Description
Calculate the signed upward gravity gradient from two supplied gravity observations and their height separation.
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.
Calculate the signed upward gravity gradient from two supplied gravity observations and their height separation.
When to use this tool
Use this tool when you need to calculate the signed upward gravity gradient from two supplied gravity observations and their height separation.
How to use the tool and how it works
- Enter upperGravityMicrogal, lowerGravityMicrogal, heightDifferenceMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.signedMicrogalPerMeter, using the stated boundary, ordering, sign and absence conventions.
Subtract lowerGravityMicrogal from upperGravityMicrogal and divide by the strictly positive vertical height difference in meters.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| upperGravityMicrogal | Signed upper-station gravity in microgal, magnitude at most 10¹⁰; use the same convention as the lower station. | Finite numeric value satisfying the stated comparisons. |
| lowerGravityMicrogal | Signed lower-station gravity in microgal, magnitude at most 10¹⁰. | Finite numeric value satisfying the stated comparisons. |
| heightDifferenceMeters | Positive upper-minus-lower height separation in meters, at most 10,000. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.signedMicrogalPerMeter | Upper-minus-lower gravity divided by height difference, in microgal/m. |
{
"input": {
"upperGravityMicrogal": 100,
"lowerGravityMicrogal": 120,
"heightDifferenceMeters": 2
},
"output": {
"result": {
"signedMicrogalPerMeter": -10
}
}
}Limitations and assumptions
- The sign is upper-minus-lower per meter. Height difference is at most 10,000 m and absolute gravity inputs at most 10¹⁰ microgal; the operation does not assume or apply a normal free-air gradient. One microgal is 10⁻⁸ m/s².
- 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
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