Full-waveform inversion using a nonlinearly smoothed wavefield

Abstract

Conventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.

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

“…Its corresponding time-lapse applications require even more computational cost, because we need more simulations. On the other hand, due to the limitation we encounter with surface seismic data in terms of signal-to-noise ratio (SNR), frequency band and offset, seismic data often admit incomplete subsurface information with limited space wavenumber (Alkhalifah, 2016;Li et al, 2018). In this work, we improve the performance of TLFWI by addressing these two issues.…”

Ultrasound Computed Tomography of Knee Joint

“…Therefore, in this study, we reconstructed sound speed distributions of knee joints to provide an imaging basis for the formulation of treatment plans. Moreover, Full waveform inversion (FWI) methods, which were used in some applications of medical [13][14][15][16][17][18] and geophysics imaging [19][20][21][22][23] , were utilized in this study because they consider higher-order diffraction effects and can estimate high-resolution images. However, for knee joints having greatly varying sound speeds, traditional FWI methods may lead to unsatisfactory outcomes, i.e., a very slow and unstable optimization process, Cycle-skipping phenomenon (CSP), and wrong convergence direction [23] .…”

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).…”