Memory‐efficient frequency‐domain Gauss–Newton method for wave‐equation first‐arrival traveltime inversion

ABSTRACT Wave‐equation traveltime inversion (WTI) can be used to automatically obtain a background near‐surface velocity model (NSM), which overcomes the high‐frequency approximation in ray theory. It is generally implemented in the time domain. However, the commonly used gradient‐based optimisation methods (such as the steepest‐descent method) in WTI have a low convergence rate and may yield less accurate results within limited iterations in geologically complex regions. To increase the convergence rate and improve the inversion accuracy, we propose a frequency‐domain truncated Gauss–Newton first‐arrival wave‐equation traveltime inversion (GN‐WTI) method to retrieve the background NSM. As only a few frequencies are used for inversion, the proposed frequency‐domain WTI method significantly reduces the computational memory requirements by more than two orders of magnitude in comparison with the conventional time‐domain WTI method. Therefore, the proposed method is especially advantageous for the building of large three‐dimensional models. In this GN‐WTI method, according to the derived explicit traveltime residual kernel, the gradient and Hessian vector products can be computed efficiently using an elegant and improved scattering integral approach as long as the source‐side wavefields and non‐redundant receiver‐side Green's functions are computed and stored in advance. The conjugate gradient approach is used to solve the Gauss–Newton normal equation to obtain the Gauss–Newton direction in inner loops. Here, the Gauss–Newton Hessians of the ray‐based traveltime inversion and WTI are compared to demonstrate the advantages of WTI. The trial runs with a simple periodic velocity model example showed that the proposed GN‐WTI method outperforms the WTI method when using the steepest‐descent and limited‐memory Broyden–Fletcher–Goldfarb–Shanno approaches in terms of the convergence rate and inversion accuracy. A complex Marmousi model was further used to illustrate the effectiveness of GN‐WTI. The proposed method should be beneficial in near‐surface velocity model building.