Cross-country faults can adversely affect the operation of protection devices. Relays whose pickup is based on overcurrent or impedance elements are more likely to fail during cross-country faults. The failure can be expressed as an unnecessary trip of all phases during a single-phase fault or even blocked relay functions. Relays may also fail to operate due to low fault currents, which is the case when power grids make use of many Invertor Based Resources (IBR) or when two simultaneous faults occur in the same phase and different locations. This paper proposes a Recursive Discrete Stockwell Transform (RDST) method for addressing the mentioned challenges. The energy content computed by the RDST is used for fault detection and faulty phase selection. A robust distance relay model is proposed to ensure correct relay performance and is combined with a directional and an impedance trajectory module. The relay is tested by applying real-time simulations for 540 different cross-country faults. Simulation results confirm the method's ability to detect different fault types, even during low fault currents, and to ensure high accuracy in phase selection.