The increasing availability of SAR time series creates many opportunities for remote sensing applications, but it can be challenging in terms of amount of data to process. This letter discusses the interest of the geometric mean to average SAR time series. First, the properties of the geometric mean and of the arithmetic mean are compared. Then, a speckle-reduction method specifically designed to improve images obtained with the geometric mean is presented. This method is based on an adaptation of the MuLoG framework to take into account the specific distribution of the geometric mean. Finally, applications of this denoised geometric-mean image are presented.