Next: Linear plus cork-screw Up: DESCRIPTION OF THE FIVE Previous: Nearest-neighbor interpolation

## Linear interpolation

This method is a two-point interpolation. We input the values of the nearest two points in the kz domain, then use the following equation to get the value of a point between them:
 (3)

where is the value of the point to be interpolated, Cn is the value of the point on its left side, and Cn+1 is the value of the point on its right side. is the value of the distance between the interpolated point and the sample point on its left side.

The linear interpolation in the frequency domain is equivalent to a convolution with a triangle function in the frequency domain Harlan (1982). In time-space domain, its counterpart is multiplication by a function. The multiplication by the causes the original values between T/2 and T to be weaker than the wraparound between -T/2 and . So in Figure 2, for which linear interpolation was used, the lower part of the section shows that the artifacts almost replace the original correct information.

Next: Linear plus cork-screw Up: DESCRIPTION OF THE FIVE Previous: Nearest-neighbor interpolation
Stanford Exploration Project
11/16/1997