Non-smooth Inversion of Non-linear Gravity Problem by Means of Particle Swarm Optimization

We have used Particle Swarm Optimization (PSO) method to solve the non-linear gravity inverse problem of imaging lateral density variations against a non-smooth interface of two layers with different densities. Such problem is ill-posed and its solutions must be stabilized. PSO is a zero-order global optimization method in which a set of particles simultaneously search for the best solution and are able to interact with each other to guide the search towards a feasible solution. The term zero-order indicates that throughout the search for the best solution, the only needed criteria is the value of the objective function itself and not its derivatives with respect to model parameters. As a result, the objective function does not need to be differentiable at every point. Such feature is particularly suitable for imaging non-smooth models with sharp edges such as those of fault systems and fractures where the L2 norm in smoothing stabilizer needs to be replaced with an L1 norm to prevent over-smoothing of the solutions. Herein, we have investigated the role of L1 smoothing stabilizer in constraining the non-linear gravity inverse problem on a non-smooth synthetic model. Our results show that using L1 norm in smoothing stabilizer outperforms L2 norm.