论文标题
$ω$ -FWI：使用基于傅立叶的度量的强大全波倒置
$ω$-FWI: Robust full-waveform inversion with Fourier-based metric
论文作者
论文摘要
全波形反演是一种用于恢复高分辨率地下模型的尖端方法。但是，主要的传统全波优化问题之一挑战是循环滑倒，通常导致我们发生不准确的本地最小模型。一条备受调查的轨道缓解了这一挑战，涉及设计更全球的不合适度量，超出样本对样本比较的模型和模型数据。但是，这些方法中的大多数都接受了相对平滑的反转结果。在这里，我们基于基于傅立叶的度量引入了一种新颖的不合适函数。该度量已成功地应用于分子物理学来求解玻尔兹曼方程，并将其调整为全波倒置。此不合适的功能可利用模型和观察到的数据之间的功率谱信息，以尽早提供低波动速度模型更新，并在接近解决方案时更新更新。因此，在二次情况下，它也可以重新重新构成加权$ \ ell_ {2} $ - 规范，这可以看作是常规全波倒置的简单扩展。因此，尽管具有循环跳过的稳健性，但它仍能够传递常规FWI的高分辨率模型。考虑到其频域利用率，我们将此反转方法称为$ω$ -FWI。 Through the synthetic Marmousi model example, this method successfully recovers an accurate velocity model, starting from a linearly increasing model even for the case of noisy observed data and the lack of low frequencies below 3 Hz and 5Hz, in which the conventional $\ell_{2}$-norm full-waveform inversion suffers from cycle skipping.
Full-waveform inversion is a cutting-edge methodology for recovering high-resolution subsurface models. However, one of the main conventional full-waveform optimization problems challenges is cycle-skipping, usually leading us to an inaccurate local minimum model. A highly investigated track to alleviate this challenge involves designing a more global measure of misfit between the observed and modelled data beyond the sample-to-sample comparison. However, most of these approaches admit relatively smooth inversion results. Here, we introduce a novel misfit function based on the Fourier-based metric. This metric has been successfully applied in molecular physics for solving the Boltzmann equation, and we adapt it to full-waveform inversion. This misfit function exploits the power spectrum information between the modelled and observed data to provide low-wavenumber velocity model updates early, and more high resolution updates as we approach the solution. Thus, it also can be reformulated as a weighted $\ell_{2}$-norm in a quadratic case, which can be seen as a simple extension for conventional full-waveform inversion. Thus, despite its robustness to cycle skipping, it is capable of delivering high-resolution models synonymous to conventional FWI. Considering its frequency domain utilization, we refer to this inversion method as $ω$-FWI. Through the synthetic Marmousi model example, this method successfully recovers an accurate velocity model, starting from a linearly increasing model even for the case of noisy observed data and the lack of low frequencies below 3 Hz and 5Hz, in which the conventional $\ell_{2}$-norm full-waveform inversion suffers from cycle skipping.
