Ground penetrating radar (GPR) is a popular remote sensing modality for buried threat detection. Many algorithms have been developed to detect buried threats using GPR data. One on-going challenge with GPR is the detection of very deeply buried targets. In this work a detection approach is proposed that improves the detection of very deeply buried targets, and interestingly, shallow targets as well. First, it is shown that the signal of a target (the target "signature") is well localized in time, and well correlated with the target's burial depth. This motivates the proposed approach, where GPR data is split into two disjoint subsets: an early and late portion corresponding to the time at which shallow and deep target signatures appear, respectively. Experiments are conducted on real GPR data using the previously published histogram of oriented gradients (HOG) prescreener: a fast supervised processing method operated on HOG features. The results show substantial improvements in detection of very deeply buried targets (4.1% to 17.2%) and in overall detection performance (81.1% to 83.9%). Further, it is shown that the performance of the proposed approach is relatively insensitive to the time at which the data is split. These results suggest that other detection methods may benefit from depth-based processing as well.