GNGTS 2015 - Atti del 34° Convegno Nazionale

A NEW INVERSION METHOD OF VERTICAL GRAVITY AND MAGNETIC SOUNDINGS A. Vitale, D. Di Massa, M. Fedi, G. Florio Dipartimento di Scienze della Terra, dell’Ambiente e delle Risorse, Università Federico II, Napoli, Italy Introduction. The purpose of this work is to present a new method for the inversion of potential fields (gravity or magnetic anomalies). The inverse problem is solved by determining the set of parameters that describes the sources of the field due to the experimental data. If the unknown parameters are the density or the magnetization this type of problem is linear and in most cases it is an indeterminate problem, since the data are less in number than the number of unknown parameters. The use of constraints, which define models geologically valid, such as intervals of maximum variation of the model parameters, can manage to reduce the ambiguity. One of the greatest difficulties in the inversion of the potential field is to obtain satisfactory information about the characteristics of the sources of interest, which may be the top and the bottom of the structures that generate anomalies plus estimates and trends of density values (or intensity of magnetization, in the case of magnetic fields) relating to them. The scientific literature is extraordinarily rich in both 2D and 3D gravity and magnetic data inversion algorithms. All these methods provide density/magnetization distributions at depth having certain properties. Green (1975) searched for a density model that minimizes its weighted norm to some reference model. Safon et al. (1977) used the method of linear programming to compute moments of the density distribution. Fisher and Howard (1980) solved a linear least-squares problem constrained for upper and lower density bounds. Last and Kubik (1983) introduced a ‘compact’ inversion minimizing the body volume. Guillen and Menichetti (1984) assumed as a constraint the minimum momentum of inertia. Barbosa and Silva (1994) suggested allowing compactness along given directions using a priori information. Li and Oldenburg (1996, 1998) introduced model weighting as a function of depth using a subspace algorithm. Pilkington (1997, 2002) used preconditioned Conjugate Gradients (CG) method to solve the system of linear equations. Portniaguine and Zhdanov (1999, 2002) introduced regularized CG method and focusing using a reweighted least squares algorithm with different focusing functional. Li and Oldenburg (2003) use wavelet compression of the kernel with logarithmic barrier and conjugate gradient iteration. Barbosa & Silva (2006) proposed a 2D method to invert potential field data by a procedure incorporating a priori knowledge. Wijns and Kowalczyk (2007) propose a semi-automatic procedure that allows defining solutions geologically reasonable. Pilkington (2009) used data space inversion in Fourier domain. Barnes and Barraud (2012) have developed instead an inversion algorithm to solve geometrical interfaces between different geological bodies, through the introduction of information concerning the depth and regularizing the solution. However, there are no 1D algorithms, since the forward problem in this case should be referred to infinite layers, which produce a constant field in space and, therefore, could not explain any gravity anomaly. Fedi and Rapolla (1990) explored for the first time the possibility to perform the inversion of “vertical gravity soundings”, which refers to a 1D inversion method. The forward problem consisted in assuming a volume of layers of different densities. The volume is however finite vertically and horizontally, this last condition is necessary to avoid the Bouguer slab effect, which would make impossible the inversion of field anomalies. The other main feature of this approach is that a multiscale dataset is inverted. The data at various altitudes are obtained by 166 GNGTS 2015 S essione 3.3