Magnetic reconnection is a topological restructuring of magnetic field lines, leading to a conversion of magnetic energy into kinetic energy and a heating of the plasma. It takes place in regions with strong magnetic gradients: the Earth's magnetopause and the plasma sheet in the magnetotail, during solar and stellar flare events, and in laboratory plasmas on the Earth. It is also involved in astrophysical phenomena like the generation of relativistic jets and processes in accretion disks. The Earth's magnetosphere is the only region where signatures of magnetic reconnection can be measured in-situ by satellites. Based on the method developed by Semenov et al. [1], we solve the direct problem of magnetic reconnection and calculate the magnetic field and plasma flow disturbances in a compressible plasma caused by transient reconnection. In order to get the reconnection rate from measured data, we invert the problem. Since the inverse problem is ill-posed, it is treated with the method of regularization. Application of this method to Cluster measurements from September 8^th, 2002, where a series of Earth-ward propagating 1-minute scalemagnetic field and plasma flow variationswere observed outside of the plasma sheet, showed good agreement for the z-component of the reconstructed magnetic field. The reconnection rate is about 1 mV/m and the reconnection region is located at about 24-25 Earth radii in the magnetotail.