A differentiated approach to the seismic tomography problem: Method, testing and application to the Western Nagano fault area (Japan)

Results of tomographic inversion enrich our understanding of the geodynamic processes in the Earth. Seismic imaging of fault zones, the shear rupture permits us to investigate the structure under gas storage areas, in districts of large hydroelectric power stations, nuclear plants. The information about the geodynamic evolution of seismic structures in areas that are close to oceans helps us in assumption of epicenters of destructive earthquakes. A differentiated approach (DA) has been developed to overcome an interference of parameterization and observation errors distorting an accuracy of the three-dimensional tomography images. We have designed a method based upon revision of Gauss elimination scheme to the modern problem of large and sparse system of equations. The best linear unbiased estimations of seismic velocity parameter have been obtained by means of incorporating criterion. We used the statistical analyze to select optimal solution having minimal dispersion of parameterization error. In order to decrease a risk of a high error rate we applied the theory of Tikhonov regularization. Due to these measures the evaluated parameters of a medium possess isometric properties and thus for them the problem of seismic anisotropy has a real chance to be solved. By using a simple arbitrary model as well as a complex one for the fault region in Western Nagano, Japan, we demonstrated that the DA method is an effective alternative for the standard method. An application of DA to the real data underlines the high capability of DA of defining the fault planes as compared to the double-difference algorithm under the same condition of experiment. The detailed DA image suggests that the narrow rupture zone after the 1984 Naganoken-Seibu earthquake still exists.