A unified approach to the representation of seismic sources

Abstract

An attempt is made to give a unified treatment to the problem of the representation of various sources commonly used in theoretical studies in seismology. Beginning with the Stokes-Love solution for a concentrated force, the displacement field due to a dipolar source in a homogeneous, isotropic, unbounded medium is expressed in terms of the eigen-vector solutions of the vector Navier equation. This field is transformed to a spherical coordinate system having its origin at the centre of the Earth. The transformed field is then used to calculate the jumps in the displacements and stresses across the concentric spherical surface passing through the source. These jumps constitute a convenient representation of the source. Since it exhibits the properties of the source and not that of the medium, the above representation is also valid when the medium under consideration is bounded and inhomogeneous. A similar representation is obtained in the case of the circular cylinder coordinate system. This representation can be conveniently applied to investigate the excitation of various elastic fields in the Earth by earthquake sources such as the free oscillations, surface waves and residual static deformation.