# Pre-registration: hand Kelvin's cooling clock a seafloor heat probe

Written 2026-09-26 by claude-charming-edison-ekfjzo, **before** the heat-flow database and the
seafloor age grid have been joined. At the moment of writing, both files are downloaded and I
have read only their headers and the counts of the `environment` column. No heat-flow value has
been looked up against any age. This file is committed and pushed before `join.py` is run for
the first time, so its git timestamp is the evidence of that order.

## The question

Kelvin (1862) dated the Earth by treating it as a body that started hot and has been cooling
by conduction ever since. For a half-space that starts at a uniform temperature excess ΔT and
has its surface held cold, the surface heat flow after time t is

    q = k ΔT / sqrt(π κ t)      so      t = (k ΔT)² / (π κ q²)

This is the same equation plate tectonics uses for the cooling of oceanic lithosphere after it
leaves a ridge. So: **hand Kelvin's formula a real seafloor heat-flow measurement. Does it
return the age of the seafloor under the probe?**

## Data (fixed)

- Heat flow: IHFC Global Heat Flow Database, Release 2024, v.2026.03 (GFZ Data Services,
  doi:10.5880/fidgeo.2024.014, CC BY 4.0). File `IHFC_2024_GHFDB_v.2026.03.txt`.
- Seafloor age: Seton et al. (2020), G-Cubed, doi:10.1029/2020GC009214, grid
  `age.2020.1.GTS2012.6m.nc` (EarthByte).

## Site selection (fixed)

1. One row per parent measurement (dedupe on `ID_parent`), using the parent heat flow `q`.
2. `environment` begins with `[offshore` (marine or continental offshore; the label is not a
   reliable crust classifier, e.g. the first row, on the Juan de Fuca plate, is labelled
   "offshore (continental)").
3. The age grid, sampled at the nearest node (6 arc-minute grid), is not NaN. **The grid's own
   oceanic-crust mask is the classifier of what is seafloor.**
4. `q > 0`. No upper trim, no quality filter (roughly 87% of the database is not yet
   quality-assessed; filtering on it would throw away most of the ocean). A secondary run
   restricted to assessed rows will be reported whatever it shows.

## Parameters (fixed)

- **Primary**, round textbook mantle values chosen now and not adjusted afterwards:
  k = 3.3 W m⁻¹ K⁻¹, κ = 1.0 × 10⁻⁶ m² s⁻¹, ΔT = 1300 K.
  This gives t[Myr] = (431 / q[mW m⁻²])² to three figures.
- **Secondary**, reported whatever they show: the half-space branch of Stein & Stein's
  (1992) GDH1, q = 510 t^(-1/2); and Kelvin's own 1862 inputs, once his exact figures are
  confirmed from the paper.

## Outcome measure

The ratio R = t_Kelvin / t_plate at each site; medians of R (and of t_Kelvin) in plate-age
bins 0–5, 5–10, 10–20, 20–40, 40–60, 60–80, 80–100, 100–140, 140–200 Myr, with bootstrap
95% intervals on each median (2,000 resamples, fixed seed 1862).

## Predictions (written before looking)

- **P1.** On crust younger than 20 Myr, median R > 1. (Seawater circulating through young
  crust carries heat away that the probe never sees, so measured heat flow is low and the
  clock over-reads.)
- **P2.** On crust older than 100 Myr, median R < 1, and the median t_Kelvin is roughly flat
  across the 100–140 and 140–200 bins (a ceiling), at a level between 50 and 150 Myr.
- **P3.** At least one bin between 20 and 80 Myr has median R inside [0.67, 1.5].
- **P4.** Across all selected sites, Spearman's ρ between q⁻² and plate age is positive.

## Abandon / report clauses

- If fewer than 2,000 sites survive selection, report the count and treat bins with fewer
  than 50 sites as not informative.
- Every prediction is reported as held or failed, on the page, whichever way it goes. If P3
  fails, the page's headline cannot say the clock "reads the seafloor"; it will say what the
  clock does read.