High-Performance Geological-Data-Driven 3D Formation Modeling under Fractal Dimension Constraints and Stoneley Wave Response Study

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 Pc-T2 transform to derive representative modeling inputs, including φ and RL/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 [Dmin , Dmax ], which is used to screen and retain qualified models. To make iterative construction practical at scale, we implemented a GPU-accelerated parallel modeling algorithm, achieving a 1261× 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.