Skip to content

Main content
Bookmark this: tool.io/geodesy/terrain-correction-hammer-zone-a

Terrain Correction Simple Hammer Zone A Estimator

Compute a flat-topped Hammer-style annular-sector terrain correction magnitude for supplied inner/outer radius, signed relief and density; no DEM sampling, fixed zone-A dimensions or complete terrain reduction.

Loading tool…

Description

Calculate an ideal annular-sector terrain gravity correction from supplied geometry, relief and density.

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 an ideal annular-sector terrain gravity correction from supplied geometry, relief and density.

When to use this tool

Use this tool when you need to calculate an ideal annular-sector terrain gravity correction from supplied geometry, relief and density.

How to use the tool and how it works

  1. Enter innerRadiusMeters, outerRadiusMeters, reliefMeters, densityKgPerM3, angularWidthDegrees using the definitions below.
  2. Run the operation. Resolve input-format errors before interpreting an output.
  3. Read result.terrainCorrectionMgal, using the stated boundary, ordering, sign and absence conventions.

Treat the terrain as one constant-relief annular sector of positive density. Use absolute relief h and evaluate 2πGρ×(angularWidth/360)×[rOuter−rInner+sqrt(rInner²+h²)−sqrt(rOuter²+h²)], using an algebraically stable equivalent and converting to mGal.1

Input fieldMeaning and unitsAccepted input
innerRadiusMetersNonnegative inner radius of the terrain sector in meters, below outerRadiusMeters.Finite numeric value satisfying the stated comparisons.
outerRadiusMetersOuter terrain-sector radius in meters, greater than inner and at most 100,000.Finite numeric value satisfying the stated comparisons.
reliefMetersSigned sector relief in meters, within ±10,000; its absolute value is used.Finite numeric value satisfying the stated comparisons.
densityKgPerM3Positive terrain density in kg/m³, at most 10,000.Finite numeric value satisfying the stated comparisons.
angularWidthDegreesSector width in degrees, strictly positive and at most 360.Finite numeric value satisfying the stated comparisons.
Output fieldInterpretation
resultObject containing the fields below.
result.terrainCorrectionMgalNonnegative modeled annular-sector terrain correction in mGal.
json
{
  "input": {
    "innerRadiusMeters": 0,
    "outerRadiusMeters": 4,
    "reliefMeters": 3,
    "densityKgPerM3": 1000,
    "angularWidthDegrees": 360
  },
  "output": {
    "result": {
      "terrainCorrectionMgal": 0.08387172739141742
    }
  }
}

Limitations and assumptions

  • Require 0≤inner<outer≤100,000 m, abs(relief)≤10,000 m, 0<density≤10,000 kg/m³ and 0<width≤360°. The name does not select a preset Hammer zone; supply the actual sector geometry. This is one idealized sector, not a DEM terrain correction.
  • 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

  1. Tool behavior and example: Terrain Correction Simple Hammer Zone A Estimator — tool.io

Similar or alternative tools

Support Tool.io