To investigate the influence of the impact angle we have performed 3D numerical simulations of an oblique (45o) impact of a 300-m-radius granite projectile into a target consisting of crystalline basement overlain by a water layer that is 800 m deep. We used the same numerical model based on a 3D version of the SOVA hydrocode (Shuvalov 1999). The spatial resolution was lower than in the 2D simulations. The initial cell size in the central high-resolution region (100x50x80 cells) was 0.025 km in both vertical and horizontal direction and increases progressively far from the center. When the blast wave reached the grid boundary, the cell size (and the size of the computational region consequently) was doubled. The maximum cell size in the high-resolution region equaled 0.1 km in vertical direction and 0.2 km in horizontal direction.

The results (initial stage) are shown in Fig. 5. We can see that the basement crater is produced by a high velocity water stream, which is generated by the shock wave propagation through water. The projectile

Fig. 6. Cratering flow 10 s after vertical (2D axisymmetrical and 3D simulations) and oblique impacts with different impactor radius R, sea depth H, and impact angle a. Water is shown by black, and the basement is gray. Atmospheric gas, projectile material, and ejecta with a low bulk density are not shown.

Fig. 6. Cratering flow 10 s after vertical (2D axisymmetrical and 3D simulations) and oblique impacts with different impactor radius R, sea depth H, and impact angle a. Water is shown by black, and the basement is gray. Atmospheric gas, projectile material, and ejecta with a low bulk density are not shown.

does not hit the basement crater floor and does not even penetrate into the crater. The crater center lies between a point of initial projectile-water contact and a point (near the boundary of the crater) where the projectile hits the sea floor.

The basement crater proves to be considerably smaller than in the vertical impact of the same projectile. In both cases (oblique and vertical impacts) approximately the same energy is released into the water, because in the vertical impact we considered an ellipsoidal projectile. The flattened projectile has a larger cross-section than an equivalent sphere, which compensates the longer trajectory of the oblique impact. As a result in both cases we have similarly-sized water transient cavities. However, the basement crater is produced by a water stream, and a vertically directed water stream creates a larger crater than an oblique water stream. Thus, the conclusion can be derived that obliquity increases the ratio between radii of water transient cavity and basement depression. At the same time the excavation flow from the basement crater (and, consequently, the overturned flap) decreases in an oblique impact of the same projectile size. To obtain the same basement crater we would need to increase the impactor size or decrease the water depth. However, the geological constraints for the Lockne crater (see "Introduction") and numerical simulations described below show that we can not decrease the sea depth below approximately 600 m, otherwise we will not obtain a large water crater and the resulting "shallow excavation".

Figure 6 shows the results of numerical simulations for several other values of sea depth, impact angle, and impactor radius. In particular, the results for the vertical impact obtained in both 2D (axisymmetrical) and 3D simulations are shown, as well as the results of 2D modeling with different spatial resolutions. These results demonstrate that 2D and 3D simulations of the axysymmetrical problem give the same distributions. The increase of spatial resolution (cells size lowered by a factor of two) only slightly influences the model output.

In all cases under consideration we obtain a basement crater diameter of approximately Lockne size (but with a somewhat different depth). The maximum water transient crater forms in a deeper sea (1000 m). This is also the modeled result that best fits the geological constraints for Lockne. Obliquity leads to asymmetry in the area cleared from water and to strong asymmetry of ejecta curtain. It is more extensive in the downward direction. However, the water surge is higher in the opposite direction. Thus we can expect that in the case of an oblique impact extensive distal ejecta deposits (up to 10 km away and more) should be found only in the downrange direction.

Fig. 7. This shows the zenith perspective of various craters formed by oblique impacts. In this figure the boundary solid surface is defined by the level at which the material density becomes equal to half of the normal density of condensed water (on the water-air boundary) or basement rocks (for the basement transient cavity). Therefore, only the denser part of the ejecta cone (with a high bulk density) is seen in the figure. In all cases the water transient crater is circular, the basement crater is also almost circular, however, the crater centers do not coincide. Both craters are shifted to a distance of 1 to 3 kilometers from the impact point, which has coordinates (0, 0). It is interesting to note that in the 45 degree alternative the basement crater is slightly elongated in the direction perpendicular to the direction of impactor flight.

Fig. 7. This shows the zenith perspective of various craters formed by oblique impacts. In this figure the boundary solid surface is defined by the level at which the material density becomes equal to half of the normal density of condensed water (on the water-air boundary) or basement rocks (for the basement transient cavity). Therefore, only the denser part of the ejecta cone (with a high bulk density) is seen in the figure. In all cases the water transient crater is circular, the basement crater is also almost circular, however, the crater centers do not coincide. Both craters are shifted to a distance of 1 to 3 kilometers from the impact point, which has coordinates (0, 0). It is interesting to note that in the 45 degree alternative the basement crater is slightly elongated in the direction perpendicular to the direction of impactor flight.

Although distal ejecta are strongly anisotropic, the overturned flap is almost symmetric. At least, a dense part (with bulk density close to the density of basement rocks) of ejecta curtain shown in Fig. 7 is almost symmetric. This correlates with the results of laboratory experiments

(Anderson et al. 2000). The overturned flap forms due to overturning of near-surface layers, not by deposition from rarefied (with low bulk density) ejecta curtain. Figure 6 also shows more or less symmetric overturned flaps, but not symmetric ejecta curtains.

A general conclusion derived from these simulations is that the oblique impact results in a larger area cleared from water (compared to the vertical impact case), can provide overturned flap, and distal ejecta deposits, however, in one direction only (downrange of the impact point). In the up-range direction the area cleared from water is smaller, and there are no distal ejecta.

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