Conversions at the surface

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Conversions at the surface

At a free surface the stress free boundary condition must be satisfied. As discussed in the appendix this results in $3\times3$ matrix operators that convert applied tractions to particle velocities and downgoing wave amplitudes, and operators that convert upgoing wave amplitudes into velocities and downgoing amplitudes.

$\begin{eqnarraystar} {\bf d}^1 = tracdown \cdot {\bf \sigma}_N \\ {\bf v}^1 = tracdisp \cdot {\bf \sigma}_N \\ \end{eqnarraystar}$

and

$\begin{eqnarraystar} {\bf v}^1 = surfdisp \cdot {\bf u}^1 \\ {\bf d}^1 = surfrefl \cdot {\bf u}^1 \\ \end{eqnarraystar}$

These four operators are required in performing steps one and six of the algorithm.

Next: Results in the domain Up: TWO WAY PHASE SHIFT Previous: Calculation of reflection and

Stanford Exploration Project
12/18/1997

	$\begin{eqnarraystar} {\bf d}^1 = tracdown \cdot {\bf \sigma}_N \\ {\bf v}^1 = tracdisp \cdot {\bf \sigma}_N \\ \end{eqnarraystar}$

	$\begin{eqnarraystar} {\bf v}^1 = surfdisp \cdot {\bf u}^1 \\ {\bf d}^1 = surfrefl \cdot {\bf u}^1 \\ \end{eqnarraystar}$