Methods and related systems are described for modified semblance criterions based on the approach of thresholding the signal energy. A first criterion is derived by posing the problem as that of detecting a signal with energy (or amplitude) greater than the specified threshold and deriving the generalized likelihood ratio test statistic. A second criterion is derived using the same method by posing the problem as that of rejecting any signal with energy (or amplitude) below a specified threshold and detecting it if its energy is above another threshold greater than or equal to the first. These appropriately modify the original semblance criterion which is shown to be equivalent to the GLRT test statistic in the absence of any threshold on the signal amplitude. In addition simpler modifications are also described. Tests on synthetic data illustrate the effectiveness of all these modifications which perform comparably well at suppressing unwanted arrivals while accurately processing the desired signals.