Dynamic fault weakening and the formation of large impact craters

Abstract

Impact craters are the most common landform on planetary surfaces; however, the mechanics of the end stages of their formation are not fully understood. The final stage of crater formation involves the collapse of a hemispherical transient cavity. Around small craters, the limited amount of collapse preserves a bowl-shaped cavity. In contrast, the observed shallow depths and complex inner morphologies of large craters require very low shear strength in the collapsing material. Because the observed amount of collapse cannot be reproduced using quasi-static values for the frictional strength of fractured rock, a temporary weakening mechanism is necessary. Here, we investigate the hypothesis that craters collapse along a network of impact-generated faults that weaken during long displacements at high slip velocities via, for example, frictional melting. Using the CTH shock physics code, we simulate the formation of about 100-km diameter impact craters using a simple strain-rate weakening model with parameters constrained by fault friction experiments on crystalline rocks. The model reduces the coefficient of friction from a quasi-static value (0.6–0.85) to a weakened value (0.1–0.2) when a parcel of fractured material exceeds thresholds for cumulative plastic shear strain (a proxy for slip distance) and shear strain rate (a proxy for slip velocity). During crater formation, the strain-rate weakening model leads to strain localizations that are interpreted to be fault zones. Fault zones are spontaneously created and slip over discrete time intervals during collapse. The strain-rate weakening model reproduces the major geologic features observed around the largest terrestrial craters (Vredefort, Sudbury, and Chicxulub), including shallow depths, fault structures, frictional melt distributions, and deep-seated central uplifts. The good agreement between calculations and observations supports the hypothesis that small volumes of transiently weakened material in fault zones control the collapse of large impact craters.

Introduction

Impact cratering is the most widespread geologic process in the solar system. Although an understanding of the early stages of impact crater formation is well established (Melosh, 1989), the process(es) that controls the mechanics of the end stages of large crater formation remains a matter of great debate and the subject of active field and theoretical investigation. In this work, we use numerical simulations to explore the role of dynamically weakened faults during the collapse of large craters.

Crater formation is divided into three stages: contact and compression, excavation, and modification (Melosh, 1989). During contact and compression, the projectile impacts the target and generates two shock waves: one traveling into the projectile and one traveling into the target. The end of contact and compression occurs when the rarefaction wave from the rear of the projectile arrives at the projectile–target interface. During the excavation stage, the rarefaction wave overtakes the shock front in the target, creating a thin hemispherical shell of high pressure that decays in amplitude with distance. The material flow field induced by the shock wave leads to excavation, which leads to the formation of a hemispherical, bowl-shaped cavity, known as the transient crater.

During the modification stage, the crater cavity collapses, primarily under the force of gravity. Small (simple) craters undergo only minimal amounts of collapse. Thus, the final crater morphology retains a bowl shape. However, the gravitational forces associated with large (complex) craters are stronger and result in dramatic collapse, forming shallow craters with a variety of interior features: e.g., flat floors, central peaks, and peak rings. Numerical models of impact cratering using laboratory measurements of the quasi-static frictional strength of fractured rocks are too strong; simulated craters are too deep and lack the observed interior features (Melosh and Ivanov, 1999). Melosh and McKinnon (McKinnon, 1978, McKinnon and Melosh, 1978, Melosh, 1977) calculated the stability of a cylindrical hole (with depths and diameters chosen to represent large transient craters) using plasticity theory. They found that the coefficient of friction must be less than about 0.03 (compared to quasi-static values of 0.6–0.85) for the entire floor to uplift, as occurs in large craters. Thus, during complex crater formation, the bulk strength of the collapsing rock mass must be extremely low to reproduce the observed structures. Because the inferred friction coefficients during collapse are much less than found in quasi-static measurements, a weakening mechanism is needed. Finally, the topographic relief observed in large craters indicates that the weakening mechanism must be transient, because otherwise the topography would be more subdued.

The best developed model for temporary strength reduction is acoustic fluidization (Melosh, 1979). In this model, high-frequency pressure oscillations initiated by the impact-generated shock wave temporarily reduce the overburden pressure, which reduces the frictional strength and allows the material to slip. Averaged over time, the bulk rheology of the weakened material is approximated by a Bingham plastic (a material that behaves as a rigid solid below the yield stress, but as a viscous fluid above the yield stress). Numerical simulations using the block-model approximation of acoustic fluidization (Melosh and Ivanov, 1999) reproduce the overall morphology of complex craters (shallow depths and interior shapes) (Collins and Wünnemann, 2005, Collins et al., 2002, Melosh and Ivanov, 1999, Wünnemann and Ivanov, 2003). However, the model parameters must be constrained empirically by fitting to observed depth to diameter ratios and dimensions of central structures (e.g., Wünnemann and Ivanov, 2003), and no definitive laboratory or field observation has confirmed whether or not acoustic fluidization operates during impact cratering.

O'Keefe and Ahrens, 1993, O'Keefe and Ahrens, 1999 also modeled crater collapse. Their model did not include a transient weakening mechanism; instead, they simply lowered the bulk shear strength of the rock to low values (0–240 MPa) (O'Keefe and Ahrens, 1999). Numerical simulations using low strength were able to reproduce observed interior morphologies (they did not report final depth to diameter ratios). In addition, models where an initially high strength was degraded permanently to low strength via damage accumulation were able to simulate the creation of rim faults and terraces (O'Keefe, et al., 2001). However, no physical basis was provided for the reduction of rock strength well below quasi-static values.

Another weakening mechanism suggested early in the study of cratering mechanics was the lubrication of faults by friction-generated melts (Dence, et al., 1977). Although the total strains and strain rates necessary to generate melt along a fault is easily achieved during crater formation, the volume of friction melt expected is very small (less than a few volume percent) compared to the mass of collapsing material (Melosh, 2005). To date, the role of frictional melting during crater collapse has not been studied numerically. Field observations of possible frictional melts occasionally revive the idea (Spray, 1997, Spray and Thompson, 1995); however, the occurrence and distribution of melts that form definitively as a result of friction around impact structures are hotly debated (Dressler and Reimold, 2004, Grieve and Therriault, 2000, Grieve et al., 2008, Killick and Reimold, 1990, Lana et al., 2003, Lieger et al., 2009, Melosh, 2005, Reimold, 1995, Reimold and Colliston, 1994, Reimold and Gibson, 2005, Reimold and Gibson, 2006, Spray, 1995, Spray, 1998, Spray and Thompson, 1995, Thompson and Spray, 1994).

Nevertheless, ongoing work in the area of fault friction has found that seismogenic faults often slip at lower friction values than expected (e.g., Brune et al., 1969, Bunds, 2001, Di Toro et al., 2006, Henyey and Wasserburg, 1971, Hickman, 1991, Mizoguchi et al., 2007, Mount and Suppe, 1987, Zoback et al., 1987). Laboratory friction experiments have discovered weakening at high slip velocities and large displacements (Di Toro et al., 2004, Di Toro et al., 2005, Di Toro et al., 2006, Han et al., 2007, Hirose and Shimamoto, 2005, Mizoguchi et al., 2007, Nielsen et al., 2008, Spray, 1987, Spray, 1988, Spray, 2005, Tsutsumi and Shimamoto, 1997, Yuan and Prakash, 2008). Multiple fault-weakening mechanisms have been identified. Consequently, we revisit the role of dynamically weakened faults during crater collapse.