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