Abstract
In clay-sand reservoirs, shale volume affects porosity and permeability, with porosity governing storage capacity; these properties influence reserve and productivity predictions, which directly affect reservoir and economic assessments. Estimates of porosity and shale volume from independent log-based methods may introduce coupled biases, whereas those from joint inversion better honor their interdependence. Joint inversion has traditionally relied on simplified assumptions or extra data; in contrast, recent data-driven approaches capture complex log patterns. However, purely data-driven methods suffer from feature-target shifts and cannot enforce inter-target dependencies. To address these limitations, a two-stage deep learning framework combining self-supervised log modeling with core-calibrated low-rank adaptation (CCLoRA) is proposed for joint porosity and shale volume prediction. First, a Conditional Score-based Diffusion Imputation (CSDI) model is self-supervised on synthetic logs generated from empirical formulas. This enables learning of plausible log sequence structures and confers partial robustness to feature-target shifts without extensive labeled data. Second, core-scale petrophysical relationships are transferred to the log scale through well-specific feature replacement using CCLoRA. This corrects residual feature-target shifts and enforces inter-target dependencies between the two parameters with minimal fine-tuning cost. Experiments on well-consolidated sandstones show the full pipeline outperforms multiple deep learning baselines, delivering accurate and physically consistent estimates.