  We report moment distribution results from a laboratory earthquake fault
experiment 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 over 800 spatial points located adjacent to the
gap allows direct determination of the moments and their spatial and temporal
distributions. We show that events consist of localized, larger brittle motions
and spatially-extended, smaller non-brittle events. The non-brittle events have
a probability distribution of event moment consistent with an $M^{-3/2}$ power
law scaling. Brittle events have a broad, peaked moment distribution and a mean
repetition time. As the applied normal force increases, there are more brittle
events, and the brittle moment distribution broadens. Our results are
consistent with mean field descriptions of statistical models of earthquakes
and avalanches.
