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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.

By Mykhailo Makarov

Sedimentary basin — Actual application image
Actual application image

What happens

A section through a basin of fifty 2 km columns: the basement subsides about a hinge at the left edge, 0.2 km/Myr at the far end; sediment enters at the hinge at 10 km² per Myr and spreads by diffusion of the surface elevation with 1000 km²/Myr on land and 300 under the sea; the far edge spills whatever stands above sea level. Solid thickness is conserved; the compacted thickness of each column follows from a porosity of 0.5 at the surface falling with a 2 km scale; a marker horizon is laid every 0.25 Myr, and the sand share of what is laid decays with distance from the source. Explicit stepping at 1 kyr with a column’s outgoing fluxes scaled together so it never gives more than it holds; one second of the experiment is one Myr.

Try this

Watch the beds pile up and the shoreline move; raise the sea and the shore retreats; raise the supply until the basin spills; read sand near the hinge against mud far out and the compacted pile against its solid.

The model and its limits

Diffusive transport with two constant diffusivities, a kinematic hinge instead of flexure or thermal subsidence, compaction from a fixed porosity law, no waves, channels or carbonate. A teaching section, not a basin model.

Equations used in the module
Equations
∂h/∂t = −∂q/∂x − s(x),  q = −K·∂h/∂x,  s = s_max·x/L
T − φ_0·λ·(1 − e^(−T/λ)) = S_solid,  φ(z) = φ_0·e^(−z/λ)
f_sand(x) = e^(−x/λ_s)
Σ S·Δx = Q_in·t − Q_out,  σ² = σ_0² + 2K·t

Related experiments

Back to catalogue
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.

Metamorphism — Actual application image

Earth

Metamorphism

Bury a shale at a kilometre per million years down a 25 K/km geotherm, hold it, and lift it back: its point moves across the pressure-temperature grid of facies, chlorite gives way to biotite, garnet and staurolite as the equilibrium shares shift, and because the reaction rate falls a thousandfold between 600 and 400 degrees the peak assemblage is carried to the surface almost untouched, a little more retrograded when the exhumation is slow. Steepen the burial under a cold gradient and the path runs into blueschist; let a pluton heat a shallow rock and it bakes to hornfels; hold a sample isothermal and its shares relax on the closed-form exponential.

Geothermal gradient — Actual application image

Earth

Geothermal gradient

Heat a 40 km column of crust from below at 30 mW/m² while its own radioactivity adds 45 more: the profile curves, steep in the sediments and flatter in the conductive lower crust, and after a few slab time constants of 23 Myr it lands on the closed-form steady state to a hundredth of a degree while the surface heat flow reaches 75 mW/m². Halve the sediments’ conductivity and the whole crust below runs 180 K hotter; double the basal flow and the Moho climbs past 1300 degrees. A uniform half-space after a surface step follows the erf solution. Heat in, made and out balance the stored heat to rounding.