from typing import Any
import numpy as np
from cratermaker.components.counting import Counting
from cratermaker.components.crater import Crater
[docs]
@Counting.register("depthcount")
class DepthCount(Counting):
"""
A basic crater counting model that uses depth-to-diameter values to estimate degradation states of craters for counting.
Parameters
----------
surface : Surface | LocalSurface
The surface or local surface view to be counted.
**kwargs : Any
|kwargs|
"""
def __init__(self, surface, **kwargs: Any):
super().__init__(surface=surface, **kwargs)
[docs]
def measure_degradation_state(self, crater: Crater, **kwargs: Any) -> float:
"""
Measure the degradation state of a crater by using a variation of the depth-to-diameter proxy for degradation state from Minton et al. (2019) [#]_ and Riedel et al. (2020) [#]_.
Parameters
----------
crater : Crater
The crater to measure.
**kwargs : Any
|kwargs|
Returns
-------
float
The estimated degradation state of the crater in m². The crater object will also have its degradation state value updated in place
References
----------
.. [#] Minton, D.A., Fassett, C.I., Hirabayashi, M., Howl, B.A., Richardson, J.E., (2019). The equilibrium size-frequency distribution of small craters reveals the effects of distal ejecta on lunar landscape morphology. Icarus 326, 63-87. `doi:10.1016/j.icarus.2019.02.021 <https://doi.org/10.1016/j.icarus.2019.02.021>`_
.. [#] Riedel, C., Minton, D.A., Michael, G., Orgel, C., Bogert, C.H. van der, Hiesinger, H., 2020. Degradation of Small Simple and Large Complex Lunar Craters: Not a Simple Scale Dependence. Journal of Geophysical Research: Planets 125, e2019JE006273. `doi:10.1029/2019JE006273 <https://doi.org/10.1029/2019JE006273>`_
Notes
-----
The technique used here is a major improvement over the one used previously in CTEM. Rather than using the depth-to-diameter directly, it instead uses the ratio of the measured depth-to-diameter to the initial computed depth-to-diameter of the crater. Fitting functions for both simple and complex craters were developed using this metric.
"""
from cratermaker.constants import _VSMALL
# A simplified transition diameter for the two morphology regimes. A more comprehensive study including other planetary bodies is needed to improve this
_DTR = 10.0e3
# The following are empirically-derived constants determined through numerical experiments
c0 = 0.2771649498066961
c1 = 0.1032775007149389
d_scale = 178.40182304735092
s0 = 0.11511000581387373
s1 = 0.017078961587273955
p0 = 2.0700104291102317
p1 = 0.0920770504148557
def a_vs_diameter(diameter):
if diameter < _DTR:
return s0 + s1 * np.log(diameter)
else:
dkm = diameter * 1e-3
dtrkm = _DTR * 1e-3
return c0 + c1 * (1.0 - np.exp((dtrkm - dkm) / d_scale))
def p_vs_diameter(diameter):
if diameter > _DTR: # In the fit, we fixed the exponent p to be constant for complex craters
diameter = _DTR
return p0 + p1 * np.log(diameter)
def K_vs_depth_over_depth_orig(depth_over_depth_orig, a, p):
return a * (depth_over_depth_orig ** (-1 / p) - 1.0) * crater.measured_radius**2
if crater.measured_depth_to_diameter is None:
return 0.0
depth_over_depth_orig = crater.measured_depth_to_diameter / crater.depth_to_diameter
if depth_over_depth_orig < _VSMALL:
depth_over_depth_orig = _VSMALL
a = a_vs_diameter(crater.measured_diameter)
p = p_vs_diameter(crater.measured_diameter)
crater.degradation_state = K_vs_depth_over_depth_orig(depth_over_depth_orig, a, p)
return crater.degradation_state
[docs]
def visibility_function(self, crater: Crater, Kv1: float = 0.30, gamma: float = 2.0, **kwargs: Any) -> float:
"""
Calculate the visibility function for a crater using eq. 7 from Minton et al. (2019) [#]_.
Parameters
----------
crater : Crater
The crater to calculate the visibility function for.
Kv1: float
The visibility function parameter Kv1 from Minton et al. (2019). Default value is 0.30 based on recalibration with Cratermaker.
gamma: float
The visibility function parameter gamma from Minton et al. (2019). Default value is 2.0.
**kwargs : Any
|kwargs|
Returns
-------
float
The visibility function value for the crater in units of m².
References
----------
.. [#] Minton, D.A., Fassett, C.I., Hirabayashi, M., Howl, B.A., Richardson, J.E., (2019). The equilibrium size-frequency distribution of small craters reveals the effects of distal ejecta on lunar landscape morphology. Icarus 326, 63-87. `doi: 10.1016/j.icarus.2019.02.021 <https://doi.org/10.1016/j.icarus.2019.02.021>`_
"""
return Kv1 * crater.measured_radius**gamma
