How to write a new transformation function in pygimli?

[jinshanmu]

I want to write a transformation of porosity to slowness: $s = \frac{1}{{v_m + (v_f - v_m) \cdot \phi}}$ for the TT simulation. This formula could not be written out by the existing functions like pygimli.trans.TransLin() and pygimli.trans.TransPower() individually. So how could I define a tailored transformation function myself?

[halbmy]

A very good question pointing out that there is a documentation missing. For an example of writing a transformation function see the SymLog under

gimli/pygimli/core/trans.py

Line 39 in c260199

class TransSymLog(pgcore.RTrans):

One has to write four methods: a constructor, a forward and reverse transformation, and a derivative, all of them should be easy to implement.

Actually, in the C++ core, there is already a (template) class TransNest for combining two transformations, however it is not (yet) available in Python. Then one could easily setup your function as a combination of TransLin and TransPower. As an example, I will rewrite TransNest.

If you want to invert for porosity instead of slowness (the intrinsic property for traveltime), you would have to invert the function, i.e. the forward function is
$$\Phi = \frac{1}{v_f-v_m} \frac{1}{s} - \frac{v_m}{v_f-v_m}$$
the inverse function as written above and the derivative is $\frac{\partial\Phi}{\partial s}$.

[jinshanmu]

Thank you for the detailed answer! I'll try to write the function following the example of TransSymLog.