Hi all.

I have faced difficulty but I cannot understand it.

So, I request any feedback.

My model is a spherical chuck model.

It has 115oE to 140oE, 25oN to 45oN. and 0 to 660 km (Northeast asia region).

I constructed three models.

One is homogenous viscosity for the entire numerical domain (10^22 Pa s) and layered density heterogeneity (0 to 20 km: 2600 kg/m^3, 20 to 30 km: 2900 kg/m^3, below 30 km: 3300 kg/m^3) (Fig. 1b).

Temperature distribution follows a reference geotherm (Fig. 1a). then laterally uniform.

The velocity boundary condition is free-slip b.c. except for top boundary.

The top is imposed by free-surface b.c.

The model is run by version 2.3.0-pre (master, f327473).

In the initial time, the result shows a downward flow at the southern boundary whereas an upward flow at the northern boundary (Fig. 1c-1f).

After 200 kyr, due to the isostatic, the flows are not significant in the central but flows are vigorous at both boundaries (Fig. 1e-1f).

Fig.1 test 1

The second one is also homogenous viscosity for the entire numerical domain (10 x 10^22 Pa s) and I adopted crustal structure from CRUST 1.0.

Temperature and velocity condition same with the first one.

First, I can see surface topography at 200 kyr (Fig. 2a) is reasonable because uplift happens at continental and subsidence happens at the oceanic. Also, the topography magnitude is also coincident with observation.

Then, I have no doubt about free surface function.

Also, the density field (Fig. 2b) shows the crustal model is well implemented through the initial material model using ASCII.

However, I can observe unexpected flows at tho boundaries (Fig. 2c-2f) after achieving isostatic adjustment.

Fig.2 test 2

The third one is the material dependence viscosity model.

I referred to material parameters from previous studies and used the viscoplastic model. The rest conditions are the same as the second one.

I can see surface topography at 100 kyr (Fig. 3a) is also reasonable and more qualitatively consistent with observations.

Viscosity structure shows high strength (10^23 to 10^24 Pa s: 0 to ~120 km) and low viscosity (10^20 to 10^21 Pa: 120 km to ~400 km) then increase till 10^22 at the bottom.

I think the viscosity structure is consistent with inferred 1-D earth models.

However, I can observe unexpected flows at tho boundaries (Fig. 2c-2f) after achieving isostatic adjustment. In addition, the abnormal flows are more distinct because middle-level depth has low viscosity structures.

Fig.3 test 3

In order to check the strong velocity field is a null space solution or not,

I tested six null space remove functions (net rotation, angular moment, net translation, translation x, translation y, and translation z).

Even with I used the functions, I cannot find differences in comparison with the test 3 model.

I concluded the vigorous flows are not null space.

So, I cannot understand the force to drive the flows.

For comparison with cartesian coordinates, I further tested test 1 and 2 models in cartesian coordinates with linear conversion (1o deg = 111 km).

The result shows a negligible flow of the test 1 model in the cartesian system (Fig. 4a-4b).

Test 2 in cartesian shows downward in oceanic and upward in continental but also I cannot find vigorous flow at the northern and southern boundaries.

Fig. 4

I just think they are driven by geometrical effects but I am not convinced.

Any comments are really helpful for me

Thanks

Sungho Lee