gFlex: Compute elastic lithosphere flexure with variable rigidity#

This is a Landlab wrapper for A Wickert’s gFlex flexure model (Wickert et al., submitted to Geoscientific Model Development). The most up-to-date version of his code can be found at github.com/awickert/gFlex.

This Landlab wrapper will use a snapshot of that code, which YOU need to install on your own machine. A stable snapshot of gFlex is hosted on PyPI, which is the recommended version to install. If you have pip (the Python package install tool), simply run ‘pip install gFlex’ from a command prompt. Alternatively, you can download and unpack the code (from github, or with PyPI, pypi.python.org/pypi/gFlex/), then run ‘python setup.py install’.

Created on Thu Feb 19 18:47:11 2015

@author: daniel.hobley (SiccarPoint @Github)

…following AW’s run_in_script_2D.py.

class gFlex(*args, **kwds)[source]#

Bases: Component

This is a Landlab wrapper for A Wickert’s gFlex flexure model (Wickert et al., 2016, Geoscientific Model Development). The most up-to-date version of his code can be found at github.com/awickert/gFlex.

Note that gFlex maintains its own internal version if the grid, but this should not affect performance.

This component will modify the topographic__elevation field only if one already exists. Note that the gFlex component demands lengths in meters, including the grid dimensions. The component also recognises the gFlex specific parameters ‘Method’, ‘PlateSolutionType’, ‘Solver’, and ‘Quiet’. See the gFlex software documentation for more details.

Examples

NB: these tests are not actually run as our automated testing becomes confused if gFlex is not installed on the testing machine!

>>> from landlab import RasterModelGrid
>>> from landlab.components import gFlex
>>> mg = RasterModelGrid((10, 10), xy_spacing=25000.0)
>>> z = mg.add_zeros("topographic__elevation", at="node", dtype=float)
>>> stress = mg.add_zeros("surface_load__stress", at="node", dtype=float)
>>> stress.view().reshape(mg.shape)[3:7, 3:7] += 1.0e6
>>> gf = gFlex(
...     mg, BC_E="0Moment0Shear", BC_N="Periodic", BC_S="Periodic"
... )  
>>> gf.run_one_step()  

N-S profile across flexed plate:

>>> z.reshape(mg.shape)[:, 5]  
array([-4.54872677, -4.6484927 , -4.82638669, -5.03001546, -5.15351385,
       -5.15351385, -5.03001546, -4.82638669, -4.6484927 , -4.54872677])

W-E profile, noting the free BC to the east side:

>>> z.reshape(mg.shape)[5, :]  
array([-0.43536739, -1.19197738, -2.164915  , -3.2388464 , -4.2607558 ,
       -5.15351385, -5.89373366, -6.50676947, -7.07880156, -7.63302576])

References

Required Software Citation(s) Specific to this Component

Wickert, A. (2016). Open-source modular solutions for flexural isostasy: gFlex v1.0. Geoscientific Model Development 9(3), 997-1017. https://dx.doi.org/10.5194/gmd-9-997-2016

Additional References

None Listed

Constructor for Wickert’s gFlex in Landlab.

Parameters:

Youngs_modulus (float) – Young’s modulus for the lithosphere.
Poissons_ratio (float) – Poisson’s ratio for the lithosphere.
rho_mantle (float (kg*m**-3)) – The density of the mantle.
rho_fill (float (kg*m**-3)) – The density of the infilling material (air, water…)
elastic_thickness (float (m)) – The elastic thickness of the lithosphere.
BC_W ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
BC_E ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
BC_N ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
BC_S ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
g (float (m*s**-2)) – The acceleration due to gravity.

__init__(grid, Youngs_modulus=650000000000.0, Poissons_ratio=0.25, rho_mantle=3300.0, rho_fill=0.0, elastic_thickness=35000.0, Method='FD', Solver='direct', PlateSolutionType='vWC1994', quiet=True, BC_W='0Displacement0Slope', BC_E='0Displacement0Slope', BC_N='0Displacement0Slope', BC_S='0Displacement0Slope', g=9.80665)[source]#

Constructor for Wickert’s gFlex in Landlab.

Parameters:

Youngs_modulus (float) – Young’s modulus for the lithosphere.
Poissons_ratio (float) – Poisson’s ratio for the lithosphere.
rho_mantle (float (kg*m**-3)) – The density of the mantle.
rho_fill (float (kg*m**-3)) – The density of the infilling material (air, water…)
elastic_thickness (float (m)) – The elastic thickness of the lithosphere.
BC_W ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
BC_E ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
BC_N ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
BC_S ({'0Displacement0Slope', '0Moment0Shear',) – ‘Periodic’} The boundary condition status of each grid edge, following gFlex’s definitions. Periodic boundaries must be paired (obviously).
g (float (m*s**-2)) – The acceleration due to gravity.

flex_lithosphere()[source]#

Executes (& finalizes, from the perspective of gFlex) the core method of gFlex.

Note that flexure of the lithosphere proceeds to steady state in a single timestep.

run_one_step()[source]#

Flex the lithosphere to find its steady state form.

The standardized run method for this component.

Parameters:: None –