Inversion-based method to mitigate noise in borehole sonic logs

Abstract

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.

Efficient Bayesian inversion of borehole geophysical measurements with a gradient‐based Markov chain Monte Carlo method

“…Most previous studies implement deterministic inversion methods. Uncertainty quantification is performed by using either a linear approximation of the covariance matrix for earth‐model properties (Wang et al., 2009; Ijasan et al., 2013a; Ortega et al., 2017), or a simplified randomized maximum likelihood (RML) algorithm (Heidari et al., 2012; Huang & Torres‐Verdín, 2016; Maalouf & Torres‐Verdín, 2018). Both methods provide an approximation of the uncertainty of inversion results and remain valid only when the forward model is linear with respect to the estimated layer properties and the measurement noise is Gaussian.…”

“…resistivity, nuclear or acoustic). These methods implement numerical simulations of borehole measurements and deterministic inversion, such as the Levenberg–Marquardt method (Huang & Torres‐Verdín, 2016; Maalouf & Torres‐Verdín, 2018; Ortega et al., 2017; Pardo & Torres‐Verdín, 2015; Wang et al., 2009) to match the available well logs with their numerical simulations. WLI applied to general borehole measurements typically relies on finite differences to calculate the gradient (or Jacobian matrix) required by the inversion (Heidari et al., 2012; Ijasan et al., 2013a).…”

Radial profiling of shear slowness from borehole acoustic measurements acquired in thinly laminated formations

“…As a result, radial variations of shear‐wave slowness estimated from this method have the limitation of low vertical resolution. Across thinly laminated formations, which are common occurrence in subsurface energy studies, borehole acoustic measurements are affected not only by the radial variations of elastic properties but also by axial averaging effects, which depend on both the geometry of receivers/transmitters and the post‐processing algorithms used to calculate slownesses (Huang et al., 2015; Maalouf & Torres‐Verdín, 2018a; Peyret & Torres‐Verdín, 2006; Sams, 1995; Sinha, 2021).…”

“…Inversion‐based interpretation methods are commonly used in the estimation of rock elastic properties from borehole acoustic logs in order to mitigate both axial spatial averaging effects and measurement noise (Huang, & Torres‐Verdín, 2016; Lei et al., 2019; Maalouf & Torres‐Verdín, 2018a). For example, to quantify axial rock heterogeneity from borehole acoustic logs due to layering, Huang and Torres‐Verdín (2016) developed an inversion‐based interpretation method via the Levenberg–Marquardt non‐linear minimization technique, which estimates layer‐by‐layer elastic properties of rock formations penetrated by vertical wells.…”