Crater densities¶

Chosen by "type" in density, distributions.

Type	What it is
`power_law`	A cumulative power law, N(>=D) = coefficient D^-exponent per m^2 with D in metres.
`piecewise_power_law`	A cumulative distribution made of power-law segments over diameter ranges.
`tabulated`	A cumulative distribution from a table of diameters and counts N(>=D), in units you choose.
`production_surface`	The craters a production function leaves on a surface of a given age, scaled by a chronology, with no erosion; cap it with an equilibrium in a minimum.
`minimum`	The least of several densities at each diameter, such as a production surface capped by an equilibrium.
`trask`	The Trask (1966) lunar equilibrium density, N(>=D) = 10^-1.1 D^-2.
`hartmann`	The Hartmann (1984) lunar equilibrium density, N(>=D) = 10^-1.14 D^-1.83 per km^2 with D in km.
`moore`	Moore's terrain-specific crater distributions for Lunar Roving Vehicle trafficability.
`viper`	The VIPER environmental specification crater density, as synthterrain uses it; kept for comparison with synthterrain.
`piecewise_uniform`	Counts per m^2 in diameter bands, each with diameters spread uniformly across it; none outside the bands.

`power_law`¶

A cumulative power law, N(>=D) = coefficient D^-exponent per m^2 with D in metres.

Key	Type	Default	Range	Unit	Description
`coefficient`	number	`0.1`	(0, inf)		Coefficient of N(>=D) = coefficient D^-exponent, the cumulative count per m^2 with D in metres; scales how many there are.
`exponent`	number	`2.0`	(0, inf)		Exponent of the power law; larger values give relatively more small craters or boulders.

Every key with its default

{
    "type": "power_law",
    "coefficient": 0.1,
    "exponent": 2.0
}

Used in: example_distributions_power_law, example_planets_asteroid_body_mesh

`piecewise_power_law`¶

A cumulative distribution made of power-law segments over diameter ranges.

segments[]: Power-law segments in strictly increasing order of start, each running to the next one's start; they must meet at their joins.

Key	Type	Default	Range	Unit	Description
`start`	number	`0.0`	[0, inf)	m	Diameter in metres where this segment begins; it runs up to the next segment's start.
`coefficient`	number	`1.0`	(0, inf)		Coefficient of N(>=D) = coefficient D^-exponent, the cumulative count per m^2 with D in metres.
`exponent`	number	`2.0`	(0, inf)		Exponent of the segment's power law; larger values give relatively more small craters.

Every key with its default

{
    "type": "piecewise_power_law",
    "segments": [
        {
            "start": 0.0,
            "coefficient": 1.0,
            "exponent": 2.0
        }
    ]
}

Used in: example_distributions_piecewise_power_law

`tabulated`¶

A cumulative distribution from a table of diameters and counts N(>=D), in units you choose.

Key	Type	Default	Range	Unit	Description
`diameters`	list of number	`[]`	(0, inf)		Table diameters in diameter units, at least two, positive and strictly increasing; counts are interpolated linearly in log D and log N between them.
`cumulative`	list of number	`[]`	(0, inf)		Cumulative count N(>=D) at each diameter, per area unit; positive and not increasing.
`diameter_unit`	number	`1.0`	(0, inf)	m	Metres per table diameter unit: 1 for metres, 1000 for km.
`area_unit`	number	`1.0`	(0, inf)	m^2	Square metres per table area unit: 1 for m^2, 1e6 for km^2.

Every key with its default

{
    "type": "tabulated",
    "diameters": [],
    "cumulative": [],
    "diameter_unit": 1.0,
    "area_unit": 1.0
}

Used in: example_distributions_tabulated

`production_surface`¶

The craters a production function leaves on a surface of a given age, scaled by a chronology, with no erosion; cap it with an equilibrium in a minimum.

