Description
Estimate Airy crustal root and compensation depth from explicit density contrast and topography.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Estimate Airy crustal root and compensation depth from explicit density contrast and topography.
When to use this tool
Use this tool when you need to estimate Airy crustal root and compensation depth from explicit density contrast and topography.
How to use the tool and how it works
- Enter topographicHeightMeters, crustDensityKgPerM3, mantleDensityKgPerM3, referenceCrustThicknessMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.rootThicknessMeters, result.compensationDepthBelowReferenceMeters, using the stated boundary, ordering, sign and absence conventions.
Calculate Airy root thickness=rhoCrust×topographicHeight/(rhoMantle−rhoCrust), then add reference crust thickness for compensation depth below the reference surface.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| topographicHeightMeters | Nonnegative topographic height in meters, at most 10,000. | Finite numeric value satisfying the stated comparisons. |
| crustDensityKgPerM3 | Positive uniform crust density in kg/m³, strictly below mantle density. | Finite numeric value satisfying the stated comparisons. |
| mantleDensityKgPerM3 | Mantle density in kg/m³, greater than crust density and at most 10,000. | Finite numeric value satisfying the stated comparisons. |
| referenceCrustThicknessMeters | Positive reference crust thickness in meters, at most 100,000. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.rootThicknessMeters | Additional Airy crustal root thickness in meters. |
| result.compensationDepthBelowReferenceMeters | Reference crust thickness plus modeled root, in meters. |
{
"input": {
"topographicHeightMeters": 1000,
"crustDensityKgPerM3": 2700,
"mantleDensityKgPerM3": 3300,
"referenceCrustThicknessMeters": 30000
},
"output": {
"result": {
"rootThicknessMeters": 4500,
"compensationDepthBelowReferenceMeters": 34500
}
}
}Limitations and assumptions
- Height is 0–10,000 m, reference thickness in (0,100,000] m, and 0<crustDensity<mantleDensity≤10,000 kg/m³. This ideal local column balance excludes flexure, lateral density variation and tectonic interpretation.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
Similar or alternative tools
- Terrain Correction Simple Hammer Zone A Estimator
Calculate an ideal annular-sector terrain gravity correction from supplied geometry, relief and density.
- Somigliana Normal Gravity Theoretical Formula Calculator
Calculate Somigliana normal gravity from an explicit ellipsoid and compatible equatorial/polar constants.