# ListricKinematicExtender: Simulate Extensional Tectonic Motion on a Listric Fault Plane#

Apply tectonic extension kinematically.

Landlab component that simulates development of an asymmetric rift on a listric fault plane.

See notebook tutorial for theory and examples.

@author: gtucker

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

Bases: `Component`

Apply tectonic extension kinematically to a raster or hex grid.

The caller specifies the strike, dip, and location of the zero-surface fault trace (i.e., where the fault plane would intersect zero elevation), and either the (x, y) components of uniform extension velocity field, or a link-based velocity field. The run_one_step() method calculates advection of an output field called “hangingwall__thickness”. The initial hanginwall thickness is defined as the difference between the starting topography field (a required input field) and a listric fault plane that is represented mathematically as an “upside-down” saturating exponential function that asymptotes to a caller-specified detachment depth, representing a decollement.

Examples

```>>> from landlab import RasterModelGrid
>>> from landlab.components import ListricKinematicExtender
>>> grid = RasterModelGrid((3, 130), xy_spacing=10.0)
>>> topo = grid.add_zeros("topographic__elevation", at="node")
>>> lke = ListricKinematicExtender(grid, fault_x0=100.0, fault_strike=90.0)
>>> for _ in range(250):
...     lke.run_one_step(dt=2000.0)
...
>>> round(grid.at_node["hangingwall__thickness"][240])
830
```

Deform vertically and horizontally to represent tectonic extension.

Parameters:
• grid (RasterModelGrid) – A landlab grid.

• extension_rate_x (float, optional) – Rate of x-directed horizontal motion of hangingwall relative to footwall (m / y), default 0.001 m/y.

• extension_rate_y (float, optional) – Rate of y-directed horizontal motion of hangingwall relative to footwall (m / y), default 0.

• fault_x0 (float, optional) – x intercept of zero-surface fault trace, m (default 0).

• fault_y0 (float, optional) – y intercept of zero-surface fault trace, m (default 0).

• fault_strike (float, optional) – Strike of zero-surface fault trace, degrees (default 45).

• detachment_depth (float, optional) – Depth to horizontal detachment (m), default 10 km.

• fields_to_advect (list of str, optional) – List of names of fields, in addition to ‘hangingwall__thickness’

• advection_direction_is_steady (bool (default False)) – Indicates whether the directions of advection are expected to remain steady throughout a run. If True, some computation time is saved by calculating upwind links only once.

__init__(grid, extension_rate_x=0.001, extension_rate_y=0.0, fault_dip=60.0, fault_x0=0.0, fault_y0=0.0, fault_strike=45.0, detachment_depth=10000.0, fields_to_advect=None, advection_direction_is_steady=False)[source]#

Deform vertically and horizontally to represent tectonic extension.

Parameters:
• grid (RasterModelGrid) – A landlab grid.

• extension_rate_x (float, optional) – Rate of x-directed horizontal motion of hangingwall relative to footwall (m / y), default 0.001 m/y.

• extension_rate_y (float, optional) – Rate of y-directed horizontal motion of hangingwall relative to footwall (m / y), default 0.

• fault_x0 (float, optional) – x intercept of zero-surface fault trace, m (default 0).

• fault_y0 (float, optional) – y intercept of zero-surface fault trace, m (default 0).

• fault_strike (float, optional) – Strike of zero-surface fault trace, degrees (default 45).

• detachment_depth (float, optional) – Depth to horizontal detachment (m), default 10 km.

• fields_to_advect (list of str, optional) – List of names of fields, in addition to ‘hangingwall__thickness’

• advection_direction_is_steady (bool (default False)) – Indicates whether the directions of advection are expected to remain steady throughout a run. If True, some computation time is saved by calculating upwind links only once.

run_one_step(dt)[source]#

Apply extensional motion to grid for one time step.

Parameters:

dt (float) – Time-step duration, y

update_fault_plane_elevation_and_hangingwall_thickness(grid, fault_x0, fault_y0, fault_strike, fault_dip, detachment_depth)[source]#

Initialize fields fault_plane__elevation and hangingwall__thickness.

Calculate and store the fault plane elevation at grid nodes using an exponential function of (signed) distance to fault, with topographic elevation as the minimum. Calculate the thickness of the hangingwall block at grid nodes by subtracting fault plane elevation from topographic elevation.

Parameters:
• fault_x0 (float) – x-intercept of zero-surface fault trace, m

• fault_y0 (float) – y-intercept of zero-surface fault trace, m

• fault_strike (float) – strike angle of fault trace, degrees ccw from +x

• fault_dip (float) – dip angle of fault at the zero elevation point, degrees

• detachment_depth (float) – depth to the point where the detachment is horizontal, m

Examples

```>>> from landlab import RasterModelGrid
>>> from landlab.components import ListricKinematicExtender
>>> grid = RasterModelGrid((3, 3), xy_spacing=1000.0)
>>> _ = grid.add_zeros("topographic__elevation", at="node")
>>> extender = ListricKinematicExtender(grid, fault_strike=90.0)
>>> round(grid.at_node["fault_plane__elevation"][4])
-1590
>>> round(grid.at_node["hangingwall__thickness"][4])
1590
```
dist_to_line(Px, Py, x0, y0, alpha)[source]#

Calculate and return the distance of point(x) (Px, Py) to the line described by x = x0 + t cos alpha, y = y0 + t sin alpha.

Parameters:
• Px (float) – x-coordinate of point(s)

• Py (float) – y-coordinate of point(s)

• x0 (float) – x intercept of line

• y0 (float) – y intercept of line

• alpha (float, degrees) – angle of line, counter-clockwise from positive x-axis

Examples

```>>> np.round(dist_to_line(1, 1, 0, 0, 90), 6)
1.0
>>> np.round(dist_to_line(0, 1, 1, 0, 90), 6)
-1.0
>>> np.round(dist_to_line(1, 1, 0, 0, 0), 6)
-1.0
>>> np.round(dist_to_line(2.0**0.5, 0, 0, 0, 45), 6)
1.0
>>> np.round(dist_to_line(0, 2.0**0.5, 0, 0, 45), 6)
-1.0
```