A scheme for the automated tsunami source reconstruction on the basis of deep-ocean tsunami wave recordings was developed. The initial water displacement in the source area is represented as a linear superposition of several "unit" sources. The initial value problem for the tsunami waves propagation from each of the unit sources in the whole of the north-eastern part of the Pacific ocean has been calculated using the Method of splitting tsunami (MOST). Using the database that includes all these calculated wave time series, a special algorithm and application software has been developed. The module effectively determines the amplification coefficients for unit sources, which makes it possible to approximate the shape of a vertical displacement of the sea surface over the tsunami source area. The algorithm in question is based on minimization of a calculated difference between the measured marigram(s) and a linear combination of pre-calculated synthetic marigrams. The method was tested against historical data of the 1996 Andreanov tsunami. This work is a pioneer attempt in developing the methodology and software for the tsunami source reconstruction in real time. Vasily Titov was the one, who handled the first deep-ocean tsunami records.