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

Abstract

Full waveform inversion (FWI) aims at a broadband reconstruction of the subsurface physical properties by fitting the entire recorded wavefield. In realistic exploration seismic surveys, however, conventional FWI often fails to retrieve the deep velocity model due to the limited penetration depth of diving waves. Joint FWI (JFWI) unifies reflection-waveform inversion (RWI) and early-arrival waveform inversion (EWI) to reconstruct simutaneously the shallow and deep subsurface kinematics. However, a number of factors limit the appeal of JFWI velocity-model-building: 1) conflict between fixed reflectivity and evolving kinematics, creating phase ambiguity at short offsets; 2) susceptibility to cycle skipping at mid-to-long offsets, thus reliance on the quality of the starting model; 3) cost of building and updating the reflective model. We present a fully operational JFWI-based methodology that systematically addresses the aforementioned issues. JFWI is re-formulated in the pseudotime domain, in order to enforce consistency between velocity and reflectivity in a cost-effective fashion, without repeated least-square migrations. A JFWI graph space optimal transport (GSOT) objective function is designed to avert cycle skipping, while non-uniqueness is mitigated at no extra cost by smoothing the velocity gradient along the structures extracted from the reflective model. A dedicated asymptotic-based preconditioner is developed for impedance waveform inversion, making it possible to obtain sharp and balanced reflective images in a fraction of the time. We demonstrate that Pseudotime GSOT-JFWI retrieves complex velocity macromodels from limited-offset datasets with minimal pre-processing, starting from non-informative initial solutions. Compared to depth-domain JFWI, the computing cost is reduced significantly, along with a simpler and less subjective design of data weighting and inversion strategy. Pseudotime GSOT-JFWI provides FWI with the necessary low-wavenumbers to converge to the broadband model, reducing the need for accurate starting models, on the road to a fully waveform-based imaging workflow.

Localized adaptive waveform inversion: regularizations for Gabor deconvolution and 3-D field data application

“…Ho wever , from the wavenumber coverage analysis (Wu & Toks öz 1987 ;Mora 1989 ;Sirgue & Pratt 2004 ), this reconstruction will be quite difficult when considering broad-band spectra of seismic data: this challenge is also reported b y se veral field applications (Sirgue et al 2010 ;Messud et al 2021 ;Pladys et al 2022 ). Combining the LAWI approach with the so-called reflection FWI method (Xu et al 2012 ;Zhou et al 2015 ;Yao et al 2020 ;Provenzano et al 2023 ) is expected to bring a better recovery of the deep velocity model: an identified near -future investigation. Besides, w hen cycle-skipping issues are w ell-resolved, full-wa vefield imaging can be realized with the FWI method (Huang et al 2021 ).…”

4D FWI with Short Offset Data: a Reflection Oriented Approach

“…We recall here the basic principle of JFWI. We rely on the recent implementation proposed in Provenzano et al (2022), which makes use of a V p − I p parameterization, a specific preconditioner for the I p reconstruction, and a pseudo-time formulation for the impedance reconstruction. We recall the main ingredients in the following.…”

“…We present the theory for the least-squares misfit function but that as for FWI any kind of misfit function can be used. To better handle potential cycle skipping issue, as what is done in Provenzano et al (2022) we choose a Graph-Space Optimal Transport misfit function (Métivier et al, 2019).…”

Coherence-enhancing anisotropic diffusion filter for 3D high-resolution reconstruction of P-wave velocity and density using full-waveform inversion: Application to a North Sea ocean bottom cable data set

“…It is thus possible to extract structural information from the updated reflectivity model to inject it to the smoothing operator applied in the reconstruction of the macro-velocity model. This strategy has been applied in Provenzano et al (2022) based on a Bessel filtering approach. The same could be performed in the frame of migration velocity analysis (Symes, 2008), which relies on the same scale separation between macro-velocity and reflectivity, and updates these two parameters in an iterative fashion.…”