On the Static Deformation of an Earth Model with a Fluid Core

Summary The concept of a purely static deformation of an Earth model, although strictly a highly artificial physical situation, nevertheless provides a useful idealization in certain problems. We derive a computational algorithm which allows one to determine any geophysically observable aspect of the purely static deformation of a non‐rotating, spherically symmetric Earth model which has an elastic mantle and a compressible fluid core. In particular, we show how to compute the static perturbation to the density, the gravitational potential, and the fluid pressure at every point within the core, as well as every aspect of the deformation in the solid elastic mantle. Because of the artificiality of the concept of a purely static deformation, the static Lagrangian particle displacement in the fluid core is indeterminate.