A major challenge in the interpretation of seismic measurements and sonic logs is the presence of deleterious noise that impacts the quality and reliability of the estimated seismic wavelets and seismic inversion products. Spatial averaging effects and borehole drilling damage can also bias the estimation of in situ stress and elastic properties from sonic logs. We have developed an inversion-based method to mitigate processing errors, spatial averaging effects, and borehole environmental noise on sonic logs, which does not require arbitrary numerical filters, effective-medium theory models, or time-consuming waveform reprocessing. The inversion-based method estimates layer-by-layer slownesses via joint inversion of shear and compressional logs measured in a vertical well, and it uses the estimated slownesses of the assumed horizontal layers to model noise-mitigated sonic logs. By making use of geometric and physical constraints for noise reduction implicit in the inversion-based method, we obtain sonic logs that more accurately reflect the physical properties of rock formations penetrated by wells. Sonic logs are efficiently modeled by invoking axial sensitivity functions. First, we test the inversion-based method with synthetic sonic logs contaminated with noise. Estimated layer-by-layer slownesses agree with those of the original model within a standard deviation of 2.5  μs/ft, while effectively reducing the numerical noise included in the input measurements. When bed-boundary locations are unknown, we perform the inversion-based method by assuming bed boundaries uniformly spaced at the same sampling interval of sonic logs; in this case, although the accuracy of the estimated layer slownesses decreases, the noise on sonic logs decreases. Then, we apply the method to sonic logs acquired in the North Sea and estimate angle reflectivity from the noise-mitigated logs. Results verify the reliability of the inversion-based method to reduce biases in the calculated angle reflectivity within a few minutes of central processing unit time.

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