Gravity Inversion Method to Produce Compact and Sharp Images Using L₀-norm Constraint with Auto-adaptive Regularization and Combined Stopping Criteria

Abstract. We present a gravity inversion method that can produce compact and sharp images, to assist the modeling of non-smooth geologic features. The proposed iterative inversion approach makes use of L₀-norm stabilizing functional, hard, and physical parameter inequality constraints, and depth weighting function. The method incorporates an auto-adaptive regularization technique, which automatically determines a suitable regularization parameter and error weighting function that helps to improve both the stability and convergence of the method. The auto-adaptive regularization and error weighting matrix are not dependent on the known noise level. Because of that, the method yields reasonable results even the noise level of the data is not known properly. The utilization of an effectively combined stopping rule to terminate the inversion process is another improvement that is introduced in this work. The capacity and the efficiency of the new inversion method were tested by inverting randomly chosen synthetic and measured data. The synthetic test models consist of multiple causative blocky bodies, with different geometries and density distributions that are vertically and horizontally distributed adjacent to each other. Inversion results of the synthetic data show that the developed method can recover models that adequately match the real geometry, location, and densities of the synthetic causative bodies. Furthermore, the testing of the improved approach using published real gravity data confirmed the potential, and practicality of the method in producing compact and sharp inverse images of the subsurface.