Scaling

The Scaling class is an abstract base class for crater scaling relationships. Use the Scaling.maker method to create a specific scaling model.

Available Implementations

Class	Argument name	Example Usage
MonteCarloScaling	“montecarlo”	scaling_model = Scaling.maker(“montecarlo”, target=”Mars”, projectile=”asteroids”)
CTEMScaling	“ctem”	scaling_model = Scaling.maker(“ctem”, target=”Mars”, projectile=”asteroids”)

class cratermaker.components.scaling.Scaling(target=None, projectile=None, rng=None, rng_seed=None, rng_state=None, **kwargs)

Bases: ComponentBase

The abstract base class for all scaling models. It defines the interface for converting between projectile and crater diameters.

classmethod maker(scaling=None, target=None, projectile=None, rng=None, rng_seed=None, rng_state=None, **kwargs)

Initialize a Scaling model with the given name or instance.

Parameters:

• scaling (str, Scaling, or None, default=None) – The name of the scaling model to initialize. If None, the default model is used.

• target (Target | str, default=”Moon”) – The target body for the impact. Can be a Target object or a string representing the target name.

• projectile (Projectile | str, default=”asteroids”) – The projectile model for the impact. Can be an Projectile object or a string representing the projectile name.

• rng (numpy.random.Generator | None) – A numpy random number generator. If None, a new generator is created using the rng_seed if it is provided.

• rng_seed (Any type allowed by the rng_seed argument of numpy.random.Generator, optional) – The rng_seed for the RNG. If None, a new RNG is created.

• rng_state (dict, optional) – The state of the random number generator. If None, a new state is created.

• **kwargs (Any) – Additional keyword arguments that are either ignored or passed to internal functions as needed.

Returns:

Scaling – An instance of the specified scaling model.

Raises:

• KeyError – If the specified scaling model name is not found in the registry.

• TypeError – If the specified scaling model is not a string or a subclass of Scaling.

Available models:

• montecarlo

• ctem

abstractmethod projectile_to_transient(**kwargs)

abstractmethod transient_to_projectile(**kwargs)

abstractmethod transient_to_final(transient_diameter, **kwargs)

abstractmethod final_to_transient(final_diameter, morphology_type=None, **kwargs)

abstractmethod recompute(**kwargs)

property target

The Target object associated with this Scaling object.

property projectile

The Projectile object associated with this Scaling object.

property model

The name of the scaling model.

MonteCarloScaling

See Scaling for inherited methods and attributes.

class cratermaker.components.scaling.montecarlo.MonteCarloScaling(target=None, projectile=None, material=None, K1=None, mu=None, Ybar=None, density=None, monte_carlo_scaling=True, rng=None, rng_seed=None, rng_state=None, **kwargs)

Bases: Scaling

An operations class for computing the scaling relationships between projectiles and craters.

This class encapsulates the logic for converting between projectile properties and crater properties, as well as determining crater morphology based on size and target properties. This implements the scaling laws similar to those in Richardson (2009) that were implemented in CTEM. However, unlike in CTEM, we apply monte carlo methods to the scaling laws to account for the uncertainty in the scaling laws. We have also included updated simple-to-complex transition diameter values from Schenk et al. (2021).

Parameters:

• target (Target | str, default=”Moon”) – The target body for the impact. Can be a Target object or a string representing the target name.

• projectile (Projectile | str, default=”asteroids”) – The projectile model for the impact. Can be an Projectile object or a string representing the projectile name.

• material (str or None) – Name of the target material composition of the target body to look up from the built-in catalogue. Options include “water”, “sand”, “dry soil”, “wet soil”, “soft rock”, “hard rock”, and “ice”.

• K1 (FloatLike, optional) – Variable used in crater scaling (see Richardson 2009)

• mu (FloatLike, optional) – Variable used in crater scaling (see Richardson 2009)

• Ybar (FloatLike, optional) – The strength of the target material, (Pa)

• density (FloatLike, optional) – Volumentric density of target material, (kg/m³)

• monte_carlo_scaling (bool, default=True) – If True, the scaling laws will be applied using monte carlo methods to account for the uncertainty in the scaling laws. If False, the scaling laws will be applied deterministically.

• rng (numpy.random.Generator | None) – A numpy random number generator. If None, a new generator is created using the rng_seed if it is provided.

• rng_seed (Any type allowed by the rng_seed argument of numpy.random.Generator, optional) – The rng_seed for the RNG. If None, a new RNG is created.

• rng_state (dict, optional) – The state of the random number generator. If None, a new state is created.

• **kwargs (Any) – Additional keyword arguments that are either ignored or passed to internal functions as needed.

