Methods and apparatus for determining error in formation parameter

Abstract

Methods and apparatus for generating an error bar (variance) log for a formation parameter are disclosed. According to the method, acoustic waveforms are detected at a plurality (M) of detectors which are a function of a source signal which has interacted with the formation and noise, and the detected waveforms are sampled and processed in order to obtain a semblance or a normalized mean square error. Using the semblance or the NMSE which is related to the semblance, a signal to noise ratio 2E/N.sub.0 can be found by recognizing that the semblance function has a non-central beta distribution whose mean is a function of the signal to noise ratio 2E/N.sub.0, the time-bandwidth product N, and M. The signal to noise ratio is then used to find the Cramer-Rao lower bound which is taken as an estimate of the variance. An error bar log is formed by repeating these steps at a plurality of locations along the borehole. The method of the invention can be used in conjunction with both attenuating and non-attenuating waves. The apparatus of the invention relates closely to the method.