Questions: Isostatic Flexure and Elastic Thickness

Question 1

The Hawaiian Islands have formed over a mantle hotspot that has built massive volcanic edifices on the oceanic plate. What pattern of seafloor topography would you expect in the region immediately surrounding (but not directly under) each major island, and farther away?

• A. The seafloor would be uniformly depressed beneath and around the island, with no distinct spatial pattern at greater distances
• B. The seafloor would be depressed in a concentric zone (moat) surrounding the island due to flexural downbending of the plate, and slightly elevated in a ring farther out (flexural bulge) where the bent plate bows upward
• C. The seafloor would be elevated immediately around the island because the volcanic material adds buoyancy that compensates for the island's weight
• D. The seafloor topography would follow Airy isostasy: each column beneath the island sinks independently, producing a depression directly below with no adjacent moat or bulge

Answer: (B)

This is the textbook flexure pattern. The lithosphere acts like an elastic beam resting on a fluid foundation: a concentrated load (the volcanic island) causes the plate to bend downward under the load (creating a moat or 'Hawaiian Deep') and upward in a ring farther away (the 'flexural arch' or outer rise). This is directly observed around Hawaii: the seafloor is depressed in an arc around each island, forming sediment-filled moats, and slightly elevated in a ring beyond. Airy isostasy would predict only local sinking with no adjacent moat or bulge — it ignores lithospheric rigidity and distributes no load laterally.

Question 2

Two oceanic plates carry similar-sized volcanic islands. Plate A has an effective elastic thickness (Tₑ) of 5 km; Plate B has Tₑ = 35 km. How would the flexural depressions around the islands differ?

• A. Plate A would show a wider, shallower moat; Plate B would show a narrower, deeper moat
• B. Plate A would show a narrower, deeper moat concentrated near the island; Plate B would show a wider, shallower moat as the load is distributed over a larger area
• C. Both plates would show identical moat geometry because the island mass is the same
• D. Plate B's moat would be wider and deeper because higher elastic thickness means greater total deflection

Answer: (B)

Effective elastic thickness controls the flexural rigidity D (proportional to Tₑ³), which governs the characteristic bending wavelength. A thin, weak plate (small Tₑ) distributes the load over a small area — the deflection is concentrated near the load, producing a narrow but deep depression, approaching the Airy (perfectly weak) limit. A thick, strong plate (large Tₑ) distributes the load over a wide area — the depression is broader but shallower because the plate resists local bending. Young oceanic lithosphere near mid-ocean ridges (low Tₑ) flexes steeply; old, cold oceanic lithosphere flexes broadly. This difference is directly measurable from the geometry of moats in gravity and bathymetric surveys.

Question 3

The effective elastic thickness (Tₑ) of the lithosphere controls how widely a surface load is distributed: a stiffer plate (larger Tₑ) spreads the load over a broader region, producing a wider but shallower flexural depression.

• T. True
• F. False

Answer: True

Flexural rigidity D is proportional to Tₑ³, and D appears in the denominator of the deflection equation — larger D means smaller maximum deflection and a longer characteristic bending wavelength. Physically, a stiff plate resists bending and transfers the load to a broader region of the underlying asthenosphere. A weak plate bends more sharply, concentrating the load and deflection near the application point. This is why measuring the width and depth of a flexural moat around a load allows you to invert for Tₑ: narrow deep moats indicate weak lithosphere; wide shallow moats indicate strong lithosphere.

Question 4

The Airy isostasy model correctly predicts the moat and flexural bulge patterns observed around oceanic volcanic islands like Hawaii, because Airy isostasy accounts for the lateral strength of the lithosphere.

• T. True
• F. False

Answer: False

Airy isostasy explicitly assumes the lithosphere has *no* lateral strength — each vertical column floats independently, like a raft of wood blocks in water. This model predicts local sinking beneath a load but *no* moat or flexural bulge. The moat (flexural depression surrounding the island) and the outer flexural arch arise precisely because the lithosphere is rigid and distributes loads laterally. The Airy model is the limiting case of flexure as Tₑ → 0. Real lithospheric responses to loads are better described by the elastic plate flexure model, which produces the observed two-zone pattern of depression and uplift.

Question 5

A foreland basin sits adjacent to a mountain belt. Explain how lithospheric flexure controls the basin's geometry, and how a geologist could use the basin's width and depth to estimate the effective elastic thickness of the plate at the time of basin formation.

Model answer: The mountain belt acts as a distributed load on the edge of the adjacent plate. The plate bends under this load, creating a foreland basin — a depression filled with sediment shed from the mountains — in the region of maximum downward flexure. The basin's width reflects the flexural wavelength: a stronger plate (larger Tₑ) produces a wider basin; a weaker plate produces a narrower one. The basin's depth reflects the magnitude of deflection controlled by both the load and Tₑ. To estimate Tₑ, a geologist builds forward flexure models: assuming a load geometry from the mountain belt, they solve the flexural equation for different Tₑ values and compare the predicted basin geometry (width, depth profile, and stratigraphy) to the observed basin. The Tₑ that best matches observations is the estimated elastic thickness at the time of loading.

This forward-modeling approach — predict basin geometry from flexure theory, compare to observations, invert for Tₑ — is the standard method in geodynamics. It ties surface observables (basin shape, gravity anomalies, seismic stratigraphy) to the mechanical properties of the lithosphere, linking geological observation to geophysical inference. The same logic applies to sedimentary basins formed by other loads (ice sheets, sediment wedges) and to the subsidence patterns around oceanic islands.