Key	Type	Default	Range	Unit	Description
`production`	one of `neukum`, `extended_neukum`, `ivanov`	`"extended_neukum"`			Production function that gives the craters' sizes.
`chronology`	one of `neukum`, `ivanov`	`"neukum"`			Chronology that gives how many craters at least 1 km across the surface holds.
`age_gyr`	number	`3.5`	[0, 4.6]	Gyr	Age of the surface in Gyr, from 0 to 4.6; older surfaces hold more craters.

Every key with its default

{
    "type": "production_surface",
    "production": "extended_neukum",
    "chronology": "neukum",
    "age_gyr": 3.5
}

Used in: example_ages_fresh, example_ages_steady_state, example_ages_uniform, example_albedo_blast_zone, example_albedo_crater_rays, example_albedo_fresh_crater, example_albedo_moon_site, example_albedo_new_crater and 20 more

`minimum`¶

The least of several densities at each diameter, such as a production surface capped by an equilibrium.

Key	Type	Default	Range	Unit	Description
`distributions`	list of crater densities	`[]`			Densities whose least cumulative count at each diameter is used; at least one.

Every key with its default

{
    "type": "minimum",
    "distributions": []
}

Used in: example_ages_fresh, example_ages_steady_state, example_ages_uniform, example_albedo_blast_zone, example_albedo_crater_rays, example_albedo_fresh_crater, example_albedo_moon_site, example_albedo_new_crater and 18 more

`trask`¶

The Trask (1966) lunar equilibrium density, N(>=D) = 10^-1.1 D^-2.

Every key with its default

{
    "type": "trask"
}

Used in: example_ages_fresh, example_ages_steady_state, example_ages_uniform, example_albedo_blast_zone, example_albedo_crater_rays, example_albedo_fresh_crater, example_albedo_moon_site, example_albedo_new_crater and 23 more

`hartmann`¶

The Hartmann (1984) lunar equilibrium density, N(>=D) = 10^-1.14 D^-1.83 per km^2 with D in km.

Every key with its default

{
    "type": "hartmann"
}

`moore`¶

Moore's terrain-specific crater distributions for Lunar Roving Vehicle trafficability.

Key	Type	Default	Range	Unit	Description
`terrain`	one of `rough_mare`, `smooth_mare`, `uplands`, `heavily_cratered`	`"rough_mare"`			Terrain type whose crater distribution of Moore's to use.

Every key with its default

{
    "type": "moore",
    "terrain": "rough_mare"
}

Used in: example_distributions_moore_rough_mare

`viper`¶

The VIPER environmental specification crater density, as synthterrain uses it; kept for comparison with synthterrain.

Every key with its default

{
    "type": "viper"
}

Used in: example_distributions_viper

`piecewise_uniform`¶

Counts per m^2 in diameter bands, each with diameters spread uniformly across it; none outside the bands.

Key	Type	Default	Range	Unit	Description
`total`	number	`0.0`	[0, inf)	1/m^2	Count per m^2 of all bands together, shared in proportion to each band's density; 0 uses the densities as given.

bands[]: Diameter bands with their counts; overlapping bands add, and gaps between them hold none.

Key	Type	Default	Range	Unit	Description
`min`	number	`1.0`	(0, inf)	m	Smallest diameter of the band in metres.
`max`	number	`2.0`	(0, inf)	m	Largest diameter of the band in metres, above min.
`density`	number	`0.01`	[0, inf)	1/m^2	Count per m^2 with diameters in the band, spread uniformly across it; a relative weight when total is set.

Every key with its default

{
    "type": "piecewise_uniform",
    "bands": [
        {
            "min": 1.0,
            "max": 2.0,
            "density": 0.01
        }
    ],
    "total": 0.0
}

Used in: example_distributions_piecewise_uniform

Crater densities¶

power_law¶

piecewise_power_law¶

tabulated¶

production_surface¶

minimum¶

trask¶

hartmann¶

moore¶

viper¶

piecewise_uniform¶

`power_law`¶

`piecewise_power_law`¶

`tabulated`¶

`production_surface`¶

`minimum`¶

`trask`¶

`hartmann`¶

`moore`¶

`viper`¶

`piecewise_uniform`¶