Unexpected or abnormal flows with spherical chunk model

[sungho]

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

[sungho]

I conducted further tests for identifying the problem.
If it is the geometric effect, I thought it must have symmetric characteristics.

As a result, the northern and southern hemispheres are symmetrical.
Despite the magnitude of abnormal velocities reduced, the equator still shows relatively large velocity fields in the northern and southern boundaries.

Fig. 5. Latitude test

Since the length for longitude is larger than latitude, I checked whether it is a size-dependent problem.
As a result, it was confirmed that when the size was increased in the direction of latitude, the flow in the north and south became stronger.

Fig. 6. Demension test

When all boundary conditions were set to free-slip, the flows disappeared.
Therefore, it can be seen as a phenomenon occurring in the combination of spherical domain + free surface.

In order to remove the effects, I devise an idea that I subtracted model results from a reference model like Fig. 3 because the flows are limited to the boundaries.

I checked effectively removing the effects.

Sungho

[bangerth]

Sungho,
just poking in the dark, but are you using a geometry that is based on WGS84 or some other ellipsoid representation of the earth? It occurs to me that we are not consistent in this because if the surface is an ellipsoid, we still use a radial gravity vector which is not perpendicular to the surface. It would not surprise me in that case that one gets a relaxation of the surface to a sphere. Does the pattern you see match a relaxation to the sphere?
Best
W.

[bobmyhill]

This looks similar to the issue that Anne posted to Github a few days ago: Chunk geometry model gives different results when not centered around zero meridian · Issue #3969 · geodynamics/aspect · GitHub … so I suspect this is a Chunk-specific problem (as opposed to a problem involving an EllipsoidalChunk with zero ellipticity).

Rotating the entire problem to the zero meridian would be a hacky workaround, but it would be much better to fix the problem. I’m afraid I can’t provide any deep insights yet.

[sungho]

Bangerth,

Thank you for your comment.
My geometry is not an ellipsoid chunk but a spherical chunk.

Radial gravity vector is supposed to be normal to the surface then there is no reason to occur relaxation?!, I guess.

But unconditionally the high-velocity fields occur at the northern and southern boundary in my model.

To resolve the problem, I’ve devised an idea that I subtracted model results from a reference model like no perturbation model which has a uniform thickness of crust and mantle with the laterally uniform temperature field because the flows are limited to the boundaries, this would be not a fundamental solution though.

Also, I’ve checked effectively removing the effects then I can see flows associated with density anomalies.

Best

Sungho