Wave Equation Radon Tomography for Early Arrivals

We present the theory of wave-equation Radon tomography (WRT) where the slopes and zero-intercept time of early arrivals in the t - p domain are inverted for the subsurface velocity structure. The early arrivals are windowed in a shot gather, but they are still too wiggly to avoid local minima with a full waveform inversion (FWI) method. To reduce their complexity, a local linear Radon t - p transform is applied to the events to focus them into few points. These points, which identify the slopes and zero-intercept time of the early arrivals, are picked to give the slowness coordinate p^obs_i at the zero-intercept time t_i. The misfit function e = ^PP_i=₁(pi - p^obs_i )² + ^PP_i=₁(t_i - t_i^obs)² is computed and a gradient optimization method is used to find the optimal velocity model that minimizes e. Results with synthetic data and field data show that WRT can accurately reconstruct the near-surface P-wave velocity model and converges faster than other wave-equation methods.