Full waveform inversion enables us to obtain high-resolution subsurface images. However, estimating the associated uncertainties is not trivial. Hessian-based method gives us an opportunity to assess the uncertainties around a given estimate based on the inverse of the Hessian, evaluated at that estimate. In this work we study various algorithms for extracting information from this inverse Hessian based on a low-rank approximation. In particular, we compare the Lanczos method to the randomized singular value decomposition. We demonstrate that the low-rank approximation may lead to a biased conclusion.