Multi-tubular inversion with automatic cost functional optimization

A method for estimating individual pipe properties of each one of a plurality of nested pipes using induction measurements, comprising:

• disposing an induction tool in a cased hole, wherein the induction tool comprises a transmitter and a receiver;
• broadcasting electromagnetic fields from the transmitter into a subterranean formation to form an eddy current;
• recording the eddy current with the receiver to produce induction measurements;
• obtaining a log comprising at least one channel from the induction measurements;
• constructing an inversion cost functional comprising a misfit term and a regularization term;
• performing a first inversion using the inversion cost functional to estimate a set of pipe properties at a first plurality of depth points;
• optimizing the inversion cost functional such that the estimated set of pipe properties at the first plurality of depth points minimize an objective functional;
• performing a second inversion using the optimized inversion cost functional to estimate a set of pipe properties at a second plurality of depth points;
• and
• displaying the set of pipe properties at the second plurality of depth points to a user.