Joint inversion of DC resistivity and potential field data under different model weighting functions

In this study we analyze the role of model weighting functions for resistivity and potential field data in both separate and joint inversion. We show that the model weighting function built with depth weighting and compacting factor, formerly formulated for the gravity and magnetics inversion, can be useful also for DC resistivity data modelling. The comparison was made using the depth weighting with different exponents and the roughness matrix under L1- and L2-norm Constrained Optimization. We then analyze the 2-D joint inversion of DC resistivity and potential field data, based on the above model weighting function and the cross-gradients constraint. We provide a number of synthetic cases to discuss the pro and cons of each model-weighting function and to examine the feasibility of the joint inversion algorithm. We then provide results from two real case datasets for mining and archeological exploration. The results show that the value of the β exponent is decisive for potential field problems, but it also leads to a faster convergence for the resistivity data inversion. Similarly, the role of compactness is important for modelling compact source from gravity and magnetic, and to warrant an even faster and compact solution for DC resistivity. On the other hand, the results of the joint inversion reveal that the cross gradient constraints allow a successful joint inversion even when resistivity and magnetic data are often not easily comparable.