# Depth dependent material models

Hi,

I am new to ASPECT and have a basic confusion while developing a depth-dependent material model.

I have a 4000 × 660 km 2-D box model, where I am interested in implementing different viscosity layers. For simplicity, I am keeping 2 layers: 0-100 km and 100-660 km. I want the top layer to have a viscosity of 1e21 Pa·s and the bottom layer to have a viscosity of 1e20 Pa·s. I am preparing the PRM file as follows:

subsection Material model
set Model name = depth dependent

subsection Depth dependent model
set Base model = simple
set Reference viscosity = 1e21
set Depth dependence method = List
set Depth list = 100.0000000e+00, 6.7000000e+05
set Viscosity list = 1.0000000e+21, 1.0000000e+20
end

subsection Simple model
set Thermal conductivity                                     = 1e-6
set Thermal expansion coefficient                      = 3e-5
set Reference density                                         = 3300
set Reference temperature                                 = 1350
set Density differential for compositional field 1  = 1
set Composition viscosity prefactor                   = 1
end
end

The resulting viscosity becomes uniform at approximately 5e23 Pa·s, and the model runs for only a few time steps (for this particular setup, it took only 6 steps) to reach 3.5 billion years.

I have tried different values for the reference viscosity and viscosity list but have never obtained the correct result.

According to the documentation and source code: [ \eta = \eta(z) * \eta(T, X, P, \ldots) / \eta(r) ]

But the result in my case looks very different. So, I am not clear on how the net viscosity is calculated using this method. Any explanation would be helpful.

Dear Jyotirmoy,

Welcome to the ASPECT community!

There are a couple of misunderstandings in your prm. First, I’ll point out the bits of the manual that are useful, and then I’ll explain what they mean for you.
Description of models
Parameters for the depth dependent model
Parameters for the simple model

The description of the Depth dependent model describes it as a compositing model - this means that it modifies the viscosity from another model. In your prm you have chosen the “simple” material model to be your “Base model”. This model has a parameter called Viscosity which has a default value of 5e24. You haven’t overwritten this value.

Your prm tells ASPECT to take the Base model viscosity (5e24), divide it by the reference viscosity (1e21) and then multiply it by the values in your viscosity list (1e21 and 1e20). Thus, the majority of your model has a viscosity of 5e24/1e21*1e20 = 5e23. You would see a 100 km thick region of higher viscosity at the top of your model, but there’s a typo in your “Depth list” parameter. The first number should be 100e3, not 100e0.

Best wishes,
Bob

Dear Bob,

Thanks for explaining. I understood the problem and fixed the issue. Now I am getting correct viscosity structure.

Best
Jyotirmoy

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