Development of quantitative geophysical proxy indicators for urban underground space use: An analysis of Stockholm and its city plan

In the absence or unavailability of geometric information about underground structures, conventional quantitative indicators of Urban Underground Space (UUS) usage become challenging to obtain. Socio-economic proxy indicators, that are reportedly well correlated with these conventional indicators, are inherently unstable measures given their susceptibility to non-linear human decision-making processes. To address this limitation, we evaluated the potential of geophysical proxy indicators, specifically the magnetic 3D analytic signal (AS), as a basis for UUS assessment. We also assessed the suitability of the magnetic susceptibility model as a framework for three-dimensional subsurface planning. Stockholm's airborne magnetic data acquired in 1995 were processed to generate an AS map that delineated its metro system (tunnelbana) and similar subsurface structures. Observed signatures, correlated with the overlain metro layout, were independently validated on an electrical current density map derived from co-acquired tensor very low-frequency electromagnetic data. Because AS emphasizes the sharp edges of magnetic contrasts, it provides a direct geophysical marker of anthropogenic underground structures and, consequently, an effective proxy indicator for UUS utilization. We introduce two new indicators: analytic signal density (ASD, expressed in nT/m per hectare, interpreted as "the amount of underground structure from a certain depth range that fits a surface area of 1 ha"), and analytic signal per capita (ASPC, expressed in nT/m per 100 person, interpreted as "the amount of underground structure from a certain depth range per capita". Both demonstrate strong correlations, comparable with those of conventional indicators, with population density (r = 0.88 and r = -0.69, respectively). The 3D magnetic susceptibility inversion model further predicted known infrastructure with a vertical accuracy of similar to 20 m, which can be improved with better data quality. Our results indicate that central Stockholm exhibited significantly higher UUS usage in 1995 (> 1.2 nT/m per hectare and < 2.0 nT/m per 100 person) than other Stockholm areas in the same year. The model for 2023, based on population density, estimated a 20-60 % increase in UUS use in central Stockholm since 1995. This trend underscores the need to integrate UUS in planning and development in both the central districts and the development focus areas of Stockholm city plan, where substantial UUS use was also evident. We conclude that, pending the establishment and adoption of standards for UUS use, Stockholm municipality needs a rethink of its population-driven (coined as "first-full first-developed") underground development strategy, identified through the comparative analysis of the geophysical proxy UUS use indicators of 1995 and model estimates for 2023. Given the rapid and extensive coverage afforded by airborne magnetic surveys, ASD and ASPC provide a novel, scalable, and tangible proxy for estimating and comparing UUS use across cities, particularly in data-limited or data-denied environments.