The elastic response to surface loading can be described adequately by linear transfer functions, Green's functions. These are bases on a radially symmetric distribution of density and elasticity and describe the response as a funnction of distance from the load. For small-scale processes the respective local earth structure has to be adjusted accordingly.
For investigations of surface deformations induced by saisonal changes in the terrestrial water cycle or in the atmosphere, the deformation is determined in relation to the elastic crustal stratification (earth structure). As a first approximation, a global set of Green's functions is calculated at each grid point for the respective crust structure which was derived from a laterally heterogeneous crustal-structure model.
Huang, P., Sulzbach, R., Tanaka, Y., Klemann, V., Dobslaw, H., Martinec, Z., Thomas, M. (2021): Anelasticity and lateral heterogeneities in Earth's upper mantle: impact on surface displacements, self‐attraction and loading and ocean tide dynamics. - Journal of Geophysical Research: Solid Earth, 126, 9, e2021JB022332.
Tanaka Y., Klemann V., Martinec Z. (2019) Surface Loading of a Self-Gravitating, Laterally Heterogeneous Elastic Sphere: Preliminary Result for the 2D Case. In: . International Association of Geodesy Symposia. Springer, Berlin, Heidelberg, DOI: https://doi.org/10.1007/1345_2019_62
Dill, R., Klemann, V., Martinec, Z., Tesauro, M. (2015): Applying local Green's functions to study the influence of the crustal structure on hydrological loading displacements. - Journal of Geodynamics, 88, p. 14-2, DOI: https://doi.org/10.1016/j.jog.2015.04.005