Sequential joint inversion of gravity and magnetic data via the cross‐gradient constraint

Abstract

Different geophysical methods use different model parameterizations and inversion algorithms. Thus, combining these different inversion systems and yet adding the nonlinear cross‐gradient constraint in a joint inversion framework might be a big challenge, for instance, as explained further by Moorkamp et al. in 2011, there is a complex interaction between the data misfit terms, regularization and cross‐gradient terms and an imperfect fit to the data is expected. In this paper, we use a sequential algorithm for a two‐dimensional joint inversion of gravity and magnetic data, which tries to avoid these issues by decoupling the gravity inversion, the magnetic inversion and the cross‐gradient minimization processes. The efficiency of the algorithm and developed code is demonstrated by the joint inversion of noisy synthetic data. The results show a significant improvement in the respective models obtained by introducing the cross‐gradient joint inversion over the models obtained by separate inversions for synthetic data and then for field data targeting potash ore source in the AjiChai salt deposit in north‐western Iran. In this application case, the lower density of salt minerals such as potash, compared to its surrounding sedimentary sequences, motivates a gravity study. Furthermore, the relative lower susceptibility of these salt minerals, alongside their diamagnetic effect, makes them a suitable target for magnetic surveys. Separate gravity and magnetic studies had been performed over the deposit; however, a constitutive relationship between density and magnetization within the area of interest supporting a joint inversion had not been established. In this paper, we apply the sequential cross‐gradient approach to perform the first full joint inversion for the AjiChai salt deposit. The magnetic inversion here is performed to recover the magnetization amplitudes rather than the magnetization vector. In fact, we assume there is no remanent magnetization and, therefore, that the magnetization vector is constant and parallel to the geomagnetic field direction. The constructed density and magnetization models are of high concordance with available geological information and previous studies including drilling results. In addition, unlike previous separate inversion models, the models are structurally and geometrically similar.

Joint Inversion of Geophysical Data for Geologic Carbon Sequestration Monitoring: A Differentiable Physics‐Informed Neural Network Model

“…In the sequential scheme, measurements with lower resolution are generally inverted first, such that low frequency models are used as initial models for the inversion of higher resolution data sets. Examples of sequential inversion of multiple geophysical data can be found in Lines et al (1988), Tveit et al (2015), and Tavakoli et al (2021), to name a few. In the simultaneous scheme, model parameters are coupled with structural (e.g., De Stefano et al, 2011;Gallardo & Meju, 2011) or rock-physics constraints (e.g., Abubakar et al, 2012;Carrillo et al, 2022;Chen & Hoversten, 2012) and the forward operator includes multi-physics models.…”

“…(2015), and Tavakoli et al. (2021), to name a few. In the simultaneous scheme, model parameters are coupled with structural (e.g., De Stefano et al., 2011; Gallardo & Meju, 2011) or rock‐physics constraints (e.g., Abubakar et al., 2012; Carrillo et al., 2022; Chen & Hoversten, 2012) and the forward operator includes multi‐physics models.…”

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

“…‘Polynomial surface fitting’ is a mathematical filtering procedure used to approximate Δ g R . It is obtained by fitting a low‐order polynomial surface to the gravity data using least square techniques (Abedi, 2018; Kebede et al., 2020; Okiwelu et al., 2010; Tavakoli et al., 2021). In this paper, we have fitted a quadratic (second‐order) polynomial.…”

“…The lower density of salt minerals, compared to its surrounding sedimentary sequences, motivates a gravity study. Furthermore, the relative lower susceptibility and diamagnetic effects of the salt minerals make them suitable targets for magnetic surveys (e.g., Abedi, 2018; Barbosa & Silva, 2011; Kearey et al., 2002; Paoletti et al., 2020; Stadtler et al., 2014; Tao et al., 2021; Tavakoli et al., 2021). Average susceptibility and density values for the different types of sediments are summarized in Table 1 (e.g., Abedi, 2018; Telford et al., 1990).…”

Intersection Constraint Weighting (ICW) Method: High-Resolution Joint Magnetic Susceptibility Inversion of Aeromagnetic and Gradient Data

“…which superimposes the original magnetic anomaly onto the magnetic gradient anomaly in a matrix to improve the precision of inversion results using weight constraints of different anomaly components [29]. Joint inversion based on structural constraints is another way to improve inversion resolution, such as the cross-gradient method, which is mostly utilized for the inversion of different types of data [30][31][32][33][34][35][36]. The structure factor of the cross-gradient has a better constraining effect on the magnetic and magnetic gradient data of the same source and different resolutions, which can improve the inversion precision and satisfy the consistency of the magnetic and magnetic gradient inversion results of the final results of the ICW method.…”