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We conducted a microgravity survey in an urban area where a sinkhole opened under railway tracks. Thanks to a novel procedure, we successfully separated the gravity signal into terrain-related (TCA) and residual (TUCA) components. The resulting TUCA map revealed a distinct negative anomaly in correspondence with the known subsurface voids in the survey area (the cavity and an underpass), confirming the method’s capability to detect near-surface mass deficits with a very limited input data and minimal processing time. Our processing allows even an independent estimation of the average terrain density. Results of our processing can be considered as intermediate products in the standard gravity processing, suitable to: 1) constrain the topographic density for producing the complete Bouguer anomalies; 2) obtain a preliminary residual map in which the topographic effects are minimized. TUCA represents a valuable a-parametric preliminary tool in gravity investigations, very useful during the survey (e.g., to optimize the location of the gravity stations based on partial survey results) and when quick decision-making is essential.