Seismic waves from non-double-couple sources

Abstract

The displacement field due to an arbitrary point source is obtained in terms of the nine spherical components of the moment tensor. It is shown that the far-field is not affected by the lack of symmetry of the moment tensor or the value of its trace. However, in the near-field, M↔ _tr shows up in the radial component of the displacement and the antisymmetric part of M↔ appears in the transverse component of the displacement. Assuming M↔ to be symmetric and traceless, the moment tensor is split into two parts, one representing a double-couple and the other a compensated linear-vector dipole (CLVD). The displacement fields due to the two sources are obtained in terms of five parameters, namely the strike, dip and slip angles of the double-couple, the strength of the double-couple and the relative strength of the CLVD. These five parameters match exactly with the five degrees of freedom in which the components of M↔ can be specified and, therefore, are suitable for inversion purposes. It is shown how the first motion observations of P waves can be used to calculate the relative strength of the CLVD. The Cartesian components of the moment tensor obtained for the double-couple and the CLVD can be used to calculate the relative excitation of surface waves by these sources.