A geology game

Frazil and microlites

Europa's double ridges may sit over pockets of water trapped in the ice (Culberg, Schroeder and Steinbrügge, 2022). Volcanoes sit over pockets of magma. Here both get the same sill a kilometer down and the same thin crack above it. Each crack is a race: the liquid climbs while its walls freeze inward. What differs is the push. Freezing water swells and cracks its ice; crystallizing basalt shrinks and pulls away from its rock until its gas comes out. The crystals left in the crack record how it went.

Water in Europa's ice

    Basalt in Earth's crust

      Does magma shrink when it cools?

      Yes. Basalt melt is about 9% less dense than the crystals it grows, so a sill that crystallizes shrinks and its pressure falls. Water is the odd one: ice takes up 9% more room than the water it came from, so a freezing sill swells and pushes on the ice around it. But magma carries water too. Crystals don't take it in, so it piles up in the melt that's left until it can't stay dissolved and comes out as gas, and the gas pushes harder than the shrinking pulls. Volcanologists call it second boiling. The chart is the push in each sill, from the same model as the game.

      How the numbers work
      • The setup is the same on both sides: a sill 2 km across and 20 m thick whose top is 1 km down, and one vertical crack from its top. The water side is Europa (gravity 1.315 m/s², ice 920 kg/m³, a surface near 100 K). The basalt side is Earth (crust 2,700 kg/m³, basalt melt 2,650 kg/m³ at 1,150 °C). The walls slider runs both from just under freezing to the coldest wall: ice from −10 °C to −173 °C, rock from 1,000 °C to 20 °C.
      • The push comes from what has to fit in the sill. Ice is 917 kg/m³ against water's 999.8, so freezing swells it 9%; basalt crystals at 2,900 kg/m³ shrink it about 9%. The sill gives like a flat crack in elastic rock or ice (Young's modulus 9.3 GPa for ice, 50 GPa for rock), and water and melt squeeze a little. The basalt holds 1% water by weight, which stays dissolved up to about 0.3 √P (P in MPa) percent, close to the basalt measurements of Dixon, Stolper and Holloway 1995; the rest is gas. The gas pressure in a crystallizing chamber follows Tait, Jaupart and Vergniolle 1989. Pressurized water under Europa's ice is from Manga and Wang 2007.
      • The crack opens when the push beats the tensile strength: 1 MPa for ice (Petrovic 2003 gives 0.7 to 3.1), 3 MPa for rock (Gudmundsson's Rock Fractures in Geological Processes, 2011). It climbs while the push at its tip stays above zero: the sill's push, plus buoyancy (water is heavier than ice, so it loses push on the way up; basalt is a little lighter than the crust), minus what the crack has drained from the sill. The liquid flows as fast as that push allows through the open gap, laminar or turbulent, whichever is slower. Water runs at a few meters a second and is turbulent in any crack wider than a few millimeters; basalt is 100 Pa·s, about 50,000 times thicker, so it runs smooth unless the crack is more than about half a meter wide.
      • The walls freeze inward as in the classic Stefan problem: liquid at its melting point against a cold half-space grows a solid layer as the square root of time (Turcotte and Schubert, Geodynamics). Cold ice conducts better than warm ice, so its heat values change with temperature (Petrenko and Whitworth 1999). It leaves out the heat the flow carries up, which can keep a fast crack open longer (Bruce and Huppert 1989), and treats basalt as freezing at one temperature, which it doesn't.
      • The crystals. Against the wall the liquid meets cold solid, and the two settle near the average of their temperatures, so the wall sees the biggest undercooling. Ice there grows straight off the wall in columns. Basalt there quenches: skeletal crystals, or glass when it's cold enough. In the middle, both liquids are undercooled the same way: by leaving the squeezed sill and rising, which lowers the pressure on them. Ice melts lower under pressure (0.074 °C per MPa), so water that started at its melting point in the sill is below it once out; that is how rising water under Antarctic ice shelves grows frazil (Jenkins and Bombosch 1995). Frazil grows only in turbulent water, as discs 1 to 4 mm across and a few micrometers to a tenth of a millimeter thick (Martin 1981); the colder the water, the more the discs grow arms (Shibkov and others 2003). Real frazil grows fast enough to warm the water back toward freezing, so the undercooling shown is what the pressure drop would give, not what a thermometer would read. Basalt melt holds less water at lower pressure, and the water that bubbles out raises its freezing point, about 40 °C per percent here, a rough reading of Almeev and others 2012. That is the main way microlites grow in rising magma (Hammer and Rutherford 2002). Microlites, crystals tens of micrometers long, go from blocky laths to hollow hoppers, swallowtails, branching dendrites and then glass as the undercooling grows (Lofgren 1974; Shea and Hammer 2013). The game leaves out how long crystals take to grow, and a crack that reaches the surface in a minute or two gives them little time.