Method to find the Minimum 1D Linear Gradient Model for Seismic Tomography

The changes in the state of a geophysical medium before a strong earthquake can be found by studying of 3D seismic velocity images constructed for consecutive time windows. A preliminary step is to see changes with time in a minimum 1D model. In this paper we develop a method that finds the parameters of the minimum linear gradient model by applying a two-dimensional Taylor series of the observed data for the seismic ray and by performing least-square minimization for all seismic rays. This allows us to obtain the mean value of the discrete observed variable, close to zero value.