The effects of measurement uncertainties in seismic-wave gradiometry

In seismic-wave gradiometry, the spatial gradient and the time derivative of the measured wavefield are used to estimate the slowness vector and changes in the radiation pattern. When using a seismic array to estimate the seismic spatial derivatives, the array aperture cannot be greater than approximately 10% of the target wavelength to avoid spatial aliasing effects. However, there has been little research into the minimum practical array aperture. In this article, we investigate the effects of measurement uncertainties on the accuracy of gradiometrically estimated wave parameters, as well as provide recommendations on design criteria for gradiometric arrays. The design parameters are based on wavefield slowness, frequency, and measurement uncertainty.