I’m comparing coseismic displacement fields between a FEM and an homogeneous halfspace using Okada. I noticed that the slip for the first and last portion of the fault-patch/line is not exactly 1 when using FEM.
So, suppose I calculate the GFs for the first 50km depth of a fault line using Okada and pylith, then the distribution of slip amplitude if i understood well, would be like the image below? And if its so, how is described this smoothing for the FEM?
You are correct that the Okada solution assumes uniform slip over each fault patch. This creates a singularity in stress at the edge of a fault or whenever the slip varies between fault patches. Green’s functions in PyLith are computed using basis functions that are continuous within cells and C0 continuous between cells. This does not create stress singularities. In general, the PyLith implementation is more physically realistic as fault slip is continuous along a fault.
If you want to make a 1:1 comparison between Okada and PyLith Green’s functions, then you will need to use very small cells with PyLith so that the linear variation occurs over short distances. As mentioned above, the Okada approach is not as physically meaningful, so this 1:1 comparison is generally a numerical experiment and is inconsistent with real-work applications in which continuous slip (as in the PyLith approach) is more realistic.