Three-dimensional regularized inversion of DC resistivity data with different stabilizing functionals

A regularized inversion with a smoothing (SM) stabilizer is commonly used in 3D inversion of direct-current (DC) resistivity data. We have developed a new 3D inversion algorithm for DC resistivity data to investigate the efficiency of various stabilizing functionals. This algorithm is capable of incorporating 3D regularized inversion with L1-norm, L2-norm, SM, minimum support (MS), minimum gradient support (MGS), first-order minimum entropy, and total variation (TV) stabilizers. This is, to our knowledge, a comprehensive study of the effects of these seven different stabilizers on the inverse solution using synthetic and field data. As expected, the structure boundaries are found to be smooth when a SM stabilizer is used in the synthetic data examples. The upper bounds of the structures are recovered close to true model with L1-norm, L2-norm, first-order minimum entropy, and TV stabilizers, but the lower bounds cannot be recovered. Moreover, these stabilizers cannot completely resolve the resistivity of structures. The boundaries and resistivity of the structures are determined to be close to the true model with MS and MGS stabilizers. Similar results are obtained from inversions of field data collected in the Kültepe archaeological site (Kayseri, Turkey). A buried wall structure is correctly identified when the inversion used MS or MGS stabilizers. The archaeological structure found in the excavation studies reveals the success of the solution using MS and MGS stabilizers. These two stabilizers are recommended for an exploration of sharp boundaries structures.