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Using the Landlab flexure component

In this example we will: * create a Landlab component that solves the two-dimensional elastic flexure equation * apply randomly distributed point loads * run the component * plot some output

A bit of magic so that we can plot within this notebook.

%matplotlib inline
import numpy as np

Create the grid

We are going to build a uniform rectilinear grid with a node spacing of 10 km in the y-direction and 20 km in the x-direction on which we will solve the flexure equation.

First we need to import RasterModelGrid.

from landlab import RasterModelGrid

Create a rectilinear grid with a spacing of 10 km between rows and 20 km between columns. The numbers of rows and columms are provided as a tuple of (n_rows, n_cols), in the same manner as similar numpy functions. The spacing is also a tuple, (dy, dx).

grid = RasterModelGrid((200, 400), xy_spacing=(10e3, 20e3))

grid.dy, grid.dx

Create the component

Now we create the flexure component and tell it to use our newly-created grid. First, though, we’ll examine the Flexure component a bit.

from landlab.components.flexure import Flexure

The Flexure component, as with most landlab components, will require our grid to have some data that it will use. We can get the names of these data fields with the intput_var_names attribute of the component class.

Flexure.input_var_names

We see that flexure uses just one data field: the change in lithospheric loading. landlab component classes can provide additional information about each of these fields. For instance, to the the units for a field, use the var_units method.

Flexure.var_units("lithosphere__overlying_pressure_increment")

To print a more detailed description of a field, use var_help.

Flexure.var_help("lithosphere__overlying_pressure_increment")

What about the data that Flexure provides? Use the output_var_names attribute.

Flexure.output_var_names

Flexure.var_help("lithosphere_surface__elevation_increment")

Now that we understand the component a little more, create it using our grid.

grid.add_zeros("lithosphere__overlying_pressure_increment", at="node")
flex = Flexure(grid, method="flexure", n_procs=4)

Add some loading

We will add loads to the grid. As we saw above, for this component, the name of the variable that holds the applied loads is lithosphere__overlying_pressure. We add loads of random magnitude at every node of the grid.

load = np.random.normal(0, 100 * 2650.0 * 9.81, grid.number_of_nodes)
grid.at_node["lithosphere__overlying_pressure_increment"] = load

grid.imshow(
    "lithosphere__overlying_pressure_increment",
    symmetric_cbar=True,
    cmap="nipy_spectral",
)

Update the component to solve for deflection

If you have more than one processor on your machine you may want to use several of them.

flex.update()

As we saw above, the flexure component creates an output field (lithosphere_surface__elevation_increment) that contains surface deflections for the applied loads.

Plot the output

We now plot these deflections with the imshow method, which is available to all landlab components.

grid.imshow(
    "lithosphere_surface__elevation_increment",
    symmetric_cbar=True,
    cmap="nipy_spectral",
)

Maintain the same loading distribution but double the effective elastic thickness.

flex.eet *= 2.0
flex.update()
grid.imshow(
    "lithosphere_surface__elevation_increment",
    symmetric_cbar=True,
    cmap="nipy_spectral",
)

Now let’s add a vertical rectangular load to the middle of the grid. We plot the load grid first to make sure we did this correctly.

load[np.where(np.logical_and(grid.node_x > 3000000, grid.node_x < 5000000))] = (
    load[np.where(np.logical_and(grid.node_x > 3000000, grid.node_x < 5000000))] + 1e7
)
grid.imshow(
    "lithosphere__overlying_pressure_increment",
    symmetric_cbar=True,
    cmap="nipy_spectral",
)

flex.update()
grid.imshow(
    "lithosphere_surface__elevation_increment",
    symmetric_cbar=True,
    cmap="nipy_spectral",
)

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