In the framework of regularization theory, a priori geologic information is included in the inversion process and formalized by means of the stabilizer. Based on available geologic information, which specific stabilizer to choose is still lack of evidence among the alternatives. In order to provide a selection strategy of the stabilizer in the unified framework, we develop a new technique to solve the inverse problems constrained by different stabilizers, called jumping regularization approach based on reconstruction of stabilizing functional. First, we reconstruct stabilizers as the weighted least-squares norm of a kernel function. Reconstruction idea in our technique provides a better understanding of how stabilizers differ from each other and what the core of minimization of stabilizing functional is. Then, in the simple and unified framework of jumping approach, which iteratively solves for model itself during the inversion, the solution to each inverse problem with the specific stabilizer can be readily achieved by replacing the form of kernel function and weight function. Each constrained inverse problem solved with our technique has been successfully tested on the synthetic data of layered magnetotelluric models. Our research provides a more reasonable basis for selecting different stabilizers in inversion, meanwhile providing a solving method for more flexible tests.
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