Notes

• The target parameter is required and must be an instance of the Target class.

• The material parameter is optional. If not provided, it will be retrieved from target. Setting it explicitly will override the value in target.

• The K1, mu, Ybar, and density parameters are optional. If not provided, they will be retrieved from the material catalogue based on the material. Setting them explicitly will override the values in the catalogue.

• The built-in material property values are from Holsapple (1993) and Kraus et al. (2011).

• Complex crater scaling parameters are a synthesis of Pike (1980), Croft (1985), and Schenk et al. (2004), with updated simple-to-complex transition diameter values from Schenk et al. (2021).

References

• Richardson, J.E., 2009. Cratering saturation and equilibrium: A new model looks at an old problem. Icarus 204, 697-715. doi:10.1016/j.icarus.2009.07.029

• Holsapple, K.A., 1993. The scaling of impact processes in planetary sciences 21, 333-373. doi:10.1146/annurev.ea.21.050193.002001

• Kraus, R.G., Senft, L.E., Stewart, S.T., 2011. Impacts onto H2O ice: Scaling laws for melting, vaporization, excavation, and final crater size. Icarus 214, 724-738. doi:10.1016/j.icarus.2011.05.016

• Pike, R.J., 1980. Control of crater morphology by gravity and target type - Mars, earth, moon. In: Lunar and Planetary Science Conference 11, 2159-2189.

• Croft, S.K., 1985. The scaling of complex craters. Proceedings of the Fifteenth Lunar and Planetary Science Conference, Part 2 Journal of Geophysical Research 90, Supplement, C828-C842.

• Schenk, P.M., Chapman, C.R., Zahnle, K., Moore, J.M., 2004. Ages and interiors: the cratering record of the Galilean satellites, Cambridge University Press.

• Schenk, P., Castillo-Rogez, J., Otto, K.A., Marchi, S., O’Brien, D., Bland, M., Hughson, K., Schmidt, B., Scully, J., Buczkowski, D., Krohn, K., Hoogenboom, T., Kramer, G., Bray, V., Neesemann, A., Hiesinger, H., Platz, T., De Sanctis, M.C., Schroeder, S., Le Corre, L., McFadden, L., Sykes, M., Raymond, C., Russell, C.T., 2021. Compositional control on impact crater formation on mid-sized planetary bodies: Dawn at Ceres and Vesta, Cassini at Saturn. Icarus 359, 114343. doi:10.1016/j.icarus.2021.114343

final_to_transient(final_diameter=None, morphology_type=None, **kwargs)

Computes the transient diameter of a crater based on its final diameter and morphology type.

This method first ensures that the morphology type of the crater is computed. It then calculates the transient crater diameter based on the final diameter using scaling factors for simple or complex crater morphologies.

Parameters:

• final_diameter (float-like) – The final crater diameter in meters for which to compute the transient diameter.

• morphology_type (str, optional) – The morphology type of the crater (“simple”, “complex”, “transitional”)

Returns:

float – Returns the crater transient diameter in meters

transient_to_final(transient_diameter, **kwargs)

Computes the final diameter of a crater based on its transient diameter and morphology type.

This method first ensures that the morphology type of the crater is computed. It then calculates the final crater diameter based on the transient diameter using scaling factors for simple or complex crater morphologies. This is a bit more complicated than the final->transient calculation because In the transition region, a particular transient crater diameter could be associate with simple, complex, or transitional crater morphologies. Therefore we need to monte carlo our way into a solution to avoid biasing in favor of one or another in the transient->final computation

Parameters:

transient_diameter (FloatLike) – The transient diameter in meters of the crater to convert to final.

Returns:

• float – The final crater diameter

• str – The morphology type of the crater

projectile_to_transient(projectile_diameter, **kwargs)

Calculate the transient diameter of a crater based on the properties of the projectile and target.

Returns:

float – The calculated transient diameter of the crater resulting from the impact.

transient_to_projectile(transient_diameter, **kwargs)

Estimate the characteristics of the projectile that could have created a given crater.

This method approximates the properties of a hypothetical projectile based on the characteristics of a known crater.

Parameters:

• transient_diameter (float) – The diameter of the crater in meters.

• **kwargs (Any) – Additional keyword arguments that are either ignored or passed to internal functions as needed.

Returns:

Crater – The computed projectile for the crater.

property material_catalogue

The material catalogue used to look up material properties. Material property values are from Holsapple (1993) and Kraus et al. (2011).

Returns:

dict – The material catalogue.

