Essential Tremor (ET) is a common movement disorder involving the presence of action tremor. While there are pharmacological treatment options, Deep Brain stimulation (DBS) of the ventral intermediate nucleus (VIM) of the thalamus is an effective and widely used surgical therapy for those patients who are intolerant of, or whose tremor is unresponsive to, medications. In this study, we recorded local field potentials (LFPs) at various depths along the trajectory to Vim in three ET patients. LFP recordings at various depths were processed by a PCA based de-noising method to remove ECG artifacts. The spectral characteristics of LFPs were investigated via frequency-vs-depth maps using a modified Welch periodogram using robust statistics, and further analyzed within different sub-bands to determine whether LFP activity encodes characteristic patterns for the identification of disease-specific subcortical areas. Our results demonstrated that a median-based spectrum estimation approach eliminates outliers better than the traditional averaging technique by preserving band-specific LFP activity. Results indicate that there was clear oscillatory beta activity around 20 Hz in two subjects. One patient displayed relatively high gamma (40 Hz) activity in the sub-thalamic region. In conclusion, despite the small number of subjects, the present study adds to existing knowledge about LFP-based pathophysiology of ET and its target-based spectral activities.