SURFACE-POTENTIAL AND GRAVITY CHANGES DUE TO INTERNAL DISLOCATIONS IN A SPHERICAL EARTH .1. THEORY FOR A POINT DISLOCATION

This paper studies the potential and gravity changes caused by dislocations in spherically symmetric earth models. We define dislocation Love numbers to describe the elastic deformation of the earth raised by point sources. We discuss the shear and tensile dislocations, which can be expressed by four independent components: a vertical strike-slip, a vertical dip-slip, a tensile opening on a horizontal plane, and a tensile opening on a vertical plane. The results for a homogeneous earth model agree very well, at least within 1-degrees, with those predicted from flat-earth theory. The far-field results indicate no larger than 10 per cent difference within 10-degrees. It makes little difference whether we use the theory on a sphere or that for a flat earth in the near field, while it is reasonable to use the spherical theory for global calculation. We proceed to calculations with a radially heterogeneous earth model (Model 1066A). The results are as a whole similar to those for a homogeneous sphere. In some cases, however, the difference between the two becomes significant. For example, the locations of the nodal lines of the gravity change differ significantly between the two models. This indicates that the vertical layering can cause considerable effects on the deformation fields.