Calculator Inputs
Formula Used
Surface heat flow method:
T(z) = Ts + (qs / k)z - (A / 2k)z²
Basal heat flow method:
T(z) = Ts + (qb / k)z + (A / k)(Lz - z² / 2)
Here, T(z) is temperature at depth. Ts is surface temperature. q is heat flow. k is thermal conductivity. A is radiogenic heat production. L is model thickness. z is depth in meters.
Statistical range = temperature rise × uncertainty rate × confidence z-score. The tool uses z-scores of 1.645, 1.960, and 2.576.
How To Use This Calculator
- Enter surface temperature in degrees Celsius.
- Add the target depth where temperature is required.
- Enter thermal conductivity for the rock column.
- Add heat flow and heat production values.
- Select a surface or basal heat flow boundary.
- Set uncertainty and confidence level for statistical limits.
- Press the calculate button to see results above the form.
- Use CSV or PDF buttons to save the output.
Example Data Table
| Case | Ts (°C) | Depth (km) | q (mW/m²) | k (W/m·K) | A (µW/m³) | Use |
|---|---|---|---|---|---|---|
| Stable Craton | 10 | 30 | 45 | 3.1 | 0.6 | Cold crust estimate |
| Sedimentary Basin | 18 | 20 | 70 | 2.3 | 1.5 | Basin screening |
| Active Province | 22 | 15 | 95 | 2.5 | 2.0 | Warm region review |
Steady State Geotherm Overview
A steady state geotherm describes temperature change with depth. It assumes heat flow does not change with time. The model is useful when rocks have reached long term thermal balance. It is often used for crust studies, basin screening, and geothermal planning.
Why This Calculator Helps
This calculator combines thermal physics with simple statistics. You can enter surface temperature, heat flow, conductivity, heat production, and depth. The tool estimates temperature at a selected depth. It also builds a depth table. That table helps you inspect the full profile instead of one point.
Statistical Value
Measured thermal inputs often contain error. Heat flow may vary between wells. Conductivity can change with lithology. Radiogenic heat production may be uncertain. The calculator lets you add a percentage uncertainty. It then reports a confidence range around the temperature estimate. This range is not a field guarantee. It is a transparent planning guide.
Model Choices
You can use surface heat flow or basal heat flow. Surface heat flow is common when shallow measurements are available. Basal heat flow is useful when mantle input is estimated first. Heat production bends the profile because heat is generated inside rock. Higher production can raise shallow temperatures, depending on the selected boundary method.
Reading The Result
The main result shows target temperature, average gradient, heat flow at depth, and uncertainty limits. The gradient is given in degrees per kilometer. The table gives values from the surface to the chosen maximum depth. Use smaller steps for a smoother profile. Use larger steps for quick reports.
Practical Notes
This model assumes one dimensional conduction. It does not include groundwater flow, magma, faults, erosion, or recent climate shifts. Use it for screening and teaching. For engineering design, compare it with local borehole data and expert interpretation.
Best Use Cases
Use the calculator to compare scenarios before expensive modeling. Try conservative, normal, and high heat flow cases. Change one input at a time. This habit shows which measurement controls the answer most. Save the CSV file for audit trails. Save the PDF file for simple sharing. Keep units consistent, because thermal equations are sensitive to scale. Recheck extreme values before using the final table in reports and reviews later.
FAQs
What is a steady state geotherm?
It is a temperature depth curve that assumes heat flow is stable over time. It is commonly used for simple conductive crust models.
Which heat flow option should I use?
Use surface heat flow when measured surface values are available. Use basal heat flow when deeper mantle input is your main boundary estimate.
What units are required?
Depth is entered in kilometers. Heat flow uses mW/m². Conductivity uses W/m·K. Heat production uses µW/m³.
Why does heat production affect curvature?
Radiogenic heat is generated inside rocks. This internal source changes the slope of the geotherm and can bend the temperature profile.
Is this a field ready engineering model?
No. It is best for screening, education, and early comparison. Field design should use local boreholes, geology, and expert review.
What does uncertainty mean here?
It is a simple percentage applied to thermal rise. The calculator multiplies it by a confidence z-score to estimate a practical range.
Can groundwater flow change the answer?
Yes. Groundwater can move heat by advection. This calculator assumes conductive heat transfer, so flowing water is not included.
Why export CSV and PDF files?
CSV is useful for spreadsheets and further analysis. PDF is useful for quick reporting, sharing, and saving the calculated profile.