Near-surface site characterization at Bishan-AMK Park, Singapore, using first-arrival adjoint tomography via the joint inversion of absolute and differential traveltimes

First-arrival traveltime tomography (FATT) is a widely used method for characterizing near-surface velocity structures in geotechnical engineering and resource exploration. We introduce an improved version of FATT, named first-arrival adjoint tomography (FAAT), which involves the joint inversion of first-arrival absolute traveltimes and differential traveltimes. Unlike absolute traveltimes, differential traveltimes, derived from common sources or receivers, offer heightened sensitivity to fine-scale structures near the receivers or sources, respectively. This dual sensitivity makes FAAT particularly effective in imaging highly heterogeneous media. However, the proximity of rays associated with differential traveltimes can lead to the instability of the inversion. To overcome this challenge, we simultaneously incorporate absolute traveltimes and differential traveltimes to update the velocity model. This approach improves the stability of the inversion process, leading to improved resolution of inverted results. We specifically employ the fast-sweeping method to solve the factored eikonal equation, providing robust solutions in models with complex geological structures. Furthermore, we address the inverse problem by computing the gradient of data misfit using the efficient adjoint-state method. Through numerical testing, we validate the effectiveness of FAAT in comparison to that using only absolute or differential traveltimes. Finally, we apply the proposed FAAT method to near-surface site characterization at Bishan-AMK Park in Singapore. Compared with FATT and validated against borehole data, FAAT demonstrates its ability to establish more reliable velocity models, revealing finer details and substantially improving geological interpretation.