Tomographic inversion by matrix transformation

We have developed a new method to build seismic velocity models for complex structures. In our approach, we use a spatially nonuniform parameterization of the velocity model in tomography and a uniform grid representation of the same velocity model in ray tracing to generate the linear system of tomographic equations. Subsequently, a matrix transformation is applied to the system of equations to produce a new linear system of tomographic equations using nonuniform parameterization. In this way, we improved the stability of tomographic inversion without adding computing costs. We tested the effectiveness of our process on a 3D synthetic data example.