A Stable and Efficient Attenuation Compensation Method based on Inversion

Abstract

Inverse Q filtering, which can compensate amplitude and correct phase, is an effective method to improve the resolution of seismic data. The conventional inverse Q method is usually based on wavefield continuation, which is unstable or under‐compensation. Based on the forward Q filtering equation in wavefield continuation, this work proposes a new attenuation compensation method, which is stable and accurate, taking advantages of the inverse theory and regularization strategy to obtain compensated seismic data eventually. It is also computationally efficient because only effective frequency components are calculated. Tests on synthetic and real data prove that the proposed method is effective.

Multichannel seismic data attenuation compensation via curvelet‐based sparsity promotion

“…For simplicity, Equation () is rewritten as $$$$\begin{equation}{{\bf d}} = {{\bf Gm}},\end{equation}$$$$where d is the observed non‐stationary seismic data, G is a forward operator containing attenuation information, m is the principal frequency spectrum of stationary data or compensated data. The compensated spectrum m 0 can be easily estimated via a damped least squares method (Wang et al., 2014): $$$$\begin{equation}{{{\bf m}}}_0 = {({{{\bf G}}}^H{{\bf G}} + \lambda {{\bf I}})}^{ - 1}{{{\bf G}}}^H{{\bf d}},\end{equation}$$$$where λ is a damping factor. Finally, the compensated spectrum m 0 is transformed to the time domain compensated signal via the inverse Fourier transform along the frequency axis.…”

“…Next, the single‐channel compensation method using a damped least squares algorithm (Wang et al., 2014) and the proposed multichannel method are performed to compensate for the deep‐part energy of the noisy attenuated data and improve its vertical resolution. The compensated results of the single‐channel method are shown in the middle column of Figure 2.…”

“…Moreover, we apply a fast iterative shrinkage–thresholding algorithm (Aster et al., 2018) to reduce the computational cost when solving the sparsity‐constrained inversion problem. Compared with the conventional single‐channel inverse Q filtering method using a damped least squares algorithm (Wang et al., 2014), the proposed multichannel method has higher accuracy and stability, which is demonstrated by synthetic data examples with different noise levels and two post‐stack field data examples.…”