Definition of dependent variables

There are two kinds of dependent variables, those that characterize the medium and those that characterize the waves. The medium is characterized by its velocity v and its reflectivity c. The waves are characterized by using U for an upcoming wave, D for a downgoing wave, P for the pressure, and Q for a modulated form of pressure. Let us say P(t,x,z) is the mathematical function to find pressure, given (t,x,z); and P' (t' ,x' ,z' ) is the mathematical function given (t' ,x' ,z' ). The statement that the two mathematical functions P and P' both refer to the same physical variable is this:

$$\begin{eqnarray} P ( t , x , z )\ \ \ &=&\ \ \ P'[t'(t,x , z ) ,\ x' ( t , x ,... ...] \\ P ( t , x , z ) \ \ \ &=&\ \ \ P' ( t' , x' , z' ) \nonumber\end{eqnarray}$$ (30)

Obviously there are analogous expressions for the other dependent variables and medium parameters like velocity v(x,z).