Development and Application of Topography-Dependent First-Arrival Double-Difference Adjoint Tomography to Active-Source 3D OBS Data from the Southwest Indian Ridge

First-arrival tomography (FAT) is widely used for crustal-scale seismic imaging based on active-source ocean-bottom seismometer (OBS) data. However, conventional FAT approaches face challenges, including the ill-posedness and the difficulty in accurately accounting for complex bathymetric variations. To overcome these limitations, we develop a novel 3D topography-dependent first-arrival double-difference tomography (3D TDFADT) method. This approach minimizes a joint cost function that combines both absolute and differential first-arrival travel-time measurements with appropriate weighting. Our method uses a boundary-conforming mesh to accurately discretize models with rugged bathymetry. By introducing a coordinate transformation between Cartesian and curvilinear coordinates, we solve a 3D topography-dependent eikonal equation to compute travel times. The inverse problem is tackled using a preconditioned quasi-Newton optimization algorithm, with the gradient and preconditioner of the data misfit efficiently computed by the adjoint-state method. This formulation enables gradient computation without the need for tedious posterior ray tracing or storage of large Fréchet matrices in curvilinear coordinates. In contrast, the preconditioner improves the stability and accelerates the convergence of the inversion by partially compensating for uneven ray coverage of first arrivals in OBS data, but this may inherently involve a trade-off with resolution. We apply TDFADT to 3D first-arrival data from airgun shots recorded by an OBS array deployed at the ultraslow-spreading Southwest Indian Ridge (SWIR). Resolution tests indicate that TDFADT reduces both absolute and differential travel-time residuals more effectively, yielding velocity models with significantly improved spatial resolution. The final SWIR velocity model from TDFADT reveals several strong anomalies, such as a high-velocity anomaly possibly related to oceanic core complexes and pronounced low-velocity anomalies in the lower crust beneath the central volcano, suggesting active magmatism due to partial melt. This case study demonstrates that the proposed method is a robust and accurate tool for crustal imaging using first-arrival data from active-source OBS surveys.