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We have established a workflow for a multi-order sequential joint inversion (MOSJI) of gravity and gravity gradients, that aims at modelling of vertically-stacked sources in various geological scenarios. We consider the joint inversion of the gravity data and one of the  h th   order derivative of the gravity data. The first step involves separate inversions, which are fundamental to fully exploit the different wavelength-content of the two quantities to invert. The joint inversion is warranted by using the scheme of a sequential joint inversion with a cross-gradient constraint. The algorithm is able to exploit different types of a priori information, such as compactness and inhomogeneous model-weighting function. Firstly, we test this approach on a realistic synthetic model from the SEg Advanced Modelling (SEAM) Phase I model, involving salt and mother salt structures. Then, we consider a synthetic model containing either shallower or deeper karst cavities. These tests produced a better modelling of both shallower and deeper sources, when compared to the separate unconstrained inversions. Thanks to these good results, we apply our method to a real case for cavity detection in Southern Spain. The method shows an accurate modelling of the expected sources. In all the aforementioned tests, we obtain a strong decrease of the cross-gradient values and a meaningful linearization in the scatter plots of physical parameters, both indicating the good performance of the joint inversion.

Multi-Order Sequential Joint Inversion of gravity data with inhomogeneous depth weighting: from near surface to basin modelling applications