GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.3 705 geology) to offset the extra non-uniqueness introduced by the additional model parameter sets to be recovered (Lelièvre and Oldenburg, 2009). We had proposed a 2D sequential inversion method (M-ID) of inverting the magnetization vectors (Liu et al. , 2015). This method is based on the factures that 2D magnitude magnetic anomaly is independent on the magnetization direction. The magnetization intensity is firstly solved from the magnitude magnetic anomaly using preconditioned conjugate gradient (PCG) method, which is transformed from the total field data in frequency-domain. Subsequently, the magnetization inclination and declination are recovered using conjugate gradient (CG) algorithm like the recovery of magnetization intensity by inverting for total field data (M-IDCG); Or the magnetization direction can be estimated from the correlation coefficients between the observed and predicted total field anomalies, where the most correlated anomaly is corresponded to the optimal magnetization direction (M-IDC). However, in 3D case, the magnitude magnetic anomaly is weakly sensitive to magnetization direction (Stavrev and Gerovska, 2000; Gerovska and Araúzo-Bravo, 2006). M-IDCG obtains non-unique magnetization directions. And M-IDC shows lower efficiency to calculate the magnetization direction. In this paper, we extend the sequential inversion method from 2D to 3D and propose a fast iteration method (M-IDI) to estimate the magnetization direction and to implement the magnetization vector inversion (Liu et al. , 2017). We compare it with previous important methods: the magnetization vector inversion in Cartesian framework (MMM) and spherical framework (MID) proposed by Lelièvre and Oldenburg (2009). Synthetic example. To test and compare the methods, we set a synthetic model that is consisted of one vertical cuboid (i.e., A) and two dipping prisms (i.e., B and C) (Liu et al. , 2017). The inclination and declination of Earth’s magnetic field are I 0 = 45° (horizontal to downward) and D 0 = 90° (east to north). The model, having moderate magnetism and representing some volcanic rocks such as basic and ultrabasic rocks, is magnetized by a constant TMVwith intensity M = 1 A/m, inclination I = 45° and declination D = 60°, where the remanent magnetization component is M r = 0.56 A/m, inclination I r = 38.90° and declination D r = 36.21°. The synthetic examples indicate that MMM method owns stable convergence of iterations. Because the inverted threemagnetization intensity components have the same unit andweighting, the iteration convergence is in low dependence on the initial model. The magnetization inclination and declination are varied in a very big range from 0° to 90° and the magnetization vectors appear a divergent feature. The magnetization inclination and declination points are located at the boundary of the first quadrant in Fig.1a polar coordinates. Lelièvre and Oldenburg (2009) pointed out adding priori information constraints is an effective way to improve the inversion results. In theMIDmethod, the solved parametersmagnetization intensity, inclination and declination have different units and their sensitivities to magnetic anomaly also are different. It is essential to use weighted coefficients to balance the parameters (Lelièvre and Oldenburg, 2009). In the synthetic example of Fig. 1b, for instance, the weight of magnetization intensity is w M = 10 -6 ; magnetization inclination and declination have the same weights: w I = w D = 1. M-ID includes three methods (i.e., M-IDCG, M-IDC, and M-IDI). When recovering the magnetization direction distributions in M-IDCG, the initial model is set to parallel the Earth’s magnetic field, which shows a lower dependence than MID method. And M-IDCG inversion results (Fig. 1c) can obtain more concentrated magnetization inclination and declination compared with that of MMM, but they have a larger range than MID results. The exhaustive and iterative methods M-IDC and M-IDI provide the same magnetization direction with error < 5° (Fig. 1d). M-IDC and M-IDI, however, are more applicable to simple and isolated anomalies because only an optimal magnetization inclination and declination are estimated. For multiple sources and complicated magnetic anomalies, a window usually is used to investigate the anomalies separately as Gerovska et al. (2009) used the correlation method to estimate the magnetization directions of multiple magnetic anomalies.