The elastic response to surface forces can be adequately parameterized by linear transfer functions, Green's functions, which are based on a radially symmetrical density and elasticity distribution in the earth's interior. The respective earth structure has to be adapted for small-scale processes.

For the investigation of surface deformations caused by seasonal changes in the terrestrial water cycle or in the atmosphere, the deformation of the earth's surface was calculated as a function of the respective elastic crust (earth structure). For this purpose, a separate set of Green's functions was calculated as a first approximation at each grid point for a laterally varying crustal structure. These describe the reaction of the solid earth as a function of the distance to the load change.

It is numerically more expensive to consistently model lateral variations in the elastic properties. These occur mainly at the tectonic plate boundaries and influence the deformation behavior. Density variations, although also relevant, have less influence. In the Earth's mantle, there is another phenomenon, anelasticity, which means that the elastic moduli decrease with the duration of the loading and the material deforms to a larger degree. Similar to the crust, also in the mantle the anelastic properties vary from place to place. They strongly depend on temperature, so their quanitfication is closely linked to studies on the dynamics of the Earth's mantle. (See also Department 2 "Geophysics")

References:

Tanaka, Y., Klemann, V., Martinec, Z. (2024): An estimate of the effect of 3D heterogeneous density distribution on coseismic deformation using a spectral finite-element approach. - In: Freymueller, J.T., Sánchez, L. (eds) X Hotine-Marussi Symposium on Mathematical Geodesy. HMS 2022. International Association of Geodesy Symposia, vol 155. Springer, Cham. p 103-111, doi.org/10.1007/1345_2023_236

Huang, P., Sulzbach, R., Klemann, V., Tanaka, Y., Dobslaw, H., Martinec, Z., Thomas, M. (2022): The influence of sediments, lithosphere and upper mantle (anelastic) with lateral heterogeneity on ocean tide loading and ocean tide dynamics. - Journal of Geophysical Research: Solid Earth, 127, 11, e2022JB025200. doi.org/10.1029/2022JB025200

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. doi.org/10.1029/2021JB022332

Tanaka, Y., Klemann, V., Martinec, Z. (2019): Surface Loading of a Self-Gravitating, Laterally Heterogeneous Elastic Sphere: Preliminary Result for the 2D Case. - In: IX Hotine-Marussi Symposium on Mathematical Geodesy, (International Association of Geodesy Symposia ; 151), 157-163. 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. 14-22.| doi.org/10.1016/j.jog.2015.04.005