Subsidence Tilt

Evaluate spatial derivative of supplied downward-positive Gaussian trough; distinct from horizontal strain and excludes building response.

Description

Tilt is the spatial derivative of a Gaussian subsidence profile.

Tilt is the spatial derivative of a Gaussian subsidence profile. The sign indicates slope under the chosen coordinate convention.

The tool returns signedTiltsMPerM (signed tilts m per m). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Subsidence Tilt

Use Subsidence Tilt when you already have positionsM, maximumSubsidenceM, troughScaleM and want signedTiltsMPerM. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Subsidence Tilt and understand its results

Enter positionsM, maximumSubsidenceM, troughScaleM using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read signedTiltsMPerM. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
positionsM	Positions m	list of number	Required
maximumSubsidenceM	Maximum subsidence m	number	Required
troughScaleM	Trough scale m	number	Required

Use positive trough scale, nonnegative maximum subsidence and a nonempty position list. Return signed dimensionless slopes.

tilt(x) = −(Smax/scale)×(x/scale)×exp(−(x/scale)²/2)

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "positionsM": [
      -10,
      0,
      10
    ],
    "maximumSubsidenceM": 1,
    "troughScaleM": 10
  },
  "output": {
    "signedTiltsMPerM": [
      0.06065306597126335,
      0,
      -0.06065306597126335
    ]
  }
}

Limitations and assumptions

This prescribed smooth profile excludes discontinuities and complex geology. It does not infer maximum subsidence or scale from observations.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Subsidence Strain: Differentiate u(x)=c·s′(x) for caller downward-positive Gaussian subsidence; positive tensile/negative compressive strain depends on supplied c. Maximum Subsidence: Apply calibrated extraction, subsidence and finite-panel factors to seam thickness; no empirical table or settlement guarantee.

Methodological background: Mine Slope and Subsidence Monitoring Partnership.^[1]

References

Mine Slope and Subsidence Monitoring Partnership — NIOSH, Centers for Disease Control and Prevention

Similar or alternative tools

Subsidence Strain
Differentiate u(x)=c·s′(x) for caller downward-positive Gaussian subsidence; positive tensile/negative compressive strain depends on supplied c.
Maximum Subsidence
Apply calibrated extraction, subsidence and finite-panel factors to seam thickness; no empirical table or settlement guarantee.