Research Note: A unifying framework for the widely used stabilization of potential field inverse problems

We present a brief review of the widely-used and well-known stabilizers in the inversion of potential field data. These include stabilizers that use L2, L1, and L0 norms of the model parameters, and the gradients of the model parameters. These stabilizers may all be realized in a common setting using two general forms with different weighting functions. Moreover, we show that this unifying framework encompasses the use of additional stabilizations which are not common for potential field inversion. INTRODUCTION Many forms of stabilizers are used for the inversion of the ill-posed potential field data problem. The aim is the reconstruction of subsurface models that provide relevant physical interpretation. In order to reduce the possibility of over-interpretation of the data, it may be desirable to reconstruct a simple model with as little structure as possible, and to eliminate arbitrary discontinuities in the solution (Constable et al., 1987). Such models can be expected to present only the important and large-scale features of the subsurface under the survey area. They can be obtained using a minimum roughness, or equivalently maximum smoothness, stabilizer that employs a L2-norm of the gradient of the model parameters in the inversion algorithm (Constable et al., 1987; Li and Oldenburg, 1996; Pilkington, 1997; Li and Oldenburg, 1998). A