Systems and methods to use triangulation through one sensor beamforming in downhole leak detection

A method includes obtaining physical signals detected by a physical sensor traveling along a wellbore. The method also includes performing a first and second frame decomposition operations on a first and second set of physical signals detected by the physical sensor at first and second locations to obtain first and second pluralities of virtual signals associated with first and second arrays of virtual sensors. Each virtual sensor of the first and second arrays of virtual sensors is located at a virtual distance relative to the first and second locations, and the virtual distance corresponds to a physical distance. Additionally, the method includes computing first and second direction of arrival estimates of the first and second locations of the single physical sensor relative to a location of a downhole leak. Further, the method includes triangulating the first and second direction of arrival estimates to estimate the location of the downhole leak.