This study presents a suite of 2D synthetic microseismic events computed using three velocity models, incorporating varying degrees of anisotropy and attenuation. An explicit second-order finite-difference method is used, capable of handling general anisotropy, up to triclinic symmetry. The microseismic source is specified as an arbitrary moment tensor, subject to be located in an isotropic layer. The anisotropy in our models is confined to VTI (Vertically Transverse Isotropic) media. Attenuation can be simulated for both isotropic and VTI medium, so the method is suited to modeling wave propagation in shale. All of the examples shown in this thesis are for a downhole acquisition geometry using a vertical monitor well. Care is required to avoid contamination of the synthetic data by edge reflections due to the ineffectiveness of currently known FD absorbing boundary for general anisotropy. Synthetic data (SEGY) are available for benchmarking purposes including hypocentre location, moment tensor inversion, etc.