Okay, Craters, Now Let’s Get in Formation

A lot has happened since our last meeting. Titan through time 4 was an amazing experience. The talks were fantastic. Let me know if you’d like to know more, I took notes on some of the most interesting talks. If you’ve never been, it’s styled into topic themed sections, where each section begins with a double-lengthened review of the current science before hearing specific findings. These were my favorite. Seeing Washington was also amazing. I hope to go back later this summer, if Zibi has time, to work one on one.

On that note, we have a running tekton file that accepts inputs (thanks to Catherine’s husband Shawn). There is still a small error, but some runs seem to return at least a partial output file. I contacted Shawn and Zibi last week and am awaiting a response, but I’ll follow up today or tomorrow (because I’ve got to be persistent ūüôā ). That said, I’ve learned some from the input file and the outfile that has been produced. Mostly, I’ve got a better idea of how the crater mesh is made and inputted.

For those of you who don’t know what a mesh is, just imagine a section of the surface, like the top of a crater and then looked down into the ground (on Titan) so that you have a cross-section view. each intersection of y and x grid likes is a node unto itself. A node is just a point in a matrix that represents that grid where the properties of that mesh is known. Finer scale grids more accurately¬†map the cross section, but more points also slow the code because it has to process more calculations. That is what finite element models do. Imagine each node has the temperature at each point. If I want to know dT/dz at say the surface (z=0m) I just look at the surface node temp, then the temp of the one below, subtract the two, and divide by the change in altitude. Its just an¬†approximation¬†of the derivative.

The grid is the foundation for the entire problem. Aside from the grid increments and size, the shape is the key component to consider. That’s what I have focused my time on is considering how craters of particular sizes will form. So, okay, craters, now let’s get in formation¬†(to understand formation we need more¬†information, get it?).

Crater formation is well understood on icy bodies. That’s the entire premise of using craters to study relaxation–because we understand them so well. Unfortunately, it’s limited. It turns out larger (150km+) craters are not well understood. Unlike the moon, we often have a liquid ocean to contend with, and that changes things because the largest craters¬†will lose their traditional crater bowl shape. Schenk 2002 detailed the relationship between icy bodies, craters, and their oceans on Callisto, Ganymede, and Europa.


icy crater
Schenk 2002 shows the transition in crater depths from regular crater processes that have to due with temp changes influencing ductility (1), to seeing anomalous crater shape due to influences from subsurface ocean (2), and poorly rimmed domed craters (3). Warmer ice is weaker at shallower depths and transitions at 2 and 3 reveal rheologic changes at depth due to temperature changes.

Schenk shows that occurs at ~150km. This means that the most anomalous craters are the really large basins like¬†Menrva (~400km). I have more up to date findings (Brey et al 2012) which goes into detail about crater shape, but for relaxation the depth and shape of the crater is the crucial part, so rim is less important. I’m inclined to work soley off of Schenks values because it seems more consistent and is still what’s used in Brey et al 2012.

Schenk provides values for crater depth, but the crater shape for the largest craters requires more research. Schenk 2002 should be enough for up to Forsetti, but I am not trying to figure out what shape to work with for Menrva. That means I’m researching basin formation and shapes.

Senft and Stewart 2011 modeled impacts on icy bodies. They did not go deep into the third transition because it was so anomalous, but their general results for 150km+ craters was that they generally agreed with Schenks numbers.

icy crater
Senft and Stewart 2011 modeled impacts on icy bodies. A 10km impactor for differing ice sheets shows how a liquid ocean can flatten the crater at formation.

I’m looking at several papers at the moment, including chapters from Melosh’s impact cratering book. I think I am close to getting what I need; I am hoping to have a shape defined before start of field school. Merchie and Head 1986 modeled Gilgemesh on Ganymede but did so with a lot of moon based assumptions which made their ~9km depression for the ~750km basin suspect. One other paper (Which is used I think by Melosh) is Impact basins by McKinnon and Melosh 9 years before his book (i.e. 1980 and 1989). The general shape will be crater floor and dome, but one question is do the walls drop gradually or instantly?

Given Schenks findings and Senft and Stewarts, by considering crater shapes based on size and ice crust thickness. Because it seems like the biggest control on crater shape is ice/water rheology.

As far as modeling goes, I have a code that accepts a 100km< crater diameter and creates a mesh and even outputs the node number and respective r and z values as formatted in the input file. Now I just need to update it for these morphologies. I think it is all coming together nicely. With this, I think my meeting with Zibi the day after our trip ends we talk more about how to implement these meshes.

(Valhalla basin on Callisto is in the featured image, Melosh 1989)

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