Fast forward modeling and inversion of borehole sonic measurements using spatial sensitivity functions
MetadataShow full item record
Borehole sonic measurements are widely used by petrophysicists to estimate in-situ dynamic elastic properties of rock formations. The estimated formation properties typically guide the interpretation of seismic amplitude measurements in the exploration and development of hydrocarbon reservoirs. Due to limitations in vertical resolution, borehole sonic measurements (sonic logs) provide spatially averaged values of formation properties in thinly bedded rocks. In addition, mud-filtrate invasion and near-wellbore formation damage can bias the elastic properties estimated from sonic logs. The interpretation of sonic logs in high angle (HA) and horizontal (HZ) wells is even more challenging because of three-dimensional geometrical effects and anisotropy. A reliable approach to account for geometrical effects in the interpretation of sonic logs is the implementation of forward modeling and inversion techniques. However, the computation time required to model the direct problem, namely wave propagation in the borehole environment, severely constraints the usage of inversion approaches in sonic-log interpretation. This dissertation develops new methods for the rapid simulation of sonic logs using the concept of spatial sensitivity functions. Sonic spatial sensitivity functions are equivalent to the Green’s function of a particular sonic measurement; they also serve as weighting matrices to map formation elastic properties into the respective measurement space. Application of sensitivity functions to challenging synthetic examples verifies that the maximum relative error in the modeled sonic logs is lower than 3% for flexural, Stoneley, and compressional (P-) and shear (S-) modes. Compared to rigorous numerical simulations, the new fast sonic modeling method reduces computation time by 98%. Using the fast sonic simulation algorithm, we develop an inversion method that combines multi-frequency flexural dispersion and P- and S- mode slowness logs to estimate layer-by-layer compressional and shear slownesses of rock formations. Synthetic verification examples as well as interpretation of field cases indicate that the estimated formation compressional and shear slownesses are within 3% of true model properties, exhibiting a maximum uncertainty of 6%. When compared to conventional sonic-log interpretation, the new inversion-based method effectively reduces shoulder-bed effects and relative errors in estimated properties by 15%, while the vertical resolution of sonic logs is improved from 1.83 m to 0.5 m. Finally, we show that multi-mode wave interference in HA/HZ wells makes it difficult to identify the low-frequency slowness asymptote of the flexural mode. We extend the sensitivity method to three dimensions to approach this latter problem and to model high-frequency dispersion logs. Because the calculated P-mode slowness log exhibits strong dependence to processing parameters, conventional waveform semblance-based processing becomes inadequate in HA wells. We introduce a new P-arrival slowness log to circumvent wave mode interference and to avoid semblance calculations. Additionally, we also develop a one-dimensional integration method to rapidly model P-arrival slowness logs when HA/HZ wells penetrate anisotropic thin beds. The fast modeling algorithm generates synthetic logs that match sonic logs simulated with rigorous modeling procedures within 5% while providing a 99% reduction in computation time.