## 1 Introduction  
Imaging of salt-tectonic-related geological features is still a challenging research matter in geophysical exploration, particularly in the oil exploration industry. Subsalt exploration is fundamental as salt domes are geological structures that often act as hydrocarbon traps, due to their impermeability to gas and oil [1; 2; 3; 4]. Although three-dimensional seismic imaging has experienced a quite significant development in recent years [5; 6; 7; 8; 9; 10], it is well known that it still tends to fail in subsalt regions due to the high-density contrasts between salt structures and their surrounding-encapsulating-rocks, yielding varying degrees of uncertainty in estimation of base and highly dipping flanks of salt bodies [11]. In this context, potential field methods are often excellent supporting tools for geophysical subsalt exploration and can provide accurate estimations of depth distribution and geometry of allochthonous salt features [12; 13]. In addition, integration of potential field methods as an aid to seismic-structural interpretation is useful for the construction of initial velocity and density models for seismic RTM and FWI migration processes [13; 14]. Among the class of potential field methods for geophysical exploration are gravity, magnetics and, more recently, Full Tensor Gradient method (FTG) [15]. Although gravity provides information of anomalies in the vertical component of deeper structures due to its a large bandwidth, FTG allows a better estimation of shallow geological structures due to the short wavelength signals which are not present in gravity data. Since the gradiometric tensor \(\mathfrak{G}\) is symmetric and traceless, its independent components allow determination of the locations of the mass center (\(\mathfrak{G}_{xz}\), \(\mathfrak{G}_{yz}\)), edges (\(\mathfrak{G}_{yy}\), \(\mathfrak{G}_{xx}\)) and corners (\(\mathfrak{G}_{xy}\)) of the anomaly; \(\mathfrak{G}_{zz}\) provides the correct spatial position of the anomaly, above the geological mass center, as conventional gravity [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. On the other side, magnetometry is sensitive to anomalies of parts-per-million, making of it a very sensitive tool of geophysical surveying [27]. Inversion of depth and geometry of geological structures through potential field methods is an ill-posed problem, yielding to non-unique non-linear solutions [28]. Under some practical considerations, the problem can be linearized, but this approach can yield to numerical instabilities and non-unique solutions [29; 30]. Thus, optimization techniques for the non-linear problem must be considered to be an alternative. Optimization-based data inversion consists in the extensive search over the parameter space [31], in a trial and error basis. This process continues until the difference between observed and synthetic data is minimized. In the case of three-dimensional inversions, allocation of huge amounts of memory for the sensitivity matrices, and a very high computational burden are required to solve the large unstructured linear systems. Among the techniques to alleviate computational burden in linear optimization, there are: (1) the use of Fourier transforms for the matrix-vector multiplication [20; 32], (2) the compression of the sensitivity matrix [19; 33], (3) the computation of only the elements of the matrix that are relevant to a determined search space [20; 34; 35], (4) solution methods that do not solve the linear system, but search solutions only in a particular space [36; 37], and (5) systematic search methods [38; 39; 40; 41]. Many systematic search methods are based on the idea of placing a seed somewhere within the search space from which the algorithm begins to optimize a solution, like those presented in [40; 42; 43]. The inversion algorithm in [40] and further refined in [44], is a systematic search method to invert gravity data.