Relationship Between Tidal and Load Love Numbers

Abstract

Love numbers are non-dimensional parameters that describe surface deformation of the earth due to external forces; tidal Love numbers (hn, ln, kn) represent earth's response to tidal force and load Love numbers (h′a, l′r, k′a) represent the response to loading on the surface of the earth. The two sets of Love numbers have been considered as independent sets and numerical calculations have been performed as such. In this study we prove that there exists a simple relation, l + kn− hn= l + k′n, valid for any non-rotating, spherically symmetric earth models. Previous calculations by several authors were examined and are found to be consistent with this relation. In addition to the two sets of Love numbers, we introduce a new set of “shear Love numbers″ (h″n, l″n, k″n), which describe the surface deformation caused by shear force applied to the surface of the earth. These three sets of Love numbers suffice to describe the earth's response of spheroidal type to any kind of external forces. © 1978, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan. All rights reserved.