An analytical approach to estimate curvature effect of coseismic deformations

Abstract

We present an analytical approach to compute the curvature effect by the new analytical solutions of coseismic deformation derived for the homogeneous sphere model. We consider two spheres with different radii: one is the same as earth and the other with a larger radius can approximate a half-space model. Then, we calculate the coseismic displacements for the two spheres and define the relative percentage of the displacements as the curvature effect. The near-field curvature effect is defined relative to the maximum coseismic displacement. The results show that the maximum curvature effect is about 4 per cent for source depths of less than 100 km, and about 30 per cent for source depths of less than 600 km. For the far-field curvature effect, we define it relative to the observing point. The curvature effect is extremely large and sometimes exceeds 100 per cent. Moreover, this new approach can be used to estimate any planet's curvature effect quantitatively. For a smaller sphere, such as the Moon, the curvature effect is much larger than that of the Earth, with an inverse ratio to the earth's radius.