Interpretation of Magnetic Anomalies of 2D Listric Faults with arbitrary magnetisation: A Polynomial-Based Automatic Inversion Approach

This study presents a fully automatic inversion technique for interpreting magnetic anomalies of two-dimensional (2D) listric fault structures with arbitrary magnetisation. Listric faults exhibit curved geometries with steep dips near the surface that decrease with depth. But most studies assume a planar fault geometry to the listric faults, which is rarely valid in reality. Accurately modelling such structures is essential because many sedimentary basins and extensional tectonic settings contain listric faults that significantly influence subsurface geometry. Forward modelling is performed using the equation derived by Ani Nibisha et al. (2021), that computes magnetic anomalies of listric faults in any component (vertical, horizontal, or total), with arbitrary magnetisation directions by incorporating both induced and remanent magnetic components. In the proposed method, polynomial function of arbitrary degree is used to represent the nonplanar fault surface. The coefficients of these polynomials, with structural parameters like depths to the top and bottom of the fault, location of the fault edge, and magnetisation intensity and direction, are estimated directly from the magnetic anomaly profile. The inversion uses Marquardt’s (1970) algorithm for optimisation. With a vertical step approximation, the initial parameters are generated automatically based on certain characteristic anomaly features like maximum and minimum anomaly points, and are updated iteratively until a predefined convergence criterion is satisfied. The misfit between observed and calculated anomalies guides model updates, and the method adaptively adjusts the damping factor to ensure stable convergence. The validity and robustness of the inversion technique are demonstrated through two examples. In the synthetic test, a fifth-degree polynomial is used to describe the fault geometry, and Gaussian noise is added to the computed anomalies for a realistic approach. The inversion successfully reconstructs the geometry, magnetisation intensity, and direction, even when lower-order polynomials (second or third degree) are used, since the optimal degree to define the fault geometry remains unknown with the absence of apriori information about the subsurface during inversion. This demonstrates that the technique can produce geologically reasonable solutions even without precise prior knowledge of the fault’s curvature. This technique is compared with the inversion technique by Murthy et al. (2001), which assumes planar fault surfaces and shows that such simplified models fail to recover realistic structures for listric faults. The method is further applied to real total-field magnetic anomalies from the western margin of the Perth Basin, Australia, which is known for hydrocarbon prospectivity and characterised by deep, curved normal faults. Using a second-degree polynomial, the technique identifies a listric fault with its top near 4 km depth and bottom near 14.8 km, yielding a close fit to observed anomalies with small residuals. The recovered geometry aligns well with seismic observations that reveals the listric nature of the fault (Middleton et al. 1993), reinforcing the reliability of the inversion approach. In contrast, inversion assuming a planar fault plane produces geologically inconsistent results. In conclusion, this technique improves the interpretation of magnetic datasets in regions dominated by extensional tectonics and curved fault structures, offering more realistic subsurface models than traditional planar-fault methods.