The analysis of microseismic measurements acquired during borehole acquisition surveys is essential for a thorough understanding of the source mechanisms in hydraulic fracturing operations. Due to the injection of high-pressure fluids, induced fractures can produce seismic events of low magnitude that can be recorded and subsequently analyzed to infer the stress field at the location of the event. The seismic moment tensor has been widely used to describe general seismic sources as it can provide information about the type of motion and the distribution of forces. Estimating such quantities from the recorded data can significantly improve the real-time microseismic monitoring operations and help to make assumptions about the structure of the reservoir. However, several challenges have to be faced when working with microseismic borehole measurements. They are characterized by a low signal-to-noise ratio and a limited angle coverage, which may ultimately affect the predictions about the location and the fracturing behavior inside the reservoir. In this thesis the inversion of microseismic measurements for retrieving the moment tensor has been tackled by using a deep feedforward neural network. The seismograms used to train the network were generated through the discrete-wavenumber method. The neural network was used to predict the six independent moment-tensor components and the fault angles from seismic sources at different positions than those used during the training. The predictive capabilities of the network were tested for realistic borehole acquisition geometries and wave propagation models. The moment-tensor components were retrieved with good accuracy when using noisy seismograms and, non-double-couple source mechanisms. As the generation of synthetic data can be expensive in terms of memory consumption, the training and prediction have been also implemented in the frequency domain using only a limited portion of the Fourier transform of the seismograms. The inversion results indicated that using narrow bands can still yield satisfactory results when predicting the moment-tensor components.