One of the key goals of microseismic processing is the accurate estimation of the source location. Applying full waveform information on passive-source datasets can potentially delineate microseismic sources. The accuracy of both P- and S- wave velocities has a strong influence on the estimation of source locations and hence the reliability of the fracture detection. We propose a methodology for passive source and velocity inversion, in which the conventional source term of the elastic wave equation is represented by an equivalent source. The equivalent source term is composed of source images and source functions, as it is inspired by elastic reflection waveform inversion. Thus, we update the source locations, source functions and velocities simultaneously by using a waveform inversion scheme. In the 2D isotropic case, the source terms are defined by two source image components and three source function components. They provide an alternative source representation of its mechanism, usually defined by the moment tensor. Waveform inversion of passive events has severe nonlinearity due to the unknown source locations in space and their functions in time. We, thus, use a source-independent objective function, based on convolving reference traces with both modeled and observed data, to avoid cycle skipping caused by the unknown sources. We first synthetically test our method on a modified Marmousi model. Then, by applying a nested inversion for these variables, the proposed method also produces good estimation of the source and background velocity for real microseismic monitoring data. We use a ball-drop event to test the accuracy as the inverted source location should match the ball-seat location. For the uncontrolled events, the estimated source distribution using waveform inversion agrees with the local stress potential information. Though the proposed method has higher computational cost than traveltime or migration based methods, the estimated event locations have significantly improved accuracy.