Abstract
A long‐spacing velocity log contains almost the same information as an ideal short‐spacing log, but in a distorted form with added noise. The distortion can be thought of as a moving average or smoothing filter. Its inverse, called a “sharpening” filter by astronomers, amplifies noise. If the inverse is to be useful, it must be designed with a balance between errors due to noise amplification and those due to incomplete sharpening. The Wiener optimum filter theory gives a prescription for achieving this balance. The result is called an optimum inverse filter. We have calculated finite‐memory optimum inverse filters using the IBM 704. We have applied them to actual data, digitized in the field, to produce synthetic short‐spacing velocity logs. These we have compared with their field counterparts. The synthetic logs have less calibration error and are free from noise spikes. The general agreement is good.
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