Regularizations in First Arrival Tomography

Ambiguity has always been an unavoidable problem in seismic inversion. How to make efficiently use of the a prior information to complement the observed data is discussed in this paper. The a prior information can be divided into three types. Usually, the three types of information are used to modify the model parameters directly after it is updated. However, ray-based tomography theory is developed under the linear approximation. So if the model is modified twice successively, it is very likely that the hypothesis is violated. If the a prior information can be integrated into the inverse equations, the constraint modification can be avoided. Regularization is a mean of achieving this task. Regularization has always been studied in inverse problems, but it is usually used to overcome the instability of the inverse algorithms. Clap and Fomel make use of regularization to incorporate geologic information into inversion. In this paper, basing on the category of the a prior information summarized above, we proposed the regularization methods relating with different kinds of the a prior information and expressed them in a formula.