Infrasonic signals have been observed from 31 earthquakes by arrays of microphones operated by the Los Alamos National Laboratory between 1983 and 2003. The properties of the signals are presented. Signal amplitudes corrected for propagation and distance show a relation with seismic magnitude. The variance in the relation is understood primarily in terms of the uncertainties or errors in the ground motion, deduced from an independent data set, and the stratospheric winds, which strongly influence signal propagation. Signal durations can extend over many minutes. A relation is found between signal duration and magnitude. To understand this, we propose a model in which regions distant from the epicenter are excited by seismic surface waves. The surface motion of these regions, in turn, produces signals which precede or follow the signals from the epicenter. Analysis failed to detect signals from 56 earthquakes during the observation period. Predicted signal-to-noise ratios for these earthquakes indicated that the signals would have been too weak for detection.