A Unified Seismic Tomography Framework Using Automatic Differentiation Applied to the Southern Appalachian Array

Seismic waveform tomography typically uses either traditional adjoint methods to compute gradients for model updates or neural-network-based (NN-based) methods to directly predict the model. However, adjoint methods require complex analytical derivations that must be reformulated for each combination of model parameters (velocity or attenuation), wave equations (elastic or viscoelastic), and misfit functions (waveform, travel time, differential time or amplitude). Here, we replace existing adjoint methods with automatic differentiation (AD), which computes accurate gradients of wave equation-based data misfits directly without any analytical derivations. Compared with NN-based methods (e.g. PINN or neural operator), our AD-based tomography framework is fully white-box and does not require any training datasets. We demonstrate both theoretically and numerically that gradients computed with AD are identical to those from adjoint methods, regardless of the domain, wave equation, or misfit function. For a field application, we apply ambient noise differential AD tomography to data from the Southeastern Suture of the Appalachian Margin Experiment (SESAME) and obtain three 2D Love-wave shear velocity (Vsh) models. The imaged Paleozoic suture zone, Mesozoic rift basins, and Moho interface are consistent with previous studies. Our results highlight the unifying role of AD in geophysical inverse problems beyond gradient computation, with promise for broader future applications across geoscience.