Waves in strata |

Nearest neighbor rounding is crude but ordinarily very reliable. I discovered a very rare numerical roundoff problem peculiar to signal time-shifting, a problem which arises in the linear moveout application when the water velocity, about 1.48 km/sec is approximated by 1.5=3/2. The problem arises only where the amount of the time shift is a numerical value (like 12.5000001 or 12.499999) and the fractional part should be exactly 1/2 but numerical rounding pushes it randomly in either direction. We would not care if an entire signal was shifted by either 12 units or by 13 units. What is troublesome, however, is if some random portion of the signal shifts 12 units while the rest of it shifts 13 units. Then the output signal has places which are empty while adjacent places contain the sum of two values. Linear moveout is the only application where I have ever encountered this difficulty. The problem disappears if we use a more accurate sound velocity or if we switch from nearest-neighbor interpolation to linear interpolation.

Waves in strata |

2009-03-16