Abstract: The paper deals with an estimation of the frequency spectrum of sea surface displacement from wave pressure records collected at any depth. Previous work on this is briefly reviewed. Based on the records of sea surface displacement and corresponding wave pressure records at a series of depths, measured in Beibu Gulf, surface displacement spectrum is calculated from the records of sea surface displacement, and from the corresponding pressure spectrum recreatively a comparison shows satisfactory agreement in low frequency domain, but a rather large discrepanty domain in the high frequency,thus suggesting that a critical frequency may exist. In view of the fact that at frequencies higher than the critical frequency one cannot succeed in computing the surface displacement spectrum from the corresponding pressure spectrum using the linear wave theory, the critical frequency is named "failure frequency" in this paper.