Joint inversion of gravity and gravity gradient data using smoothed L0 norm regularization algorithm with sensitivity matrix compression

Improving efficiency and accuracy are critical issues in geophysical inversion. In this study, a new algorithm is proposed for the joint inversion of gravity and gravity gradient data. Based on the regularization theory, the objective function is constructed using smoothed L (0) norm (SL0), then the optimal solution is obtained by the non-linear conjugate gradient method. Numerical modeling shows that our algorithm is much more efficient than the conventional SL0 based on the sparse theory, especially when inverting large-scale data, and also has better anti-noise performance while preserving its advantage of high accuracy. Compressing the sensitivity matrices has further improved efficiency, and introducing the data weighting and the self-adaptive regularization parameter has improved the convergence rate of the inversion. Moreover, the impacts of the depth weighting, model weighting, and density constraint are also analyzed. Finally, our algorithm is applied to the gravity and gravity gradient measurements at the Vinton salt dome. The inverted distribution range, thickness, and geometry of the cap rock are in good agreement with previous studies based on geological data, drilling data, seismic data, etc., validating the feasibility of this algorithm in actual geological conditions.