Gravity wave packets excited by a source of finite duration and size possess a broad frequency and wave number spectrum and thus span a range of temporal and spatial scales. Observing at a single location relatively close to the source, the wave components with higher frequency and larger vertical wavelength dominate at earlier times and at higher altitudes, while the lower frequency components, with shorter vertical wavelength, dominate during the latter part of the propagation. Utilizing observations from the Na lidar at Utah State University and the nearby Mesospheric Temperature Mapper at Bear Lake Observatory (41.9°N, 111.4°W), we investigate a unique case of vertical dispersion for a spectrally broad gravity wave packet in the mesopause region over Logan, Utah (41.7°N, 111.8°W), that occurred on 2 September 2011, to study the waves' evolution as it propagates upward. The lidar-observed temperature perturbation was dominated by close to a 1 h modulation at 100 km during the early hours but gradually evolved into a 1.5 h modulation during the second half of the night. The vertical wavelength also decreased simultaneously, while the vertical group and phase velocities of the packet apparently slowed, as it was approaching a critical level during the second half of the night. A two-dimensional numerical model is used to simulate the observed gravity wave processes, finding that the location of the lidar relative to the source can strongly influence which portion of the spectrum can be observed at a particular location relative to a source.