Least‐squares inversion of in‐situ sonicQmeasurements: Stability and resolution

Abstract

We minimize the effect of noise and increase both the reliability and the resolution of attenuation estimates obtained from multireceiver full‐waveform sonics. Multiple measurements of effective attenuation were generated from full‐waveform sonic data recorded by an eight‐receiver sonic tool in a gas‐bearing sandstone reservoir using two independent techniques: the logarithmic spectral ratio (LSR) and the instantaneous frequency (IF) method. After rejecting unstable estimates [receiver separation <2 ft (0.61 m)], least‐squares inversion was used to combine the multiple estimates into high‐resolution attenuation logs. The procedure was applied to raw attenuation data obtained with both the LSR and IF methods, and the resulting logs showed that the attenuation estimates obtained for the maximum receiver separation of 3.5 ft (1.07 m) provide a smoothed approximation of the high‐resolution measurements. The approximation is better for the IF method, with the normalized crosscorrelation factor between the low‐ and high‐resolution logs being 0.90 for the IF method and 0.88 for the LSR method.