Questions for different Viscosity average scheme in Visco Plastic section

Hi! I am Xiang and now using ASPECT to run some small tests. Recently I am testing how a spherical hot material in the deep mantle will contribute to the surface dynamics topography when a plate boundary is on the top. I use Visco Plastic section but only include radial viscosity variation and set the plate boundary material’s maximum and minimum viscosity to around 1e20:

set Model name = visco plastic

subsection Visco Plastic


# reference stuff
set Reference temperature =   1573
#set Reference viscosity   =   1.0e21
set Minimum strain rate   =   1.e-20
set Adiabat temperature gradient for viscosity =   9.24e-09 # 0.3 K/km
#set Adiabat temperature gradient for viscosity =   0 # 0 K/km


# Set up phase transitions so that dislocation becomes inactive in the lower mantle for all fields.
set Phase transition depths           =   background: 100e3|660e3 , plbd: 100e3|660e3
set Phase transition widths           =   background: 1e3|1e3 , plbd: 1e3|1e3
set Phase transition temperatures     =   background: 1573|1573, plbd: 1573|1573
set Phase transition Clapeyron slopes =   background: 0|0, plbd: 0|0


# Viscosity cut offs
set Minimum viscosity   =   background: 1.0e18|1.0e18|1.0e19, plbd: 0.99e20|0.99e20|0.99e20
set Maximum viscosity   =   background: 1.0e23|1.0e23|1.0e24, plbd: 1.01e20|1.01e20|1.01e20


# density-related parameters (crust has mantle density = 3300 at T = 273 K) 
set Thermal diffusivities  =   1.e-6
set Heat capacities        =   750
set Densities              =   background: 3300|3300|3300, plbd: 3300|3300|3300
set Thermal expansivities  =   3e-5


# viscosity-related parameters
set Viscous flow law            =   diffusion
#set Viscous flow law            =   composite
set Viscosity averaging scheme  =   geometric

# None of this matters for plate boundaries, which we already pegged above at 1e20
# dislocation creep (just z < 660 km)
# We set the prefactor to a very low value in the lower mantle to effectively turn off dislocation creep.
set Prefactors for dislocation creep          =   background: 1e-40|1e-40|1e-40 , plbd: 1e-40|1e-40|1e-40

set Stress exponents for dislocation creep    =   3.0
set Activation energies for dislocation creep =   480.e3
set Activation volumes for dislocation creep  =   background: 0.0|0.0|0.0 ,  plbd: 0.0|0.0|0.0

# diffusion creep, (gives lower/upper mantle viscosity = 100)
set Prefactors for diffusion creep              =   background: 4.58017051e-11|5e-21|5e-23| , plbd: 4.58017051e-11|5e-21|5e-23|
set Stress exponents for diffusion creep        =   1
set Grain size exponents for diffusion creep    =   0
set Activation energies for diffusion creep     =   background: 300e3|0|0 , plbd: 300e3|0|0
set Activation volumes for diffusion creep      =   background: 0|0|0 ,  plbd: 0|0|0

# Plasticity parameters using drucker-prager
# Lower mantle - turn off using high cohesion
# Upper mantle - turn on by using 200 MPa
set Cohesions                   =   background: 1e20|1.0e20|1.0e20 , plbd: 1e20|1.0e20|1.0e20
#set Cohesions                   =   background: 20.e6|20.e6,   plbd: 20.e6|20.e6
#set Angles of internal friction =   0.0  # Friction coefficient of ~0.6
#set Maximum yield stress = 1e12

end

The question is, viscosity average scheme: geometric and harmonic show different reults for the top dynamics topography, even at the step 0 (I use no advection, single stokes to solve this) Does anyone have some ideas for this?
Harmonic:

Geometric

Spherical hot anomaly beneath lithosphere

Geometric.prm (10.7 KB)
Harmonic.prm (10.7 KB)

Thanks for your time!

Best regards,
Xiang He

Hi Xiang,

Thanks for posting this question and I’m glad we had an opportunity to discuss this question in person.

To summarize our discussion, the output may not be entirely unexpected given the expected effects of harmonic versus geometric averaging, resolution of the plate boundary weak zone, and Post processing options (set Write higher order output = false). The next step is to try using a higher resolution within the weak zone and/or set Write higher order output = true.

Cheers,

John

Thanks John! I also felt glad to talk with you!

I will follow your suggestions to test those two factors to see what will happen and then tell you what I get.

Thanks again for you time!

I tried both increasing mesh resolution and setting higher order output. And a higher mesh resolution for plate boundary works:
Harmonic


Geometric

Harmonic with higher resolution

Geometric with higher resolution

So, yes, I think the harmonic somehow make things smoother. Now they show similar “hamburger” shape after increasing the mesh resolution both in harmonic and geometric scheme. And I tried an even higher resolution and it does not change the pattern too much.
Harmonic with much higher resolution

Thanks a lot!