Chapter 6 - Decomposition and Continuation of Seismic Wave Field

Abstract

In the previous chapter, we have discussed the solutions of the wave equation with boundary and initial value conditions. In this chapter, we will discuss the decomposition and extrapolation of seismic wave field. We should discuss the inverse problem of the wave equation in the following chapter. By discussing the decomposition and extrapolation of seismic wave field, we introduce a mathematic ideal called the expansion of wave differential operators. Although it is not easy to explain clearly the expansion of wave differential operators for engineers, the expansion ideal has wide applications in engineering. In matrix operation, we have discussed the singular value decomposition method for solving difficult linear equations, which is a good example of the numerical expansion of differential operators. Insight of the expansion of wave operators in inhomogeneous media is very useful for understanding the nature of wave propagation.