Getting a part of the invert of Si function I'm working on an algorithmus that sould  need the inverse of the SI function. 

since this last once isn't oviouse to calculate, I'm trying to get only the parobla part from the SI function, to be clair , say I have this figure : 


I'm only interessted in the part from the max of each curve tell the point of intersection with the following one. So my question what is the fomula for the "parabola part " in si function.

the ploted function are all : si(3pi X /4)  

thanks for any help.
There are two problems, I think: fitting a parabola to the higher part, and moving the parabola to the next part of the sequence. This will address fitting the parabola.

I'd just use a least squares technique to find the $a$, $b$, and $c$ parameters.

This shows the part of the paper of interest: