The classical electromagnetic time reversal (EMTR) fault location method in power systems can be time consuming, especially when a high location accuracy is desired. To cope with this issue, the concept of EMTR in mismatched media has recently been introduced, substantially improving the fault location efficiency. In this paper, we present a theoretical study and rigorous demonstration of the mismatched-media-based mirrored minimum energy property. Firstly, we infer a direct-reversed-time transfer function and present a theorem according to which, at the fault switching frequency and its odd harmonics, the mirror-image point of the fault location with respect to the line center corresponds to a local minimum of the squared modulus of the transfer function. Next, it is proved that the mirrored minimum energy property is a corollary of this theorem. Based on these theoretical findings, we propose an algorithm that uses the reversed-time voltage energy as a fault location metric in the frequency domain, instead of the original time-domain approach. We further propose applying a data-driven strategy to maximize the computation efficiency of the algorithm. The applicability and robustness of the frequency-domain fault location metric, together with the computational efficiency of the accelerating algorithm, are numerically and experimentally validated.