The Silverpit crater is a recently discovered, 60-65 Myr old complex crater, which lies buried beneath the North Sea, about 150 km east of Britain [1].  High-resolution images of Silverpit's subsurface structure, provided by three-dimensional seismic reflection data, reveal an inner-crater morphology similar to that expected for a 5-8 km diameter terrestrial crater.  The crater walls show evidence of terrace-style slumping and there is a distinct central uplift, which may have produced a central peak in the pristine crater morphology.  However, Silverpit is not a typical 5-km diameter terrestrial crater, because it exhibits multiple, concentric rings outside the main cavity.

External concentric rings are normally associated with much larger impact structures, for example Chicxulub on Earth, or Orientale on the Moon.  Furthermore, external rings associated with large impacts on the terrestrial planets and moons are widely-spaced, predominantly inwardly-facing, asymmetric scarps.  However, the seismic data show that the external rings at Silverpit represent closely-spaced, concentric fault-bound graben, with both inwardly and outwardly facing fault-scarps [1].  This type of multi-ring structure is directly analogous to the Valhalla-type multi-ring ba-sins found on the icy satellites.  Thus, the presence and style of the multiple rings at Silverpit is surprising given both the size of the crater and its planetary set-ting.

A further curiosity of the Silverpit structure is that the external concentric rings appear to be extensional features on the West side of the crater and compres-sional features on the East side [2].  The crater also lies in a local depression, thought to be created by post-impact movement of a salt layer buried beneath the crater [2].

Theoretical and numerical modeling of multi-ring craters [3,4] suggests that external ring formation is a consequence of the basal drag exerted on a brittle, elastic surface layer by a more mobile substrate as it flows inwards to compensate for the absence of mass in the excavated crater.  This model has been further constrained for Valhalla-type multi-ring basins.  The formation of closely-spaced, concentric fault-bound graben, appears to require that the elastic upper layer be thin and that the mobile substrate be confined to a relatively thin layer [5,6,7].  This rheologic situation is easily explained in the context of the icy satellites; however, the presence of a thin highly mobile layer just below the surface is not a common occurrence on rocky bodies in the Solar System.  In the case of the apparently unique Silverpit structure, it has been suggested that the mobile subsurface layer was caused by the presence of overpressured chalk layers at depth that acted as detachments and expedited inward flow of a thin subsurface layer [1].

We have begun to test the proposed model for the formation of the Silverpit crater using three contrasting yet complementary numerical tools:  SALES 2, SALEB and Tekton.  SALES 2 is a Lagrangian hydrocode capable of modeling the dynamic collapse of large impact craters.  It has been successfully applied to the problem of central peak and peak-ring formation [8].  SALEB is a multi-material Eulerian hydrocode, which has been used extensively for simulations of impact crater formation [9,10].  Both SALES2 and SALEB are direct descendents from the SALE hydrocode [11]. Tekton is a finite-element code designed to be applied to a wide range of tectonic problems, where displacements are relatively small and the dynamics are less important.  It has been used ex-tensively to simulate the relaxation of large craters and the formation of exterior rings in multi-ring basins [3]. 

Using SALEB, we investigate the formation of the Silverpit crater assuming an impact energy appropriate for forming a transient crater 3-km in diameter.  Using SALES-2 and Tekton, we simulate the gravity-driven collapse of a bowl-shaped transient crater, 1-km deep and ~3-km in diameter.  We model the target to a radial distance of >10 km and a vertical depth of 10 km to avoid boundary effects.  All three of our models consist of three, originally-horizontal layers.  For the SALES-2 and Tekton simulations these layers are deformed using the Z-model approximation of the excavation flow.  The top two layers are assigned appropriate rheologic parameters to represent the brittle upper layer and the lower mobile layer at Silverpit.  The bottom layer oc-cupies the remainder of the mesh. 

For simplicity in our early calculations, we assume that the target is compositionally homogeneous; we use the ANEOS equation of state for calcite in the SALEB calculations and the Tillotson equation of state for limestone in SALES-2.  The important differences be-tween the brittle upper layer and the mobile layer are rheologic.  The mobile layer may be repressented by an inviscid, or Newtonian fluid, or a fluid with a constant yield strength (Bingham fluid).  The upper layer is modeled as an elastic-plastic solid with a pressure-dependent shear strength and a constant tensile strength, which are both degraded by damage.  Damage accumulation in shear is determined using a Johnson and Holmquist-type algorithm [12], where damage increases linearly with plastic strain up until the plastic strain at failure.  At this point and beyond, damage is complete and the material is modeled as a cohesionless Coulomb material.  Tensile damage is accumulated either using the Grady-Kipp model, for calculations in SALES-2 [13], or using a simple, single-flaw growth model in SALEB.

