Correction of velocity estimation bias caused by phase-shift beamforming in acoustic Doppler velocity logs

The performance of Doppler velocity logs (DVLs) in terms of velocity estimate error is directly linked to the geometry of the beam and the pulse transmitted. Beyond a specific transmitted bandwidth, the phase-shift beamformer can introduce significant errors in velocity estimation. To delineate the operating mechanism of phase-shift errors within a phased array of acoustic DVLs, the correlation between bottom echo and velocity distribution, in conjunction with the power-weighted function, was initially examined predicated on spectral estimation theory. Subsequently, numerical and analytical models of the Gaussian-shaped Doppler spectrum were formulated. The models are employed to evaluate the velocity estimation inaccuracies attributed to phase shifts in extant DVLs, and the comparative results with field experiments corroborate the model's efficacy in forecasting errors. The theoretical findings evaluate the performance limitations of the current phased array transducer design and provide insights for developing new designs. Pool experimental results show that this design effectively reduces the velocity estimation error caused by phase shift under static conditions and in the presence of Doppler frequencies to a level of almost complete elimination of the error compared to conventional configurations.