Geometrical-Feature-Preserving Adjoint Tomography of Near-Surface Structure with Seismic Early Arrival

Early arrival waveform inversion (EWI) is an essential approach to obtaining velocity structures in near-surface. Due to suffering from a cycle‐skipping issue, it is difficult to reach the global minima for conventional EWI with the misfit function of least-squares norm (L2‐norm). Following the optimal transportation theory, we developed an EWI solution with a new objective function based on quadratic‐Wasserstein‐metric (W2-norm) to maintain the geometric characteristics of the distribution and improve the stability and convexity of the inverse problem. First, we gave the continuous form of the adjoint source and the Frechet gradient of the Wasserstein metric for seismic early arrival, which leads to an easy and efficient way to implement in the adjoint-state method. Then, we conducted two synthetic experiments on the target model containing some velocity anomalies and hidden layers to test its effectiveness in mapping accurate and high-resolution near-surface velocity structure. The results show that the W2-normed EWI can mitigate cycle-skipping issues compared with the L2-normed EWI. In addition, it can deal with hidden layers and is robust in terms of noise. The application to a real dataset indicates that this new solution can recover more details in the shallow structure, especially in the aspect of dealing with hidden layers.