Abstract
A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of “approximate transmission wavefield,” which is calculated based on the non-reflecting acoustic equation. The proposed method can effectively avoid a huge amount of calculation and storage required by the Hessian matrix or approximated Hessian matrix and can overcome the influence of reflected waves, multiples, and other wavefields on the gradient in gradient preconditioning based on seismic wave energy (GPSWE). The numerical experiments, compared with that using GPSWE, show that LSRTM using the gradient preconditioning based on transmitted wave energy (GPTWE) can significantly improve the imaging accuracy of deep target and accelerate the convergence rate without trivial increased calculation.
Highlights
Compared with traditional migration techniques such as Kirchhoff integral migration, reverse time migration (RTM) based on the two-way wave equation is widely favored by researchers (Baysal et al, 1983; McMechan, 1983; Yoon and Marfurt, 2006; Symes, 2007; Fletcher et al, 2009; Liu et al, 2011; Sun et al, 2016) because of its obvious advantages in accurate imaging of complex media
When adopting the operator of gradient preconditioning based on seismic wave energy (GPSWE), we discovered that the wavefield used to calculate the operator is simulated by the acoustic wave equation, which contains a lot of reflected waves besides transmitted waves
To solve the previous problem, we developed an least-squares reverse time migration (LSRTM) algorithm using the gradient preconditioning based on transmitted wave energy (GPTWE), which obtains the forwardand back-propagated “approximate transmission wavefield” based on the non-reflecting acoustic equation and applies the energy of “approximate transmission wavefield” to precondition the original gradient
Summary
Compared with traditional migration techniques such as Kirchhoff integral migration, reverse time migration (RTM) based on the two-way wave equation is widely favored by researchers (Baysal et al, 1983; McMechan, 1983; Yoon and Marfurt, 2006; Symes, 2007; Fletcher et al, 2009; Liu et al, 2011; Sun et al, 2016) because of its obvious advantages in accurate imaging of complex media (especially high-steep structure and subsalt structure). To solve the previous problem, we developed an LSRTM algorithm using the gradient preconditioning based on transmitted wave energy (GPTWE), which obtains the forwardand back-propagated “approximate transmission wavefield” based on the non-reflecting acoustic equation and applies the energy of “approximate transmission wavefield” to precondition the original gradient This method requires neither the calculation nor storage of the Hessian matrix or the approximated Hessian matrix but can effectively improve the imaging accuracy without significantly increasing the amount of calculation. Wr(x) is the energy of back-propagated wavefield and is defined as follows: FIGURE 6 | Imaging results of LSRTM after 60 iterations: (A) without gradient preconditioning; (B) using GPSWE; and (C) using GPTWE. The forward modeling based on the non-reflecting acoustic wave equation (Baysal et al, 1984) (as shown in Eq 14) is used to obtain the forward-propagated “approximate transmission wavefield” with the seismic wavelet as the source.
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