A data-driven azimuthal gamma-gamma density method for improved formation evaluation

Accurate formation density measurement during logging while drilling (LWD) is often compromised by dynamic tool standoff variations, especially in eccentric or enlarged boreholes. Traditional methods struggle with errors caused by asymmetric standoff and rotational tool movement. To overcome these limitations, an optimized azimuthal gamma density method based on the weighted fusion of sixteen-sector measurement data is presented. By leveraging the tool's spatial nuclear response characteristics, a directional quality factor is assigned to each sector. A first-order Fourier expansion is then used to identify the optimal azimuthal direction that best reflects the true formation signal. Within a ±90° window centered on this optimal direction, high-quality sector data are selectively fused to compute a more accurate formation density. This approach effectively suppresses azimuthal noise and enhances measurement reliability under complex wellbore conditions. Validation through numerical simulations and field data demonstrates significant improvements: in a vertical well section (X500-X600 m), the proposed method achieved a root mean square error (RMSE) of 0.038 g/cm3 and a mean absolute error (MAE) of 0.029 g/cm3; in a deviated section (Y650-Y750 m), the RMSE and MAE were further reduced to 0.036 g/cm3 and 0.028 g/cm3, respectively—representing over 30% improvement compared to conventional methods. These results demonstrate the method's effectiveness and adaptability for real-time formation evaluation and geosteering applications.