Derive reflection travel$-$time equations for a single zero dipping and single dipping interface. Sketch and label the travel$-$time graphs for these situations.

Table below shows the seismic reflection data. Please determine the velocities and thickness for three layers using the following seismic reflection data:

$\backslash$table$[[$Offset x $($m$),\backslash$table$[[$Reflection $1],[($ms$)]],\backslash$table$[[$Reflection $2],[($ms$)]],\backslash$table$[[$Reflection $3],[($ms$)]]],[4,21\mathrm{.}4,62\mathrm{.}3,79\mathrm{.}4],[8,25,62\mathrm{.}4,79\mathrm{.}5],[12,30\mathrm{.}1,62\mathrm{.}6,79\mathrm{.}6],[16,36\mathrm{.}1,62\mathrm{.}9,79\mathrm{.}9],[20,42\mathrm{.}5,63\mathrm{.}2,80\mathrm{.}1],[24,49\mathrm{.}2,63\mathrm{.}6,80\mathrm{.}5],[28,56\mathrm{.}2,64\mathrm{.}1,80\mathrm{.}9],[32,63\mathrm{.}3,64\mathrm{.}7,81\mathrm{.}3],[36,70\mathrm{.}4,65\mathrm{.}4,81\mathrm{.}8],[40,77\mathrm{.}6,66\mathrm{.}1,82\mathrm{.}4],[44,84\mathrm{.}9,66\mathrm{.}9,83\mathrm{.}0],[48,92\mathrm{.}2,67\mathrm{.}7,83\mathrm{.}7]]$

Hints:

First, draw a graph of $t^{2}vs{x}^2$ values for all the three reflections. Then, use the first intercept and the singlelayer travel time formula to determine the thickness of layer $1.$ The slope for the first reflector is simply $\frac{1}{V_1^2},$ but for the deeper reflectors the slope corresponds to the RMS velocity.

Then, from the slope and intercept values, use the Dix Formula to compute the interval velocities for layers $2$ and $3.$ Finally, use the fact that $t_n-t_{n-1}=2\frac{z_n}{V_n}$ to compute the thickness for layers $2$ and $3.$