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The material of Earth's crust is constantly subjected to forces and it deforms in response to them. The figure at the top illustrates a slab of crustal rock with a simplified geometry. Equal but oppositely directed forces act tangent to the red and blue planes on the boundary of the slab. The stress is defined as the magnitude of the force divided by the area of the planes. Because of the stress, the slab is deformed from the cuboid shape it would have in the absence of applied forces. The figure shows that the red plane is displaced downward a distance y relative to the blue plane, and that the separation distance of the two planes is x. The strain in the slab is, by definition, y/x. The strain is proportional to the stress with the constant of proportionality depending on the material from which the slab is made. The ratio of stress to strain is called the rigidity of the slab material, m. When the slab is infinitesimal, the preceding discussion defines the stress and strain at the point enclosed by the slab.

In Earth's crust there are planes that can support only relatively low stresses before rupturing. These weak planes are called fault planes. In a simple model, an earthquake is precipitated when the stress on a fault plane exceeds the static frictional stress, s₀. Plates on either side of the fault experience a relative displacement, or slip, D over an area S, as illustrated in the middle figure. The displacement may be as great as 10 m, but the linear dimension of a fault in the direction of the displacement is typically tens of kilometers so that the contact area is essentially unchanged as the plates move. As sliding commences, the frictional stress drops to a lower kinetic stress, s_f. The drop is not instantaneous; over the time during which friction drops, the plates slip a distance, D_c, as illustrated in the graph at the bottom. When D_c is small, the dynamic stress drop, Ds_d = s₀ - s_f, initially drives the sliding. The sliding stops when the shear stress drops below a final frictional stress, s₁. A variety of mechanisms can stop sliding, such as geometric and compositional heterogeneity, and dynamically changing velocity- or history-dependent friction, and so s₁ is not necessarily equal to s_f. The difference between initial and final frictional stresses is the static stress drop, Ds_s = s₀ - s₁.

With seismological methods, one can determine D, S, and the slip velocity, v_D. Given the rigidity of crustal rocks, m, and the shear-wave velocity, b, the dynamic and static stress drops are Ds_d = v_Dm/b and Ds_s = mD/S^1/2. Both stress drops typically range from 1 to 10 MPa, although there are exceptions. Seismological methods measure only transient processes, so they determine stress differences, not the values of the physically important stresses s₀ and s₁.

A convenient measure of the overall size of an earthquake is the seismic moment defined by M₀ = mSD. The seismic moment is measured in energy units, but it does not directly represent the energy released by an earthquake. The magnitude, M, of an earthquake is given in terms of the seismic moment by M = (log M₀ - 9.1)/1.5.

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© 2001 American Institute of Physics