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Sets of equations and unknowns

Our system of equations is constituted by collecting relations (4), (6), (7), (8), and (13):  
 \begin{displaymath}
\left\{ \begin{array}
{ccc}

 \xi(p_g,t_g)\frac{{\bf p}_g}{p...
 ... p}_s + {\bf p}_g) \cos \theta(p_0,t_0)

 \end{array} \right. .\end{displaymath} (14)
Because the ${\bf x}$ and ${\bf p}$ vectors are two-dimensional, the first, second, and sixth relations of system (14) give $3\times2$ equations, yielding a set of nine equations.

The unknowns are ${\bf p}_s$, ${\bf p}_g$, ts, tg, t0, and ${\bf x}_0$. As described in the preamble, the ${\bf p}$ vectors have only two unknown parameters, px and py (or p and $\phi$). Similarly, ${\bf x}_0$ is a two-dimensional unknown vector. Therefore, system (14) relates nine unknowns with the known parameters ${\bf p}_0$, tsg, ${\bf x}_s$, ${\bf x}_g$, and the ray tracing tables $\xi(p,t)$, $\tau(p,t)$, and $\theta(p,t)$.


previous up next print clean
Next: Solving the system Up: DERIVING THE SYSTEM OF Previous: The relationship between the
Stanford Exploration Project
11/17/1997