santisoler
commented
3 weeks ago I think I tracked down what's going on with this. The issue is coming when evaluating the kernel_en function, and particularly the safe_log, and due to machine precision.
The issue arises when evaluating the kernel on the two prism vertices that fall below the observation point (the two nodes marked in green circles):
When the observation point falls exactly above the nodes, the kernels are well evaluated and the result is correct.
But when the observation point is slightly away from it, then the evaluation on the nodes falls into a problem:
- On the upper node (closest to the observation point), its shifted northing coordinate will be very small (1e-6 in the previous example), its shifted easting coordinate will be zero, and its shifted upward will be negative (and significantly larger than 1e-6). The radius will be something very close to the shifted upward coordinate plus a small amount due to the small shift in the northing. The safe_log function will then assume that this observation point doesn't fall above the node.
- On the lower node something similar happens, but now its shifted upward coordinate is much larger in magnitude, making the radius actually equal to the upward coordinate. What's happening is that the slight shift in the northing component falls under the machine error. Therefore, the safe_log function will then assume that this node falls below the observation point.
This leads to evaluate the kernels on this two nodes using different branches of the safe_log function and therefore creating this discontinuity.
I'll think how we can solve this and comment back with some ideas.
Description of the problem:
Today I found that the current forward modelling functions for magnetic fields experience some discontinuities when being evaluated on lines above one of the edges of the prism.
I found this misbehavior when exploring the values of
magnetic_ealong a N-S profile that falls right above one of the horizontal edges of the prism.Full code that generated the error
Output
System information
main(eaf80e78329fabe52f45c047950d76d6fadb2b35)conda listbelow:Output of conda list