I introduce sparse constraints into potential field data inversion to obtain the sparse inversion results. The sparse constraints have now been used in many types of geophysical domains, such as geophysical data processes. The new stabilized is a common practice, which should be minimized in the inversion method. This new inversion method mainly obtains the sub-surface nonzero density contrast, and the gravity data produced by the nonzero density contrast must fit the observed residual gravity data. Emphasizing L0 norm sparse constraints ensures that the inverse results are simple, and no unnecessary structures are expected as required by the potential field data. Minimizing the quasi-norm tends to penalize smooth variations, and it promotes a more blocky character in the solution. It is well known that the minimization of the L0 norm is an NP-complex problem in combinatorial optimization, which indicates that optimization algorithms solving the problem cannot be completed in polynomial terms. There are several methods to solve this NP-complex problem. In this paper, this sparse-constraints norm has been imposed on the gravity data inverse problems to obtain the density contrast distribution.


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