High-quality seismic data are critical for characterizing complex geological reservoirs, yet persistent noise contamination remains challenging. Parameterization methods separate signals from noise by expressing seismic data as mathematical models. While linear approaches like Tucker decomposition effectively impose low-rank constraints to isolate structured seismic reflections, they lack the nonlinear expressiveness required for complex stratigraphic features. Conversely, like implicit neural representations (INR), nonlinear parameterization achieves enhanced expressiveness through continuous nonlinear mappings, leveraging spectral bias to suppress high-frequency noise. However, this strength paradoxically becomes a limitation in high-frequency regimes: without explicit structural guidance, INRs sacrifice structural fidelity and struggle to distinguish subtle geological features (e.g., fault edges, pinch-outs) from spectrally overlapping noise, resulting in over-smoothed structures or amplified high-frequency artifacts. Recent advances in reparameterization methods demonstrate promising noise suppression through enhanced model expressiveness. To resolve this expressiveness-stability tradeoff, we propose Stacked Tucker Implicit Seismic Reparameterization (STISR), a hybrid framework that synergizes Tucker's low-rank structural anchors with INR's high-expressiveness nonlinear approximation. Tucker decomposition in STISR provides a noise-reduced, structured initialization to guide INR optimization, effectively regularizing the neural representation to maintain coherent reflection structures. Then, the neural network nonlinearly reparameterizes the Tucker decomposition, further enhancing its expressiveness and recovering subtle features beyond linear subspace constraints. A progressive hierarchical re-decomposition strategy applies linear reparameterization to the Tucker core tensor, iteratively optimizing it across scales and reinforcing low-rank stability while adaptively allocating expressiveness to resolve fine-scale features. To address the heterogeneity of noise in field seismic data, we introduce l1 regularization, which adjusts the sparsity threshold based on residual noise, enabling targeted handling of diverse noise distributions. Validation on synthetic and field pre-stack datasets confirms STISR's superiority in balancing computational efficiency, structural fidelity, and noise rejection compared to conventional tensor decomposition or pure neural network approaches.