landlab.components.flexure.flexure

Deform the lithosphere with 1D or 2D flexure.

Landlab component that implements a 1 and 2D lithospheric flexure model.

Examples

Create a grid on which we will run the flexure calculations.

>>> from landlab import RasterModelGrid
>>> from landlab.components.flexure import Flexure
>>> grid = RasterModelGrid((5, 4), xy_spacing=(1.0e4, 1.0e4))
>>> lith_press = grid.add_zeros("lithosphere__overlying_pressure_increment", at="node")

Check the fields that are used as input to the flexure component.

>>> Flexure.input_var_names
('lithosphere__overlying_pressure_increment',)

Check the units for the fields.

>>> Flexure.var_units("lithosphere__overlying_pressure_increment")
'Pa'

If you are not sure about one of the input or output variables, you can get help for specific variables.

>>> Flexure.var_help("lithosphere__overlying_pressure_increment")
name: lithosphere__overlying_pressure_increment
description:
  Applied pressure to the lithosphere over a time step
units: Pa
unit agnostic: True
at: node
intent: in

>>> flex = Flexure(grid)

In creating the component, a field (initialized with zeros) was added to the grid. Reset the interior nodes for the loading.

>>> dh = grid.at_node["lithosphere__overlying_pressure_increment"]
>>> dh = dh.reshape(grid.shape)
>>> dh[1:-1, 1:-1] = flex.gamma_mantle

>>> flex.update()

>>> flex.output_var_names
('lithosphere_surface__elevation_increment',)
>>> flex.grid.at_node["lithosphere_surface__elevation_increment"].reshape(grid.shape)
array([[0., 0., 0., 0.],
       [0., 1., 1., 0.],
       [0., 1., 1., 0.],
       [0., 1., 1., 0.],
       [0., 0., 0., 0.]])
class Flexure[source]

Bases: Component

Deform the lithosphere with 1D or 2D flexure.

Landlab component that implements a 1 and 2D lithospheric flexure model.

Examples

>>> from landlab import RasterModelGrid
>>> from landlab.components.flexure import Flexure
>>> grid = RasterModelGrid((5, 4), xy_spacing=(1.0e4, 1.0e4))
>>> lith_press = grid.add_zeros(
...     "lithosphere__overlying_pressure_increment", at="node"
... )

>>> flex = Flexure(grid)
>>> flex.name
'Flexure'
>>> flex.input_var_names
('lithosphere__overlying_pressure_increment',)
>>> flex.output_var_names
('lithosphere_surface__elevation_increment',)
>>> sorted(flex.units)
[('lithosphere__overlying_pressure_increment', 'Pa'),
 ('lithosphere_surface__elevation_increment', 'm')]

>>> flex.grid.number_of_node_rows
5
>>> flex.grid.number_of_node_columns
4
>>> flex.grid is grid
True

>>> np.all(grid.at_node["lithosphere_surface__elevation_increment"] == 0.0)
True

>>> np.all(grid.at_node["lithosphere__overlying_pressure_increment"] == 0.0)
True
>>> flex.update()
>>> np.all(grid.at_node["lithosphere_surface__elevation_increment"] == 0.0)
True

>>> load = grid.at_node["lithosphere__overlying_pressure_increment"]
>>> load[4] = 1e9
>>> dz = grid.at_node["lithosphere_surface__elevation_increment"]
>>> np.all(dz == 0.0)
True

>>> flex.update()
>>> np.all(grid.at_node["lithosphere_surface__elevation_increment"] == 0.0)
False

References

Required Software Citation(s) Specific to this Component

Hutton, E., Syvitski, J. (2008). Sedflux 2.0: An advanced process-response model that generates three-dimensional stratigraphy. Computers & Geosciences. 34(10), 1319-1337. https://dx.doi.org/10.1016/j.cageo.2008.02.013

Additional References

Lambeck, K.: Geophysical Geodesy, The Slow Deformations of the Earth, Clarendon Press, Oxford, UK, 718 pp., 1988.

Initialize the flexure component.

Parameters:

  • grid (RasterModelGrid) – A grid.

  • eet (float, optional) – Effective elastic thickness (m).

  • youngs (float, optional) – Young’s modulus.

  • method ({'airy', 'flexure'}, optional) – Method to use to calculate deflections.

  • rho_mantle (float, optional) – Density of the mantle (kg / m^3).

  • gravity (float, optional) – Acceleration due to gravity (m / s^2).

  • n_procs (int, optional) – Number of processors to use for calculations.

__init__(grid, eet=65000.0, youngs=70000000000.0, method='airy', rho_mantle=3300.0, gravity=9.80665, n_procs=1)[source]

Initialize the flexure component.

Parameters:

  • grid (RasterModelGrid) – A grid.

  • eet (float, optional) – Effective elastic thickness (m).

  • youngs (float, optional) – Young’s modulus.

  • method ({'airy', 'flexure'}, optional) – Method to use to calculate deflections.

