Harrison [J. Acoust. Soc. Am. 125, 3511-3513 (2009)] presented a mathematical explanation for a sign-inversion induced to the passive fathometer response by minimum variance distortionless response (MVDR) beamforming. Here a concise mathematical formulation is offered, which decomposes the cross-spectral density matrix into coherent and incoherent components and allows the matrix inversion to be obtained exactly by eigendecomposition. This shows that, in the region containing the bottom reflection, the MVDR fathometer response is identical to that obtained with conventional processing multiplied by a negative factor.