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A family of nearest-neighbor interpolations

Let an integer k range along a survey line, and let data values xk be packed into a vector $\bold x$.(Each data point xk could also be a seismogram.) We plan to resample the data more densely, say from 4 to 6 points. For illustration, I follow a crude nearest-neighbor interpolation

scheme by sprinkling ones along the diagonal of a rectangular matrix that is  
 \begin{displaymath}
\bold y \eq \bold B \, \bold x\end{displaymath} (10)
where  
 \begin{displaymath}
\left[ 
 \begin{array}
{c}
 y_1 \  
 y_2 \  y_3 \  y_4 \...
 ...{array}
{c}
 x_1 \  
 x_2 \  x_3 \  x_4
 \end{array} \right]\end{displaymath} (11)
The interpolated data is simply $\bold y = (x_1, x_2,x_2,x_3, x_4,x_4)$.The matrix multiplication (11) would not be done in practice. Instead there would be a loop running over the space of the outputs $\bold y$ that picked up values from the input.



 
next up previous print clean
Next: Looping over input space Up: NORMAL MOVEOUT AND OTHER Previous: Nearest-neighbor interpolation
Stanford Exploration Project
10/21/1998