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Seismology: seismos: earthquake logos: knowledge Seismology: Study of earthquakes Study of interior of the Earth Needed: wave propagation
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Seismology - Universiteit Utrecht

Mar 19, 2022

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Page 1: Seismology - Universiteit Utrecht

Seismology: •  seismos: earthquake •  logos: knowledge

Seismology:

•  Study of earthquakes

•  Study of interior of the Earth

Needed: wave propagation

Page 2: Seismology - Universiteit Utrecht

Seismic wave propagation: Propagation of small displacements (perturbations) from equilibrium position.

Continuum mechanics: Mechanics of a continuous medium -> Properties are continuous and differentiable functions

Newton’s 2nd law F=ma

In a continuous, homogeneous medium:

Force per unit volume: f(x,t) Mass per unit volume, density: ρ (constant) Displacement: u(x,t)

Page 3: Seismology - Universiteit Utrecht

We therefore have:

Two classes of forces: •  Body forces, proportional to volume •  Surface forces (acting on a surface), proportional to surface area: tractions

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Tractions

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Traction on surface with normal n:

with summation convention

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Normal stresses: ?

Shear stresses: ?

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Principal stresses σ1 , σ2 , σ3: eigenvalues of stress tensor σ

Principal stress axes: corresponding eigenvectors

Now we can finally derive the equation of motion …

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Summing the three terms, adding the body force component, and equating this net force to the density times this component of the acceleration yields

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Now we will derive the strain tensor which describes the deformation due to differential motion within the body.

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Although we are interested in deformation that distorts the body, there can also be a rigid body translation or a rigid body rotation, neither of which produces deformation. To distinguish these effects, we add and subtract and then separate it into two parts

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