Technical Advancements of Laterally Constrained Inversion for Geophysical Datasets

Laterally Constrained Inversion (LCI) is presently a popular method for robust interpretation of geophysical data, particularly in defining subsurface structures with greater lateral continuity. The traditional standalone 1D inversion methods, while computationally efficient, often produce unrealistic discontinuities between adjacent soundings in the retrieved models. LCI overcomes this limitation by enforcing lateral constraints that enforce smooth variation across adjacent models, producing quasi-2D results that are more realistic in some geological settings. This paper presents a systematic review of the recent advancement in LCI and its methodological extensions like Weighted LCI (WLCI), Iterative LCI (ILCI), Minimum Gradient Support LCI (MGS-LCI), and Bayesian LCI. All these techniques offer more flexibility while handling heterogeneous subsurface conditions, hard contacts, and uncertainty estimation. A full methodology is given, with emphasis on mathematical formulae and regularization strategies for controlling lateral as well as vertical smoothing. Incorporation of a priori geological knowledge and constraint design, resolution versus smoothness trade-offs, and computational considerations are also covered. A case study from the Horn River Basin, Canada, demonstrates the application of LCI approaches to airborne TEM data and indicates improved model continuity, geological coherence, and interpretability. This review points out that while LCI methods have significantly enhanced the potential of geophysical inversion, future research has to be focused on hybrid methods, automatic tuning of constraints, large-scale algorithms, and multi-modal data fusion. These developments will be crucial to dealing with increasingly larger and more complex datasets and delivering more accurate and reliable subsurface models for a variety of geoscientific and engineering applications.