How to using nondimensional model for complex rifting

Hello, i’m undergrade student that research to rifting and need your help to use nondimensional model. I’m looking for a dimensionless way to solve the problem of model collapse due to static pressure in Rift models with continental-ocean crust. So i think that using nondimensional model is solving for this problem. But nondimensional model can’t input multi parameter for multi composition. Even if combine nondimensional model and viscoelastic model using for Compositing model it not working. So i finded user manual that how create plugin template and make that .cc code, because i need to in my rifting model remove static pressure or make them nondimensialized. Before make .cc code, can your help me know the other ways that solve this problem?

I hope your help, please tell me way out this problem.

Dear Minseok,

Welcome and thank you for posting to the forum!

If I understand correctly, you would like to construct models where rifting occurs due to lateral variations in lithostatic pressure (changes in topography +/- crustal structure?) and associated “collapse”. The models will contain the continent-ocean boundary.

Is the above summary correct?

If so, my first question would be why is it a necessity to use a nondimensional form of the equations? As you noted, there are some material models that do this in ASPECT and it is also possible to adjust the material properties in most material models to have something akin to a non-dimensional model.

However, for the problem you described I don’t think this is necessary as I’m aware of a few projects that have done a collapse problem with the Visco Plastic material model (multi-component, nonlinear rheology, etc).

Can you outline in more detail why a non dimensional model is necessary? Also, happy to help point out the relevant model features others have used for “collapse-style” rifting problems.


Hi John, Thank you for the reply about my question. Sorry for not explaning in detail for my model problem last time.

First, my rifting models(Use visco plastic model) problem is topography collapse, because crust have lateral anisotrophy density like continental-oceaninc. the oceanic crust is heavier than the continental crust, it sinks the oceanic crust and lifts the continental crust. I used free surface, so Ignoring the boundary conditions, the continental crust rises unrealistically.

Here is a picture of the model results. I think Maybe pictures better than explain model set up.
One shows speed and the other shows composition. The boundary condition is to tension left and right, but here the effects of descent and ascending back and forth due to static pressure are so strong that they are ignored.

Two, the reason I want to use the dimensionless model is to get faster computation speed and to solve the above collapse problem. This is because I think that the calculation through the reference density removes the static pressure from within the model and makes it work only with dynamic pressure (probably I was wrong). One of the ways to solve the collapse problem due to static pressure is to arbitrarily change the calculation using Plugin .cc code. Like limiting the movement of matter in a certain direction or removing static pressure.

How can this problem fixed it? Any advice would be appreciated.


Hi Minseok,

Thank you for the follow-up explanation and pictures, which definitely clarified the issues.

The issue you outlined (rapid vertical movements) is expected if the model is not isostatically compensated (equal pressure at a given depth). Effectively, the vertical movements you obtain is the model isostatically adjusting towards an equilibrium state.

My general experience from projects looking at similar processes (extension due to topographic collapse) is that as the compensation depth gets closer to the surface (ex: LAB -> Moho -> mid-curst) the initial vertical adjustments in the model get smaller and smaller. I think this makes intuitive sense as well given that deeper uncompensated lithospheric columns will lead to longer wavelength adjustments. Typically I’ve used Pratt (density adjustments), rather than Airy, isostasy to enforce isostatic equilibrium at various depths.

Of course, where to enforce isostatic compensation is highly dependent on what region you like at, and in some locations topography is clearly being supported mantle flow (i.e., dynamic topography). In reality, the most realistic isostatic compensation to use is the core-mantle boundary, but that is not particularly practical in most studies :slight_smile:

In summary, I think the solution to the issues observed in your models is to enforce isostatic compensation at some depth. Given the high vertical velocities observed in your model are driven by pressure gradients, I don’t think removing a static pressure reference column (or reference density) will help.

Happy to discuss this further!


Hi John, I appreciate your advice.

Already, i known that rapid vertical movement is induce collapse because density anisotrapy. But, many exploration data shown density instability(Probably because of low resolution) and i should to more realistc modeling. So i wondered, in ASPECT have self solution that remove static pressure or make nondimensialization(unfortunately this solution is unrealistic).

My model have to isostatic compensation in moho, and i know make them Airy or Pratt compensation(this solution is compromise about static pressure). Maybe i trying to changing density isostatic my model, instead of use plugin.

So, returning to the original question. Inevitably, i have to use nondimensional model because for faster computational. How nondimesional model working about multi composition and apply?

And, Thank you again help.


Hi Minseok,

Yes, I would strongly recommending adjusting the density in your models to enforce isostatic compensation at a given depth.

I don’t think removing the static pressure is going to help with stability or speed, as it is density variations driving the observed behavior. I suppose a simple way to “approximately” remove the static pressure would be to subtract a reference density (say 2700 kg/m3^) from the density of each different material type. This would then just leave the density variations. You can also convert all relevant quantities to be non-dimensional by choosing characteristic values for length, time, etc, although I confess I have not done this exercise in many many years :slight_smile:

Another reason to avoid using a non dimensional form of the equations is that the pressure term in the viscous creep laws and plasticity formulation no longer is meaningful.

Again, I strongly suspect the behavior you are observing is a reflection of large and uncompensated pressure variations arising from the imposed density structure. The options are to reduce the initial instabilities by isostatically compensating and/or letting the model run for a few for some time to reequilibrate.



Hi John.

I’m studying this model simulation almost 3 month, I can only solve it now.
Now, I’m fix my model isostatic compensation in moho, make getting equal pressure. My model Computation get pretty long time, but this time i think will working.

Thanks your help, John. This advice can make my model get next step.