Earth
Magnetic reversals
Run a ridge from six million years ago to today at 20 mm/yr and watch the crust leave it in stripes, normal and reversed, each as wide as the spreading rate times the chron it formed in, so the Brunhes stripe spans 15.6 km on each flank and the whole pattern mirrors about the axis. Read the magnetometer’s profile, the thin-sheet anomaly of every stripe summed, symmetric about the ridge; double the rate and the stripes and the profile stretch to match; tow the sensor twice as high and the anomalies blur into one another. The chron table and the block widths are the closed forms.
What happens
A mid-ocean ridge spreads at the half rate while the field follows a polarity table of the last six million years, so the crust on each flank carries blocks of alternating magnetization whose width is the half rate times the chron’s duration, mirrored about the ridge; the model clock runs from six million years ago to the present. A magnetometer 3 km above the vertically magnetized 500 m sheet of 5 A/m reads the summed thin-sheet anomaly B_z = (μ_0·M·t/2π)·Σ s·[(x − x_1)/((x − x_1)² + h²) − (x − x_2)/((x − x_2)² + h²)]: the profile is symmetric, stretches with the rate and smooths with the sensor’s height. One second of the experiment is one Myr.
Try this
Watch the stripes grow out from the axis and the profile follow; double the half rate; raise the sensor and see the anomalies blur; read the Brunhes width against rate times duration.
The model and its limits
A simplified polarity table, vertical magnetization of uniform intensity and thickness, a two-dimensional sheet, no transition zones or sediment. Field values are those of the thin-sheet model.
Equations used in the module
Equations x_j = v·(a_j − a_ridge), Δx = v·Δa B_z(x) = (μ_0·M·t/2π)·Σ s_j·[(x − x_1)/((x − x_1)² + h²) − (x − x_2)/((x − x_2)² + h²)] B_z(−x) = B_z(x) B_scale = μ_0·M·t/(2π·h)
