How to set an adiabatic temperature gradient of 0.5K/km for the mantle below the lithosphere?

ASPECT
1

Hello everyone!
I am designing a 2D mid-ocean ridge model. In the initial temperature model, my aim is that the lithosphere follows the half-space cooling model, and the mantle temperature below the lithosphere increases from the bottom of the lithosphere with an adiabatic temperature gradient of 0.5K/km to the bottom of the model (670km). I have written the alf-space cooling model, but I don’t know how to achieve a mantle temperature gradient of 0.5K/km? Thank you all.I would be very grateful if any friends could help me solve the problem
initial temperature model.txt (459 Bytes)

2

Hi @sxj,

Thank you for posting the question to the forum and apologies for taking some time to get to it.

I have written the alf-space cooling model, but I don’t know how to achieve a mantle temperature gradient of 0.5K/km?

My suggestion would be to precompute the depth where you reach 1643 K, and then modify the function expression to include a conditional statement that if you are below that depth the temperature should increase by 0.5 K/km. A rough example is below.

subsection Initial temperature model
      set Model name = function
      subsection Function
        set Variable names = x,y
        set Function constants = ymax=670e3, vsub=9.512e-10, \
                                               Tm=1643, Ts=273, kappa=1e-6, y_Tm = 570e3
        set Function expression = if (y> y_Tm, \
                                                     Ts + (Tm-Ts)*(1-erfc((ymax-y)/(2*sqrt(kappa*(x/vsub)))), \
                                                     Tm + (y_Tm - y)*0.5/1.e3)
                                               
      end
end
1 Like
3

Thank you for answering my question. I also have this idea, but when determining how deep 1643K can reach, my model is at a distance of 1670km from the mid-ocean ridge. When working backward from the half-space cooling model to y, the obtained y value is infinitely large, and it is impossible to determine how deep 1643K can be reached. What’s your opinion on this? Thank you very much!

4

@sxj - This question is really more on the theoretical side, rather than ASPECT side. I suggest trying different approaches in python (or similar), looking at relevant cookbooks in the ASPECT repository (one such example), and reviewing the literature to see how other researchers designed similar models.

5

Thank you for your answers and suggestions. Next, I will rethink how to design. Thank you again