  • rho_mantle (float, optional) – Density of the mantle (kg / m^3).

  • gravity (float, optional) – Acceleration due to gravity (m / s^2).

  • n_procs (int, optional) – Number of processors to use for calculations.

static __new__(cls, *args, **kwds)
property alpha

Flexure parameter (m).

cite_as = '\n    @article{hutton2008sedflux,\n        title={Sedflux 2.0: An advanced process-response model that generates\n               three-dimensional stratigraphy},\n        author={Hutton, Eric WH and Syvitski, James PM},\n        journal={Computers \\& Geosciences},\n        volume={34},\n        number={10},\n        pages={1319--1337},\n        year={2008},\n        publisher={Pergamon}\n        }'
property coords

Return the coordinates of nodes on grid attached to the component.

property current_time

Current time.

Some components may keep track of the current time. In this case, the current_time attribute is incremented. Otherwise it is set to None.

Return type:

current_time

definitions = (('lithosphere__overlying_pressure_increment', 'Applied pressure to the lithosphere over a time step'), ('lithosphere_surface__elevation_increment', 'The change in elevation of the top of the lithosphere (the land surface) in one timestep'))
property eet

Effective elastic thickness (m).

classmethod from_path(grid, path)

Create a component from an input file.

Parameters:

  • grid (ModelGrid) – A landlab grid.

  • path (str or file_like) – Path to a parameter file, contents of a parameter file, or a file-like object.

Returns:

A newly-created component.

Return type:

Component

property gamma_mantle

Specific density of mantle (N/m^3).

property gravity

Acceleration due to gravity (m/s^2).

property grid

Return the grid attached to the component.

initialize_optional_output_fields()

Create fields for a component based on its optional field outputs, if declared in _optional_var_names.

This method will create new fields (without overwrite) for any fields output by the component as optional. New fields are initialized to zero. New fields are created as arrays of floats, unless the component also contains the specifying property _var_type.

initialize_output_fields(values_per_element=None)

Create fields for a component based on its input and output var names.

This method will create new fields (without overwrite) for any fields output by, but not supplied to, the component. New fields are initialized to zero. Ignores optional fields. New fields are created as arrays of floats, unless the component specifies the variable type.

Parameters:

values_per_element (int (optional)) – On occasion, it is necessary to create a field that is of size (n_grid_elements, values_per_element) instead of the default size (n_grid_elements,). Use this keyword argument to acomplish this task.

input_var_names = ('lithosphere__overlying_pressure_increment',)
property method

Name of method used to calculate deflections.

name = 'Flexure'
optional_var_names = ()
output_var_names = ('lithosphere_surface__elevation_increment',)
property rho_mantle

Density of mantle (kg/m^3).

property shape

Return the grid shape attached to the component, if defined.

subside_loads(loads, row_col_of_load=None, out=None)[source]

Subside surface due to multiple loads.

Parameters:

  • loads (ndarray of float) – Loads applied to grid node. loads can be either an array of size n_nodes, in which case the load values are applied at their corresponding nodes, or an array of arbitray length, in which case loads are applied at locations supplied through the row_col_of_load keyword.

  • row_col_of_load (tuple of ndarray of int, optional) – If provided, the row and column indices where loads are applied. The first element of the tuple is an array of rows while the seconds element is an array of columns.

  • out (ndarray of float, optional) – Buffer to place resulting deflection values. If not provided, deflections will be placed into a newly-allocated array.

Returns:

Deflections caused by the loading.

Return type:

ndarray of float

subside_loads_slow(loads, out=None)[source]

Subside surface due to multiple loads.

Parameters:

  • loads (ndarray of float) – Loads applied to each grid node.

  • out (ndarray of float, optional) – Buffer to place resulting deflection values.

Returns:

Deflections caused by the loading.

Return type:

ndarray of float

unit_agnostic = True
units = (('lithosphere__overlying_pressure_increment', 'Pa'), ('lithosphere_surface__elevation_increment', 'm'))
update()[source]

Update fields with current loading conditions.

classmethod var_definition(name)

Get a description of a particular field.

Parameters:

name (str) – A field name.

Returns:

A description of each field.

Return type:

tuple of (name, *description*)

classmethod var_help(name)

Print a help message for a particular field.

Parameters:

name (str) – A field name.

classmethod var_loc(name)

Location where a particular variable is defined.

Parameters:

name (str) – A field name.

Returns:

The location (‘node’, ‘link’, etc.) where a variable is defined.

Return type:

str

var_mapping = (('lithosphere__overlying_pressure_increment', 'node'), ('lithosphere_surface__elevation_increment', 'node'))
classmethod var_type(name)

Returns the dtype of a field (float, int, bool, str…).

Parameters:

name (str) – A field name.

Returns:

The dtype of the field.

Return type:

dtype

classmethod var_units(name)

Get the units of a particular field.

Parameters:

name (str) – A field name.

Returns:

Units for the given field.

Return type:

str

property youngs

Young’s modulus of lithosphere (Pa).