GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.2 GNGTS 2024 Individual inversions are carried out through the open-source pyGIMLi package (Rücker et al., 2017) properly adapted to work with the newly implemented structured mesh, and, for beter comparison between separate and joint inversion results, the same inversion parameters, including regularizaton setngs, inital model and forward modelling are used during each inversion step. Method Gallardo and Meju (2004) developed a structural procedure for two-dimensional simultaneous joint inversion in which the cross-gradient penalty functon is applied to improve the resoluton of common boundaries. This dimensionless functon, which defnes the geometrical similarity of two models as a distributon of gradients, is defned as: where m r and m v are resistvity and seismic velocity models, in our work variable in a two- dimensional space. Adding the term in Eq.1 to the objectve functon, we obtain: In Eq.2 D r and D v are data weightng matrices, f( m r ) and f( m v ) the forward responses, d r and d v the observed data vectors, λ r and λ v weightng factors, C r and C v regularizaton matrices and λ CG the cross-gradient weightng term. The objectve functon is nonlinear, since forward problems as well as the cross-gradient constraint are nonlinear, so to minimize it we used a frst-order Taylor expansion (i.e. the Gauss-Newton method) and consequently solved the resultng system using the conjugate gradient algorithm. The visual representaton of the unchanged cross-gradient is rather complex, as it varies by several orders of magnitude and very diferently from case to case, preventng a consistently accurate mode. Gallardo and Meju (2004) represented this quantty setng a minimum and maximum threshold. Observing that the unvaried cross-gradient always showed a Gaussian distributon, we defned a new standardizaton of it shown in Eq.3: (1) t CG ( x , y , z ) = m r ( x , y , z ) m v ( x , y , z ) (2) ( m r , m v ) = D r ( f ( m r ) − d r ) D v ( f ( m v ) − d v ) + λ r λ v C r m r C v m v + λ CG t CG ( m r , m v ) → min (3) NCG = t CG t CG 68