Questions: Elastic Plate Flexure and Lithospheric Loading

Question 1

A large volcanic island forms on oceanic crust. Which observation most clearly demonstrates that the lithosphere responds with elastic flexure rather than simple local (Airy) isostasy?

• A. The island gradually subsides over millions of years as the oceanic lithosphere cools and thickens
• B. A moat-shaped depression surrounding the island and a subtle upward bulge (forebulge) in a ring several hundred kilometers away
• C. The island's crustal thickness increases in proportion to its topographic height, maintaining a constant surface elevation
• D. Gravity anomalies are close to zero directly under the island, indicating nearly complete isostatic compensation

Answer: (B)

Local (Airy) isostasy treats each crustal column independently — the surface simply sinks in proportion to the load directly above it, with no lateral coupling. If that were the case, you would see subsidence only under the island itself. Instead, elastic flexure distributes the load over a broad region: the plate bends like a diving board, creating a depression not just under the island but in a moat around it, and an upward forebulge further out where the plate's bending moment produces uplift. The Hawaiian Islands sit in exactly such a flexural moat with a forebulge ~250 km away — definitive evidence of plate rigidity.

Question 2

Two volcanic islands of similar mass load on oceanic lithosphere of different ages: one on 5 Ma crust near a ridge, one on 80 Ma crust far from a ridge. How does the flexural response differ?

• A. Both produce identical depressions because total load mass, not lithosphere age, determines the flexural shape
• B. The island on younger crust produces broader, gentler flexure because young oceanic crust has a higher effective elastic thickness
• C. The island on older crust produces broader, gentler flexure because old, cold oceanic lithosphere has a higher effective elastic thickness (Te 30–40 km vs 5–10 km near ridges)
• D. The island on younger crust sinks more rapidly but produces less total deflection because young crust is less dense

Answer: (C)

Effective elastic thickness (Te) controls the width and depth of flexural bending. Young oceanic crust near a mid-ocean ridge is hot and weak — Te may be only 5–10 km — so it bends sharply and locally, similar to Airy isostasy. Old, cold oceanic lithosphere has Te of 30–40 km and behaves as a stiff plate, distributing the load broadly to produce a wide, gentle flexural depression with a prominent forebulge. Option B reverses this: young crust is weaker, not stronger. Age is a proxy for thermal state, and thermal state controls mechanical strength.

Question 3

Airy isostasy — in which each crustal column independently floats on the mantle — is a special limiting case of elastic plate flexure that applies when the effective elastic thickness approaches zero.

• T. True
• F. False

Answer: True

This is the key conceptual relationship between the two models. The elastic plate equation contains a bending rigidity term proportional to Te³. When Te → 0, the plate has no lateral stiffness, and the equation reduces to a balance between the load and the local buoyancy force — exactly Airy isostasy. As Te increases, loads are supported over progressively broader regions (regional isostasy). Airy isostasy is not wrong; it is the zero-rigidity end-member of a continuum. Real lithosphere falls somewhere along that continuum, with Te varying from near-zero in hot rifts to over 100 km in cold cratons.

Question 4

The effective elastic thickness (Te) of the lithosphere is equal to the total physical thickness of the lithospheric plate, measured from the surface down to the asthenosphere.

• T. True
• F. False

Answer: False

Te is the mechanical thickness of the portion of the lithosphere that behaves elastically — not its total physical thickness. The deep lithosphere may be too hot and ductile to sustain elastic stress on geological timescales, so it contributes to plate mass but not plate rigidity. Te is therefore always less than or equal to the total lithospheric thickness. In practice, Te is estimated from geophysical observations (gravity-topography relationships) and represents the integrated mechanical strength of the plate, not a directly measurable physical boundary.

Question 5

Explain how geophysicists use the relationship between gravity anomalies and surface topography to estimate the effective elastic thickness (Te) of the lithosphere.

Model answer: If Te = 0 (Airy isostasy), each topographic high is locally compensated by a crustal root, and gravity anomalies closely mirror topography — every peak has a corresponding free-air gravity high. With high Te, the plate supports loads regionally, so the mass is distributed across a broad area; gravity varies more smoothly than topography. Geophysicists compute the admittance — the ratio of gravity to topography as a function of spatial wavelength — and compare it to predictions from elastic plate models. Where observed admittance matches a high-Te model (gravity smoother than topography), the plate is stiff; where it matches a low-Te model (gravity tracking topography closely), the plate is weak.

In practice, this is done in the spectral domain: short-wavelength topography is always locally compensated regardless of Te, so only intermediate-to-long wavelengths discriminate between plate strength models. The analysis yields Te as the single parameter that best explains the observed gravity field given the known topographic load. This connects isostasy (a conceptual framework) and flexure (a physical model) to real observations that can test and quantify lithospheric strength across different tectonic environments.