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.
Description
Tephra thickness declines away from a vent.
Tephra thickness declines away from a vent. Integrating thickness over concentric rings estimates deposit volume under an assumed radial profile.
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.
When to use Tephra Volume Weibull Integration
Use this tool to 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.
Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
How to use Tephra Volume Weibull Integration and understand its results
- Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
- Enter centerDepositThicknessM, radialScaleM, radialShapeExponent, maximumRadiusM, simpsonPanels, denseRockDensityKgPerM3, depositBulkDensityKgPerM3 using the field table and calculation rules, then run the tool.
- Read integratedBulkTephraVolumeM3, denseRockEquivalentVolumeM3. 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 |
|---|---|---|---|
| centerDepositThicknessM | Center deposit thickness m | number | Required |
| radialScaleM | Radial scale m | number | Required |
| radialShapeExponent | Radial shape exponent | number | Required |
| maximumRadiusM | Maximum radius m | number | Required |
| simpsonPanels | Simpson panels | integer | Required |
| denseRockDensityKgPerM3 | Dense rock density kg per m3 | number | Required |
| depositBulkDensityKgPerM3 | Deposit bulk density kg per m3 | number | Required |
Supply positive scale, shape and densities, nonnegative center thickness and radius, and an even panel count from 2 to 16384. Apply composite Simpson quadrature and convert bulk volume to DRE using the density ratio.1
bulk volume = ∫₀ᴿ 2πr T₀ exp(−(r/scale)^shape) dr Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| integratedBulkTephraVolumeM3 | Integrated bulk tephra volume m3 | number |
| denseRockEquivalentVolumeM3 | Dense rock equivalent volume m3 | number |
{
"input": {
"centerDepositThicknessM": 1,
"radialScaleM": 10,
"radialShapeExponent": 2,
"maximumRadiusM": 20,
"simpsonPanels": 2048,
"denseRockDensityKgPerM3": 2000,
"depositBulkDensityKgPerM3": 1000
},
"output": {
"integratedBulkTephraVolumeM3": 308.4052377011309,
"denseRockEquivalentVolumeM3": 154.20261885056544
}
}Limitations and assumptions
Finite truncation and numerical approximation exclude the infinite tail and nonaxisymmetric dispersal.
Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use 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. For a complementary task, use DRE To Tephra Volume Conversion: Convert declared whole-deposit DRE to bulk tephra volume by mass conservation, splitting supplied juvenile/lithic mass share; packing, vesicles and interclast pores are already embodied in measured bulk density.
References
-
Tephra Volume Weibull Integration — tool.io
Similar or alternative tools
- 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.
- DRE To Tephra Volume Conversion
Convert declared whole-deposit DRE to bulk tephra volume by mass conservation, splitting supplied juvenile/lithic mass share; packing, vesicles and interclast pores are already embodied in measured bulk density.