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Earth

Rift valley formation

Stretch a continent and watch the crust thin over the rift, sag into a valley of stepped blocks and fill with sediment and water; the crust that leaves the window is booked, so crust plus exported area never changes, and the profile stays mirror-symmetric. Stretch fast over a viscous mantle and the floor lags its equilibrium depth; turn the sediment off and the valley floor lies deeper on the same basement.

By Mykhailo Makarov

Rift valley formation — Actual application image
Actual application image

What happens

A 300 km section of crust in 60 columns extends at a set rate: the strain rate is a Gaussian zone normalized so the plates separate at that rate, each column thins by the exact exponential of its strain, and the crust that leaves the window is booked, so crust plus exported area is constant to rounding. Airy isostasy gives the equilibrium surface - the thinned crust sinks, the sediment loads it further - and the actual surface relaxes to it with the mantle’s viscous time constant; sediment at the supply rate fills the lowest column while it lies below sea level. The stretching factor β is the initial over the thinnest crust; one second of the experiment is one Myr.

Try this

Watch the centre thin and sag and the sediment fill the floor; stretch faster over a slower mantle and read how far the surface lags its equilibrium; turn the sediment off and compare the depths.

The model and its limits

A prescribed strain zone instead of fault mechanics, pure-shear thinning, local Airy isostasy with one relaxation time, sediment laid in one column. A teaching section, not a basin model.

Equations used in the module
Equations
dh_i/dt = −v·f_i·h_i/Σ f_j·Δx,  h_i(t) = h_0·e^(−v·f_i·t/Σ f_j·Δx)
e = ((ρ_m − ρ_c)·(h − h_0) + (ρ_m − ρ_s)·s)/ρ_m
dE/dt = (e − E)/τ
β = h_0/h_min

Related experiments

Back to catalogue
Hotspot island chain — Actual application image

Earth

Hotspot island chain

Move an ocean plate over a mantle plume and read the chain it leaves: distance over age difference is the plate’s speed, the islands subside with the cooling lithosphere and erode once above the sea until the oldest are seamounts, and a change of course at 40 Myr bends the chain by exactly the change of azimuth without touching the old islands. Let the plume drift and the chain shifts with it.

Sedimentary basin — Actual application image

Earth

Sedimentary basin

Watch a 100 km basin fill over ten million years: the basement sinks faster the farther from the hinge, sediment arrives at the hinge and spreads downslope by diffusion, faster on land than under water, and every quarter million years a marker bed is laid. Sand stays near the source and mud travels on; porosity squeezes out with depth so the compacted pile stands taller than the solid it holds. Raise the sea and the shoreline retreats; triple the supply and the basin overfills and spills past its far edge. Supplied, exported and held sediment balance to rounding, and a diffusing mound spreads its variance by exactly 2 K t.

Folding of strata — Actual application image

Earth

Folding of strata

Squeeze a 100 m sandstone bed a hundred times stiffer than its shale along its length: every wavelength seeded in it grows, but the one near Biot’s 2 pi h (eta_l / 6 eta_m)^(1/3) grows fastest and the bed buckles into regular folds, their amplitude the exponential of the growth integrated over the shortening history. Double the thickness and the folds double in wavelength; raise the contrast and they lengthen as the cube root; take the contrast away and the bed only thickens with its matrix. The viscous power of the shortening is read in watts per metre of fold.