Deep-Sea Bathymetry From Geosynchronous SAR via DTCWT-Enhanced Spatial-Correlation Wave Imaging and Multiparameter Time-Series Inversion

Deep-sea bathymetry inversion from geosynchronous synthetic aperture radar (GEO SAR) offers persistent wide-area monitoring capabilities but faces two fundamental challenges: the defocusing of topography-induced sea-surface waves due to their nonlinear space-variant motions during long integration times, and the ill-posed nature of retrieving seabed topography from surface signatures due to the nonlinear, depth-dependent filtering effect of the stratified water column. To address these issues, this article builds upon our previous GEO spatial-correlation (SC) SAR spatial-correlation imaging framework and existing sea-surface parameter retrieval modules, and introduces two new components for this task: a GEO dual-tree complex wavelet transform (DTCWT)-SC SAR imaging algorithm and a StratiFormer inversion network. On the imaging side, we develop the GEO DTCWT-SC SAR algorithm: oriented DTCWT subbands represent nonlinear, space-variant kinematics with a set of direction-separable and 2-D cross-directional residual modes that parameterize a motion-compensated spatial-correlation kernel. Applied point-by-point to the echoes, this kernel corrects the phase history, restores the slow-time spatial correlation of the sea-surface pattern, and enables closed-loop, correlation-driven motion refinement. On the inversion side, we introduce StratiFormer, a hierarchical spatiotemporal network that performs multiparameter time-series inversion from sea-surface height and 2-D current sequences to deep-sea bathymetry. Unlike static image-to-depth models, StratiFormer ingests the multiparameter time series into a three-stage hierarchical encoder with learnable interstage feature fusion. The hybrid-phase decoupling and current-retrieval steps are used as an integrated retrieval and observation-construction interface rather than as new contributions of this article. Controlled echo-to-depth simulations, reanalysis-informed surface-field experiments, and terrain-disjoint diagnostics support the algorithmic feasibility of the proposed workflow under controlled and reanalysis-informed settings, while operational validation with measured GEO-SAR observations and collocated bathymetric truth remains necessary.