Modification of Gaussian Elimination for the Complex System of Seismic Observations

A method for solving large and sparse systems with complex seismic observations has been developed by revising the classical Gaussian elimination. The observation matrix is divided into a set of smaller cells that can be determined based on clusters of seismic activity. Reliable inversion solutions with minimum error rating are selected within each cell; solutions that are unstable with respect to the same unknown are rejected. After the final sifting, the found unknowns are eliminated from the initial system, subsequently decreasing its dimension. A numerical example is provided to demonstrate how the method can be applied to a real dataset (a case study of the Nagano fault area in central Japan). The result of processing a huge volume of data showed that the P-wave velocity structure is much more complex than the synthetic model, which has been used to check the method effectiveness. The importance of the results for the Earthquake Early Warning (EEW) system is briefly discussed.