Figure 1 shows the effect of the mobile middle layer on final crater structure and extent of the damaged region. In the simulation illustrated in the lower panel, the mobile layer was treated as a Bingham fluid with a small (5 bar) yield strength and a viscosity of 107 Pa s. The upper layer was modeled with an un-damaged tensile strength of 10 MPa, a cohesion of 100 MPa and a coefficient of friction of 1.0 for undamaged material and 0.5 for completely damaged material.  The plastic strain at failure was defined to be 1% at low confining pressures increasing to 10% at 100 MPa.  The final crater has a diameter of 5-6 km with a well pronounced central uplift.  The damaged region of the crater extends well away from the crater rim but is con-fined to the upper half of the brittle layer.

Figure 1:  Comparison of the final crater structure and extent of damage (shading) for two axisymmetric SALEB simulations. The upper panel shows the result of an impact into a uniform target, the lower panel illustrates the effect of the weak mobile layer.  In the lower panel the damaged re-gion (shaded lighter) is much more extensive.  The "crater rim" is at around 2.5-3 km radius in both cases, but in the lower panel the central region is slightly elevated.

Figure 2:  Close-up of a simple, axisymmetric two-layer collapse simulation performed using SALES-2.  The shading denotes the amount of damage (black = completely damaged, white = undamaged).

To investigate the formation of the exterior rings at Silverpit we have also performed numerous crater collapse simulations.  Figure 2 shows the results of one such model.  In this case, the initial crater is a cylindri-cal hole with a radius of 3 km.  During the simulation, the mobile lower layer flows inward causing the elasto-plastic layer above to sag downward.  The flexure in the brittle layer causes extensional faulting in the top half of the upper layer.

Silverpit is a fascinating and unique terrestrial impact structure.  The proposed model for the formation of the external rings at Silverpit is supported by our modeling results.  Inward flow of the mobile middle layer causes flexure of the upper layer and produces extensional faulting in the top half of the upper layer.  Results from our preliminary simulations suggest that the brittle upper layer must be ~1-km thick in order to reproduce observed fault patterns and the central uplift.  The asymmetry in the nature of the ex-ternal rings at Silverpit may be due to thickness variations in the mobile layer, or post-impact subsidence related to the salt movement. Further work is required to investigate this thoroughly.

Collins, G. S., E. P. Turtle and H. J. Melosh, Numerical Simulations of Silverpit Crater Collapse, 2003, 3rd Large Meteorite Impacts Conf., Abstr. #, CD-ROM.

Collins, G. S., E. P. Turtle and H. J. Melosh, Numerical Simulations of Silverpit Crater Collapse, 2003, Lunar and Planet. Sci. Conf. XXXIV, Abstr. #2115, CD-ROM.

Collins, G. S., E. P. Turtle, H. J. Melosh, Numerical Simulations of Silverpit Crater Collapse: A Comparison of Tekton and SALES-2, 2003, In: Impact Cratering: Bridging the Gap Between Modeling and Observation, LPI Contribution No. 1155, Lunar and Planetary Institute, Houston, p 18.

[1] Stewart, S. A. and Allen, P. J. (2002) Nature 418, 520-523.
[2] Allen, P. J. and Stewart, S. A. (2003) LPSC XXXIV.  #
[3] Turtle, E.P., (1998) Ph.D. Thesis, University of Arizona.
[4] Melosh, H. J. and McKinnon, W. B. (1978) Geophys. Res. Lett. 5, 985-988.
[5] McKinnon, W. B. and Melosh, H. J. (1980) Icarus 44, 454-471.
[6] Melosh, H. J. (1982) JGR 87, 1880-1890.
[7] Allemand, P and Thomas, P. (1999) JGR E 104, 16501-16514. 
[9] Ivanov, B. A., DeNeim, D. and Neukum, G. (1997) Int. J. Imp. Eng. 20, 411-430.
[10] Ivanov, B. A. and Deutsch, A. (1999) Spec. Paper GSA 339, 389-397. 
[11] Amsden, A.A., Ruppel, H.M., and Hirt, C.W., (1980) LANL Report LA-8095, Los Alamos, NM.
[12] Johnson, G. R. and Holmquist, T.J. (1994) In: High-Pressure Science and Technology ? 1993, AIP Press, Woodbury NY, 981-984.
[13] Melosh, H. J., Ryan, E. V. and Asphaug, E. (1992) JGR 97 #E7, 14735-59.