On the Scaling of the Update Direction for Multi-parameter Full Waveform Inversion: Applications to 2D Acoustic and Elastic Cases

Target-oriented refraction waveform inversion: A Brazilian pre-salt case study

“…, N iter , where N iter is the total number of iterations, α > 0 is the step-length (Nocedal and Wright, 2006), H −1 E and ∇E are, respectively, the inverse of the Hessian matrix and the gradient of the objective function E. The optimization problem for the acoustic FWI may be parametrized as a function of the P -wave velocity in different ways, for instance, m = 1/c (slowness) or m = 1/c 2 (squared slowness). Our choice is consistent with the observations of Carneiro et al (2018) which found that squared slowness exhibits better convergence properties. We tested both parametrizations and found squared slowness more useful because the forward problem becomes linear when squared slowness is selected.…”

Research note: Application of refraction full‐waveform inversion of ocean bottom node data using a squared‐slowness model parameterization

“…In contrast, in the squared‐slowness case, the model parameters do not influence the gradient preconditioner, which only depends on the radiation pattern of the secondary Born source. This decoupling of the model parameters from the gradient preconditioning seems to be the reason for faster convergence in the squared‐slowness case, at least as far as our real application case is concerned, as suggested in previous works using synthetic data (Carneiro et al., 2018; Park et al., 2020). The results also indicated that the squared slowness model parameterization provides a satisfactory compromise between the quality of the reconstruction of the deep pre‐salt target area and the convergence rate, leading, in our case, to a 50% saving in execution time compared to the velocity and slowness cases.…”

“…Most frequently, a velocity parameterization is employed. Considering elastic and acoustic FWI, Carneiro et al (2018) compared velocity, slowness and squared slowness model parameterization. Anagaw and Sacchi (2018) also considered these three parameterization in acoustic time-domain FWI.…”

Inner product preconditioned trust-region methods for frequency-domain full waveform inversion

“…It is here chosen that the subsurface model parameter is the slowness squared distribution s 2 [s 2 /km 2 ] (also called the sloth), as could be guessed from the expression of the Helmholtz operator A ω (s 2 ) := ∆ + ω 2 s 2 . The slowness squared s 2 is actually the squared inverse of the velocity v. Several other parametrizations are also possible but it has been shown that the slowness squared can yield a fast convergence and accurate results [2,5,18,39]. Implementation of any of the above described local optimization algorithms requires an efficient procedure to compute the misfit and the gradient for a given slowness squared distribution s 2 and the action of the Hessian operator for any given slowness squared perturbation δs 2 .…”