Subsurface geology detection from application of the gravity-related dimensionality constraint

Geophysics aims to locate bodies with varying density. We discovered an innovative approach for estimation of the location, in particular depth of a causative body, based on its relative horizontal dimensions, using a dimensionality indicator (I). The method divides the causative bodies into two types based on their horizontal spread: line of poles and point pole (LOP-PP) category, and line of poles and plane of poles (LOP-POP) category; such division allows for two distinct solutions. The method's depth estimate relates to the relative variations of the causative body's horizontal extent and leads to the solutions of the Euler Deconvolution method in specific cases. For causative bodies with limited and small depth extent, the estimated depth (z^{^}₀) corresponds to the center of mass, while for those with a large depth extent, z^{^}₀ relates to the center of top surface. Both the depth extent and the dimensionality of the causative body influence the depth estimates. As the depth extent increases, the influence of I on the estimated depth is more pronounced. Furthermore, the behavior of z^{^}₀ exhibits lower errors for larger values of I in LOP-POP solutions compared with LOP-PP solutions. We tested several specific model scenarios, including isolated and interfering sources with and without artificial noise. We also tested our approach on real lunar data containing two substantial linear structures and their surrounding impact basins and compared our results with the Euler deconvolution method. The lunar results align well with geology, supporting the effectiveness of this approach. The only assumption in this method is that we should choose between whether the gravity signal originates from a body within the LOP-PP category or the LOP-POP category. The depth estimation requires just one data point. Moreover, the method excels in accurately estimating the depth of anomalous causative bodies across a broad spectrum of dimensionality, from 2 to 3D. Furthermore, this approach is mathematically straightforward and reliable. As a result, it provides an efficient means of depth estimation for anomalous bodies, delivering insights into subsurface structures applicable in both planetary and engineering domains.