A method to assess event magnitude and target water depth for marine-target impacts. Part 2: The physics behind the observations

Abstract

We present a mathematical model for the study of the aquatic settling process of resurge sediments after a marine-target impact with cratering of the seafloor. Fragments from the solid target are mixed with the seawater. After an initial turbulent phase the suspended solid particles begin to settle. Previous studies of resurge sediments in drill cores from several craters indicate a relationship between the sedimentology, the target water depth, and the magnitude of the event [1]. Here we investigate the physics behind the relationship.

1. Introduction

In this study, we assume that size segregation is correlated to the concentration of the solid particles [2,3] giving rise to the different settling patterns observed in the core samples. The density and viscosity of the solid-water mixture depend on the solid concentration causing a different settling velocity of the particles. For low concentrations, velocities of coarse particles are higher and fine particles are excluded from the lower part of the sediment while for high values of the concentration the settling of the coarse clasts become hindered by the higher concentration of fine grains in the solid-water mixture, thus reducing the packing of coarse fragments at the bottom of the sediment column.

2. Mathematical model

For the study of the size segregation during the particle settling, a fractal model is proposed [4-10]. Two types of particles are considered: (1) Fine particles, s, with radius R_s < R_p, and (2) Coarse particles, p, with radius R_p < R_pL, being R_pL the upper limit for the fractal behavior. The fractal model developed by Filgueira et al. [6,7] is applied in two steps, taking the settling time for the coarse particles in pure water, t_max, as a time reference:

- Step 1: Settling of fine particles with R_s < r < R_p for t_max in pure water: At this step, the settling of the fine particles is calculated, independently on the solid-water concentrations.

- Step 2: Settling of coarse particles with R_p < r < R_pL for t_max in a solid-water mixture: The coarse particles are assumed to be immersed in a fluid mixture whose density and viscosity depend on the solid concentration. The deposited mass fraction of coarse particles for t_max is calculated at this step, and therefore, the number of settled coarse particles per unit length, i.e. the mean clast frequency <N>, can be approximated.

3. Impact cratering

After a meteorite impact, the transient crater diameter, D_t, can be related to the impactor diameter, d [11]. Considering a column of excavated material as a solid-water mixture column of height H = H_exc = H_w + H_sol, and taking into account that H_exc ≈ D_t /10 [12], the impactor diameter, d, can be written as a function of the solid concentration.

4. Results

As explained in previous sections, the mean clast frequency, <N>, and the impactor diameter, d, can both be written in terms of the solid concentration. Therefore it should be possible to represent <N> as a function of the impactor diameter over the depth of the water layer, d/H_w (Figure 1). This function indicates that for small values of d/H_w, i.e. either for small impacts and/or deep water bodies, the sediment pattern will show a higher number of coarse particles per unit length than for the case of very large impacts or very shallow water bodies (or both). This seems to be directly related to the solid concentration which is obviously greater in the case of large impacts and/or shallow seas.

To test the function trend obtained with the presented model, published data from five drill cores have been studied. These data have been presented for four natural impact craters, namely Lockne, Tvären, Flynn Creek (2 cores) and Wetumpka [1]. All the drill cores are from the deeper parts of the craters (e.g. moat). The values of d/H_w have been obtained performing numerical computations with the code iSALE-2D [13-15]. Figure 1 shows the model result (blue curve) along with the five drill cores’ data sets (dark dots). The model reproduces very well the trend based on observational data.

Figure 1: Mean clast frequency vs impactor diameter over the water depth.

5. Conclusions

A fractal model for the study of size segregation and particle settling after an impact event in a marine target is presented. The model assumes that the coarse particles will develop a different settling velocity depending on the volumetric concentration of fine particles, giving rise to a variety of size segregation patterns depending on the solid-water mixture properties. The model is able to reproduce the experimental tendency for five cores from four impact craters, for which the core samples were extracted in the deepest parts. However, a larger sample of craters would be desirable in order to further validate the proposed model.

Acknowledgements

The authors would like to gratefully acknowledge CSIC financial support for i-LINK project LINKA20203 and the Spanish State Research Agency (AEI) for project MDM-2017-0737.

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