Parsimonious truncated Newton method for time-domain full-waveform inversion based on the Fourier-domain full-scattered-field approximation

Abstract

In order to exploit Hessian information in Full Waveform Inversion (FWI), the matrix-free truncated Newton method can be used. In such a method, Hessian-vector product computation is one of the major concerns due to the huge memory requirements and demanding computational cost. Using the adjoint-state method, the Hessian-vector product can be estimated by zero-lag cross-correlation of the first-order/second-order incident wavefields and the second-order/first-order adjoint wavefields. Different from the implementation in frequency-domain FWI, Hessian-vector product construction in the time domain becomes much more challenging as it is not affordable to store the entire time-dependent wavefields. The widely used wavefield recomputation strategy leads to computationally intensive tasks. We present an efficient alternative approach to computing the Hessian-vector product for time-domain FWI. In our method, discrete Fourier transform is applied to extract frequency-domain components of involved wavefields, which are used to compute wavefield cross-correlation in the frequency domain. This makes it possible to avoid reconstructing the first-order and second-order incident wavefields. In addition, a full-scattered-field approximation is proposed to efficiently simplify the second-order incident and adjoint wavefields computation, which enables us to refrain from repeatedly solving the first-order incident and adjoint equations for the second-order incident and adjoint wavefields (re)computation. With the proposed method, the computational time can be reduced by 70% and 80% in viscous media for Gauss-Newton and full-Newton Hessian-vector product construction, respectively. The effectiveness of our method is also verified in the frame of a 2D multi-parameter inversion, in which the proposed method almost reaches the same iterative convergence of the conventional time-domain implementation.

Multi‐scale elastic full‐waveform inversion in a hybrid domain based on deconvolution objective function

“…However, this method relies on too many assumptions, and when the model is complex, good inversion results cannot be achieved just through the calculating of a few single‐frequency data. Besides, single‐frequency inversion can lead to a strong aliasing phenomenon (Yong et al., 2022). In order to avoid these problems, we choose multi‐frequency inversion strategy, that is, each frequency group composed of several single frequencies is iterated several times, and the gradient is the superposition of the single‐frequency gradient in the group.…”

Robust and efficient waveform-based velocity-model building by optimal transport in the pseudotime domain: Methodology

“…In order to adapt it to our time-domain FWI approach, we implement the proposed preconditioned gradient using discrete-fourier-transform (DFT). Source and receiver DFT wavefields are built on-the-fly during the incident field computation and stored at a set of discrete frequencies to compute Γ, as done by Yong et al (2022) for the computation of Hessian-vector products in the Truncated-Newton algorithm. Unlike in previous time-domain implementations (Li et al, 2019), this effectively implements the deconvolution imaging condition in equation 20, without relying on the assumption of frequencyindependence of the incident wavefield (Schleicher et al, 2008).…”

“…A significant frequency decimation is applied on the positive frequencies, to make the approach memory-affordable also in 3D. As shown in Yong et al (2022), a number of frequencies lower than Nyquist might be used, as long as it is sufficient to avoid wrap-around effects.…”

Localized adaptive waveform inversion: theory and numerical verification

“…The recommended width parameter in the Gabor transform is σ = 0.35 s. Besides, the two scaling values for water-level parameters and η are chosen as 10 −3 and 10 −2 for this example. Optimization is carried out with the preconditioned -BFGS algorithm ( = 5), and the pre-conditioner is based on energy compensation (Yong et al 2022). For synthetic tests, there is an interest to track the model error evolution with iterations.…”