On computing the geoelastic response to a disk load

Abstract

We review the theory of the Earth’s elastic and gravitational response to a surface disk load. The solutions for displacement of the surface and the geoid are developed using expansions of Legendre polynomials, their derivatives and the load Love numbers. We provide a MATLAB function called diskload that computes the solutions for both uncompensated and compensated disk loads. In order to numerically implement the Legendre expansions, it is necessary to choose a harmonic degree, nmax, at which to truncate the series used to construct the solutions. We present a rule of thumb (ROT) for choosing an appropriate value of nmax, describe the consequences of truncating the expansions prematurely and provide a means to judiciously violate the ROT when that becomes a practical necessity