Summary • Different kinds of seismic sources • Green’s function and Representation Theorem • GFs for several important cases – Acoustic, homogeneous whole space, explosion – Elastic homogeneous whole space, point forces
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Summary
• Different kinds of seismic sources
• Green’s function and Representation Theorem
• GFs for several important cases – Acoustic, homogeneous whole space, explosion
– Elastic homogeneous whole space, point forces
Stokes, 1849
Earthquake as shear dislocation
Difficulties for “Internal” Sources
• Wave equation not satisfied everywhere – Discontinuity of displacement
– Boundary conditions unknown
• Kinematic description – Distributed slip along fault, u(x, t)
1920s~1960s
Can we find body forces that are equivalent to earthquake faulting, in terms of producing the same seismic responses everywhere?
YES!!!
Seismic Moment Tensor
Moment and Moment Rate Function
Response for a force couple
Displacement due to M0(t)
Radiation Pattern
Displacement due to M0(t)
Static deformation
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