VELOCITY ANALYSIS

We know about two operators that map a point in $(\tau,m)$-space onto a hyperbola in (t,x)-space. These operators are $\bold P$ and $\bold H^{\bold T}$. If we sum along parabolas (operator $\bold P$) passing through one point in $(\tau,m)$-space, we obtain a hyperbola in (t,x)-space. A hyperbola is also obtained when a point in $(\tau,m)$-space is spread onto a hyperbola in (t,x)-space (operator $\bold H^{\bold T}$). Therefore, to obtain a velocity analysis panel $\bold u$, we solve  

$$\bold P \bold u = \bold d$$ (6)

or  

$$\bold H^{\bold T} \bold u = \bold d.$$ (7)