Math 2.0

Geophysics Definition

Elastic-rebound theory

Builds on Linear elasticityStressHooke's law

Definition

Consider a fault that separates two crustal blocks whose far-field parts move relative to each other at a steady velocity vv. Elastic-rebound theory is the model of earthquakes with the following three assumptions.

  1. Between earthquakes the fault is locked and the rock around it deforms elastically. The shear stress on the fault grows at a rate proportional to vv.
  2. An earthquake starts when the shear stress on the fault reaches the frictional strength of the fault.
  3. During the earthquake the fault slips suddenly, the slip relieves the accumulated strain, and the rock near the fault returns towards its unstrained shape.

Remarks

Example: the spring-slider model. A block rests on a surface and is pulled by a spring of stiffness kk whose far end moves at speed vv. By Hooke's law the spring force is k(vt−x)k(vt - x), where xx is the position of the block. The block stays at rest until the force reaches the static friction FsF_s, and then slides until the force drops to the dynamic friction Fd<FsF_d < F_s. So each slip has size Δx=(Fs−Fd)/k\Delta x = (F_s - F_d)/k, and the slips recur with period T=Δx/v=(Fs−Fd)/(kv)T = \Delta x / v = (F_s - F_d)/(kv). The three clauses hold: the locked phase is clause 1, the threshold is clause 2, and the drop of the force is clause 3. Non-example: steady aseismic creep, where the fault slides continuously at rate vv, fails clause 1, since no strain accumulates. Real faults are only roughly periodic, because strength, loading and interactions with other faults vary.

Reading path

To understand this page from the ground up, read these 11 pages in order. The foundations come first.

Show the path as a graph
Cauchy stress tensor, concept, no evidence levelCauchy stress tensorconceptElasticity tensor, concept, no evidence levelElasticity tensorconceptLamé equations of elasticity, concept, no evidence levelLamé equations of ela…conceptLamé parameters, concept, no evidence levelLamé parametersconceptLinear elasticity, concept, no evidence levelLinear elasticityconceptPoisson's ratio, concept, no evidence levelPoisson's ratioconceptStrain tensor, concept, no evidence levelStrain tensorconceptStress, concept, no evidence levelStressconceptYoung's modulus, concept, no evidence levelYoung's modulusconceptHooke's law, statement, no evidence levelHooke's lawstatementElastic-rebound theory, definition, no evidence levelElastic-rebound theorydefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Cauchy stress tensor concept
  2. Elasticity tensor concept
  3. Lamé equations of elasticity concept
  4. Lamé parameters concept
  5. Linear elasticity concept
  6. Poisson's ratio concept
  7. Strain tensor concept
  8. Stress concept
  9. Young's modulus concept
  10. Hooke's law statement
  11. Elastic-rebound theory definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Elastic-rebound_theory
About this page
Tag38W3EMX00B
URIm2://38W3EMX00B
Kinddefinition
WritingW0 stub
MSC86A15, 74R10
DefinesElastic-rebound theory
UsesLinear elasticity, Stress, Hooke's law
Changed3 November 2026

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