Time-lapse waveform inversion regularized by spectral constraints and Sobolev space norm

Abstract

Imperfect illumination from surface seismic data due to lack of aperture and frequency content leads to ambiguity and resolution loss in seismic images and in full-waveform inversion (FWI) results. The resolution of time-lapse velocity updates can, however, be improved enforcing the sparsity of the parameter changes. Edge-preserving regularizations and constraints are typically used to promote sparsity. However, different choice of regularization parameters leads to different inversion results and optimal parameters are hard to identify, especially for real data. In particular it is not straightforward to balance the inversion between sparsity constraint and data fit. Fortunately, it is possible to estimate local spatial wavenumbers in a velocity model that are best illuminated by the data. We propose to constrain part of the model difference spectrum that is well illuminated by the data and optimize the rest of the spectrum to enhance sparsity. We approximate correctly retrieved model wavenumbers by simply picking large enough values in the inverted spectrum and constrain that part of model spectrum. Then we adjust the rest of the wavenumbers to reduce the value of a Sobolev space norm (SSN). SSN reduction promotes sparsity of time-lapse updates, while spectral constraints ensure that the part of the modeled spectrum retrieved from the data is completely retained. Application to synthetic noisy data for a perturbation of the Marmousi II model shows that the model resolution can be improved by using our method to extrapolate the model spectrum.

Target-oriented time-lapse waveform inversion using deep learning-assisted regularization

“…Time-lapse full waveform inversion (TLFWI) aims to quantitatively estimate the property changes in the subsurface induced by fluid injections using time-lapse seismic data (Hicks et al, 2016;Maharramov et al, 2016;Kazei and Alkhalifah, 2018). High-resolution delineation of the property changes is a major goal of time-lapse inversion.…”

Target-oriented time-lapse waveform inversion using redatumed data: Feasibility and robustness

“…Full waveform inversion (FWI) has emerged as a promising technique for retrieving subsurface properties by solving a data-driven optimization problem iteratively (Tarantola, 1984;Vigh et al, 2014;Choi and Alkhalifah, 2011;Li et al, 2018;Song and Alkhalifah, 2020). Time-lapse FWI is a straightforward extension of FWI to time-lapse seismic data and has gained considerable interest (Hicks et al, 2016;Kazei and Alkhalifah, 2018). Despite that the time-lapse FWI technique inherits the high resolution of conventional FWI, the computational burden for practical scale applications becomes even more intense because more FWI runs are involved (Yuan et al, 2017;Li et al, 2020).…”

Seismic model low wavenumber extrapolation by a deep convolutional neural network

“…Despite significant efforts and progress made over the past decades in FWI methodology (e.g. Pratt et al, 1996;Warner et al, 2013;van Leeuwen and Herrmann, 2013;Alkhalifah, 2016;Kazei et al, 2016;Gray, 2016;Kazei and Alkhalifah, 2018;Ovcharenko et al, 2018a;Kalita et al, 2018;Yao et al, 2019;Guo and Alkhalifah, 2017), the non-linear iterative optimization procedure is still prone to stagnation in local minima when initiated from a poor assumption and applied to a geologically complex region. Thus, building a plausible initial model becomes an important task and extrapolation of missing middle wavenumbers in the model could significantly improve the convergence.…”