Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion

Abstract

Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversion (FWI) of wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challenging because of the increased nonlinearity introduced by free-surface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting model if low frequencies are unavailable in the data. We evaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm thatoutperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin (DG) method on triangular mesh, which allows accurate modeling of free-surface effects. Sequential inversions of increasing frequencies define the most natural level of hierarchy in multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complex-valued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Among the possible strategies for sampling frequencies in the inversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when considering complex wave phenomena.

Resolving the fine-scale velocity structure of continental hyperextension at the Deep Galicia Margin using full-waveform inversion

“…Initial applications of FWI were performed in the time domain, but were limited given the high computational demand of the method (Kolb et al 1986). Three decades later and FWI is still performed based on these underlying principles, with modern codes capable of performing FWI in either the time or frequency domain, in two or three dimensions, approximating either the acoustic or elastic wave equation, and can include the effects of seismic attenuation and anisotropy (e.g., Pratt 1999; Brossier et al 2009;Warner et al 2013). It has also been shown that the maximum achievable resolution using these codes is on the order of half the seismic wavelength, making it superior to travel-time tomography .…”

Variance-based Salt Body Reconstruction

“…To enhance the signal-to-noise ratio, FWI often uses several bands of frequencies (Brossier et al, 2009) in a multi-scale approach (Bunks et al, 1995). The common approach in frequency-domain FWI is stacking multiple misfit functionals for single frequencies.…”

“…This guides FWI to a local minima of the objective function and prevents further model improvements, especially in deep explorations. Gradual offset increase (Brossier et al, 2009) or various misfit functions (Choi and Alkhalifah, 2015, e.g. ) can help mitigate the problem in the data domain.…”

Acceleration strategies for elastic full waveform inversion workflows in 2D and 3D

“…Many choices of E functionals exist, L 2 being the most common choice. However, some other norms have been successfully applied to the FWI problem, such as the L 1 norm [7,8,45,48], the Huber norm [19] or separating phase and envelope misfits in the time-frequency domain [16,24]. In this study, we employ the normalized least square criterion L 2 given by…”

“…Additional mathematical insights such as preconditioning and regularization also play an important role in reducing the non-linearity of the problem and are often required in order to ensure convergence [3,12,20]. On the other hand, FWI becomes very challenging as at least two parametres must be determined either independently or using constrains, and hence, the parametre space becomes larger and more complex [7,8,46].…”