References

• Holsapple, K.A., 1993. The scaling of impact processes in planetary sciences 21, 333-373. doi:10.1146/annurev.ea.21.050193.002001

• Kraus, R.G., Senft, L.E., Stewart, S.T., 2011. Impacts onto H2O ice: Scaling laws for melting, vaporization, excavation, and final crater size. Icarus 214, 724-738. doi:10.1016/j.icarus.2011.05.016

recompute()

Computes and sets the internal attributes for transition factors between simple and complex craters.

property transition_diameter

The transition diameter between simple and complex craters in m.

property transition_nominal

The nominal transition diameter between simple and complex craters in m.

property simple_enlargement_factor

The enlargement factor for simple craters.

property complex_enlargement_factor

The enlargement factor for complex craters.

property final_exp

The exponent used in the final rim radius to simple crater radius relationship.

property K1

The K₁ term in the crater scaling relationship.

property mu

The μ term in the crater scaling relationship.

property Ybar

The Ȳ term in the crater scaling relationship, which is the strength of the material in Pa.

property catalogue_key

The key used to identify the property used as the key in a catalogue.

property material

The name of the material composition of the target body.

property monte_carlo_scaling

If True, the scaling laws will be applied using monte carlo methods to account for the uncertainty in the scaling laws. If False, the scaling laws will be applied deterministically.

Usage example

from cratermaker import Scaling
scaling_model = Scaling.maker("montecarlo", target="Mars", projectile="asteroids")

CTEMScaling

See MonteCarloScaling for inherited methods and attributes.

class cratermaker.components.scaling.ctem.CTEMScaling(target=None, projectile=None, material=None, K1=None, mu=None, Ybar=None, density=None, **kwargs)

Bases: MonteCarloScaling

An operations class for computing the scaling relationships between projectiles and craters.

This class encapsulates the logic for converting between projectile properties and crater properties, as well as determining crater morphology based on size and target propertiesImplements the scaling laws described in Richardson (2009) that were implemented in CTEM.

Parameters:

• target (Target | str, default=”Moon”) – The target body for the impact. Can be a Target object or a string representing the target name.

• projectile (Projectile | str, default=”asteroids”) – The projectile model for the impact. Can be an Projectile object or a string representing the projectile name.

• material (str or None) – Name of the target material composition of the target body to look up from the built-in catalogue. Options include “water”, “sand”, “dry soil”, “wet soil”, “soft rock”, “hard rock”, and “ice”.

• K1 (FloatLike, optional) – Variable used in crater scaling (see Richardson 2009)

• mu (FloatLike, optional) – Variable used in crater scaling (see Richardson 2009)

• Ybar (FloatLike, optional) – The strength of the target material, (Pa)

• density (FloatLike, optional) – Volumentric density of target material, (kg/m³)

• **kwargs (Any) – Additional keyword arguments that are either ignored or passed to internal functions as needed.

Notes

• The target parameter is required and must be an instance of the Target class.

• The material parameter is optional. If not provided, it will be retrieved from target. Setting it explicitly will override the value in target.

• The K1, mu, Ybar, and density parameters are optional. If not provided, they will be retrieved from the material catalogue based on the material. Setting them explicitly will override the values in the catalogue.

• The built-in material property values are from Holsapple (1993) and Kraus et al. (2011).

• Complex craater scaling parameters are a synthesis of Pike (1980), Croft (1985), and Schenk et al. (2004).

References

• Richardson, J.E., 2009. Cratering saturation and equilibrium: A new model looks at an old problem. Icarus 204, 697-715. doi:10.1016/j.icarus.2009.07.029

• Holsapple, K.A., 1993. The scaling of impact processes in planetary sciences 21, 333-373. doi:10.1146/annurev.ea.21.050193.002001

• Kraus, R.G., Senft, L.E., Stewart, S.T., 2011. Impacts onto H2O ice: Scaling laws for melting, vaporization, excavation, and final crater size. Icarus 214, 724-738. doi:10.1016/j.icarus.2011.05.016

• Pike, R.J., 1980. Control of crater morphology by gravity and target type - Mars, earth, moon. In: Lunar and Planetary Science Conference 11, 2159-2189.

• Croft, S.K., 1985. The scaling of complex craters. Proceedings of the Fifteenth Lunar and Planetary Science Conference, Part 2 Journal of Geophysical Research 90, Supplement, C828-C842.

• Schenk, P.M., Chapman, C.R., Zahnle, K., Moore, J.M., 2004. Ages and interiors: the cratering record of the Galilean satellites, Cambridge University Press. Cambridge University Press, Cambridge, UK.

recompute()

Computes and sets the internal attributes for transition factors between simple and complex craters.

Usage example

from cratermaker import Scaling
scaling_model = Scaling.maker("ctem", target="Mars", projectile="asteroids")