We report moment distribution results from a laboratory experiment, similar in character to an isolated strike-slip earthquake fault, consisting of sheared elastic plates separated by a narrow gap filled with a two-dimensional granular medium. Local measurement of strain displacements of the plates at 203 spatial points located adjacent to the gap allows direct determination of the event moments and their spatial and temporal distributions. We show that events consist of spatially coherent, larger motions and spatially extended (noncoherent), smaller events. The noncoherent events have a probability distribution of event moment consistent with an M-3 /2 power law scaling with Poisson-distributed recurrence times. Coherent events have a log-normal moment distribution and mean temporal recurrence. As the applied normal pressure increases, there are more coherent events and their log-normal distribution broadens and shifts to larger average moment.