Inversion is rarely unique, and it's not due to the precision with which the field is measured.

https://earthsciences.anu.edu.au/study/student-projects/nove...

https://inside.mines.edu/~rsnieder/snieder_trampert_00.pdf

Epilogue:

    Linear inverse problem theory is an extremely powerful tool for solving inverse problems. Much of the information that we currently have on the Earth’s interior is based on linear inverse problems

    Despite the success of linear inverse theory, one should be aware that for many practical problems our ability to solve inverse problems is largely confined to the estimation problem.