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A frequency-domain waveform inversion for microseismic sources in anisotropic media is described that combines the efficiency of ray theory with waveform fitting. The inversion returns estimates of the moment tensor and source function. A new moment tensor decomposition produces source parameters free from the distortions due to anisotropy at the source, and a new 3D graphical object intuitively visualizes the new source parameters. The techniques are illustrated on an event from a dual receiver array data set.