Plinian Dispersal Axis Isopach Area

Estimate contour-volume from supplied elliptical axes, trapezoidal thickness-area annuli, caller inner plateau and independently supplied outer tail; no dispersal-axis coordinate extraction or infinite-tail extrapolation.

Description

An isopach joins locations of equal deposit thickness.

An isopach joins locations of equal deposit thickness. Elliptical contours reduce mapped deposits to a thickness-versus-area integration.

When to use Plinian Dispersal Axis Isopach Area

Use this tool to estimate contour-volume from supplied elliptical axes, trapezoidal thickness-area annuli, caller inner plateau and independently supplied outer tail; no dispersal-axis coordinate extraction or infinite-tail extrapolation.

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.

How to use Plinian Dispersal Axis Isopach Area and understand its results

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
Enter isopachSemiMajorAxesM, isopachSemiMinorAxesM, isopachThicknessesM, innerPlateauThicknessM, outerTailVolumeM3 using the field table and calculation rules, then run the tool.
Read ellipticalContourAreasM2, representedBulkVolumeM3. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
isopachSemiMajorAxesM	Isopach semi major axes m	list of number	Required
isopachSemiMinorAxesM	Isopach semi minor axes m	list of number	Required
isopachThicknessesM	Isopach thicknesses m	list of number	Required
innerPlateauThicknessM	Inner plateau thickness m	number	Required
outerTailVolumeM3	Outer tail volume m3	number	Required

Supply positive semi-axes with major at least minor, increasing contour areas and nonincreasing thickness. Require plateau thickness at least the innermost contour thickness. Add independently supplied nonnegative outer-tail volume.^[1]

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.

volume = first area × inner plateau + trapezoidal thickness-area integral + outer tail

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
ellipticalContourAreasM2	Elliptical contour areas m2	list of number
representedBulkVolumeM3	Represented bulk volume m3	number

json

{
  "input": {
    "isopachSemiMajorAxesM": [
      10,
      20,
      30
    ],
    "isopachSemiMinorAxesM": [
      5,
      10,
      15
    ],
    "isopachThicknessesM": [
      3,
      2,
      1
    ],
    "innerPlateauThicknessM": 4,
    "outerTailVolumeM3": 100
  },
  "output": {
    "ellipticalContourAreasM2": [
      157.07963267948966,
      628.3185307179587,
      1413.7166941154069
    ],
    "representedBulkVolumeM3": 3084.5130209103036
  }
}

Limitations and assumptions

Axes, plateau and tail must be supplied; no dispersal mapping or infinite-tail extrapolation is performed.

Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Tephra Volume Weibull Integration: Integrate axisymmetric Weibull-form radial tephra thickness to a supplied truncation radius by bounded Simpson quadrature; caller panels control approximation and no infinite-tail volume or mapped dispersal is inferred. For a complementary task, use Isomass Loading GM2 Contour Tool: Locate a target isomass contour by log loading versus square-root enclosed area; supplied areas require no coordinates, circular radius is an equivalent proxy, not a mapped boundary.

References

Plinian Dispersal Axis Isopach Area — tool.io

Similar or alternative tools

Tephra Volume Weibull Integration
Integrate axisymmetric Weibull-form radial tephra thickness to a supplied truncation radius by bounded Simpson quadrature; caller panels control approximation and no infinite-tail volume or mapped dispersal is inferred.
Isomass Loading GM2 Contour Tool
Locate a target isomass contour by log loading versus square-root enclosed area; supplied areas require no coordinates, circular radius is an equivalent proxy, not a mapped boundary.