向下追踪一个单一的次锥脊，可以发现每个脊在一段距离后分支成两个对称相等的次锥脊。这种模式被重复以形成新的分支。我们提出，次锥脊表示凹凸弯曲的断裂面，它们的交点对应于分岔轴。特征发散条纹被解释为分隔每个子锥的相交线。多对称裂纹分支是断裂快速扩展的结果，可能接近罗利波速。我们提出了一个现象学模型，它完全构造了任意阶的破碎锥几何。整个锥体的几何形状，包括包络锥体的顶点角和凹度（马尾），在很大程度上是由次锥体脊的凸度决定的。如果子锥的凸度较低（30度），则形成各种顶角、恒定斜率和恒定分叉角的直锥。子锥凸度越大，马尾效应越强，分叉角随距包络锥顶点距离的增加而增大。该模型预测了包络锥角、分岔角和次锥角的可能三重值。对来自不同撞击结构和岩性的四个破碎锥的这些量的测量与模型预测吻合得很好。
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 degrees). 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.