Earthquakes can trigger the eruption of mud. We use eruptions in Azerbaijan, Italy, Romania, Japan, Andaman Islands, Pakistan, Taiwan, Indonesia, and California to probe the nature of stress changes that induce new eruptions and modulate ongoing eruptions. Dynamic stresses produced by earthquakes are usually inferred to be the dominant triggering mechanism; however static stress changes acting on the feeder systems of mud volcanoes may also play a role. In Azerbaijan, eruptions within 2-10 fault lengths from the epicenter are favored in the year following earthquakes where the static stress changes cause compression of the mud source and unclamp feeder dikes. In Romania, Taiwan, and some Italian sites, increased activity is also favored where the static stress changes act to unclamp feeder dikes, but responses occur within days. The eruption in the Andaman Islands, and those of the Niikappu mud volcanoes, Japan are better correlated with amplitude of dynamic stresses produced by seismic waves. Similarly, a new island that emerged off the coast of Pakistan in 2013 was likely triggered by dynamic stresses, enhanced by directivity. At the southern end of the Salton Sea, California earthquakes increase the gas flux at small mud volcanoes. Responses are best correlated with dynamic stresses. The comparison of responses in these nine settings indicates that dynamic stresses are most often correlated with triggering, although permanent stress changes as small as, and possibly smaller than, 0.1 bar may be sufficient to also influence eruptions. Unclamping stresses with magnitude similar to Earth tides (0.01 bar) persist over time and may play a role in triggering delayed responses. Unclamping stresses may be important contributors to short-term triggering only if they exceed 0.1-1 bar.