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 [Formula: see text], 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.

Detecting vertical transversely isotropic (VTI) formations and quantifying the magnitude of anisotropy are fundamental for describing organic mudrocks. Methods used to estimate stiffness coefficients of VTI formations often provide discontinuous or spatially averaged results over depth intervals where formation layers are thinner than the receiver aperture of acoustic tools. We have developed an inversion-based method to estimate stiffness coefficients of VTI formations that are continuous over the examined depth interval and that are mitigated for spatial averaging effects. To estimate the coefficients, we use logs of frequency-dependent compressional, Stoneley, and quadrupole/flexural modes measured with wireline or logging-while-drilling (LWD) instruments in vertical wells penetrating horizontal layers. First, we calculate the axial sensitivity functions of borehole sonic modes to stiffness coefficients; next, we use the sensitivity functions to estimate the stiffness coefficients of VTI layers sequentially from frequency-dependent borehole sonic logs. Because sonic logs exhibit spatial averaging effects, we deaverage the logs by calculating layer-by-layer slownesses of formations prior to estimating stiffness coefficients. The method is verified with synthetic models of homogeneous and thinly bedded formations constructed from field examples of organic mudrocks. Results consist of layer-by-layer estimates of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. We observe three sources of error in the estimated coefficients: (1) bias error originating from deaveraging the sonic logs prior to the sequential inversion, (2) error propagated during the sequential inversion, and (3) error associated with noisy slowness logs. We found that the relative bias and uncertainty of the estimated coefficients are largest for [Formula: see text] and [Formula: see text] because borehole modes exhibit low sensitivity to these two coefficients. The main advantage of our method is that it mitigates spatial averaging effects of sonic logs, while at the same time it detects the presence of anisotropic layers and yields continuous estimations of stiffness coefficients along the depth interval of interest.

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