High-performance geological-data-driven 3D formation modeling under fractal dimension constraints and Stoneley wave response study

Abstract Stoneley-wave simulation is an effective approach for evaluating near-borehole heterogeneity and fluid effects, yet many existing studies still rely on simplified geometries. Here, we developed a high-performance, geology-driven, and fractal-dimension–constrained workflow to construct complex 3D formation models for Stoneley-wave response analysis. Core-scale porosity, MICP, and NMR measurements are jointly interpreted through a $P_c$–$T_2$ transform to derive representative modeling inputs, including $\phi$ and $R_{L/S}$. A heterogeneous background is generated using random-media theory, and vugs are embedded under connectivity constraints to honor mesoscale vug architecture and macroscopic heterogeneity. CT-derived digital cores are analyzed with box-counting to define an admissible fractal-dimension range [$D_{{\rm min}}$, $D_{\max }$], which is used to screen and retain qualified models. To make iterative construction practical at scale, we implemented a Graphics Processing Unit (GPU)-accelerated parallel modeling algorithm, achieving a 1261$\times$ speedup over a serial baseline. Staggered-grid finite-difference simulations show that, for a fluid-saturated thin layer, increasing thickness attenuates the main Stoneley peak and delays the first arrival. In the frequency domain, spectra evolve from unimodal to multimodal, with low-frequency enhancement, mid-frequency splitting, and high-frequency decay, while the reflected component develops a strengthened multi-peak signature. These thickness-dependent features support quantitative thin-layer evaluation near the borehole and provide an efficient, accurate forward-modeling framework for acoustic remote-detection logging in strongly heterogeneous carbonate formations.