In this article, we find that the transformational matrix between the natural logarithm of the acoustic impedance and the reflection coefficient is a

Most acoustic impedance sparse inversion methods include two parts: reflectivity inversion and extraction of acoustic impedance from reflectivity. Thi

Seismic acoustic impedance (AI) inversion is widely used in geophysics as AI can indicate rock characteristics and facilitate stratigraphic analysis. However, traditional AI inversion suffers from a multi-solution problem. To overcome this barrier, anisotropic total p-variation (ATpV) regularization has been applied in inversion as it can improve the accuracy by Lp quasi-norm. Nevertheless, this regularization results in the staircase effect and the scattering effect. To reduce these two effects, we introduced the mixed second-order variations and the fractional difference in AI inversion based on ATpV and proposed a novel AI inversion method using mixed second-order fractional anisotropic total p-variation (MSFATpV) regularization. Moreover, the alternating direction method of multipliers (ADMM) algorithm is used to build the inversion framework. Numerical experiments demonstrate that the fractional difference and the mixed second-order variant can reduce the staircase and scattering effects. The proposed method reduces the multiplicity and improves the accuracy than some state-of-the-art methods based on anisotropic total variation (ATV).

Seismic denoising is a core task of seismic data processing. The quality of a denoising result directly affects data analysis, inversion, imaging and other applications. For the past ten years, there have mainly been two classes of methods for seismic denoising. One is based on the sparsity of seismic data. This kind of method can make use of the sparsity of seismic data in local area. The other is based on nonlocal self-similarity, and it can utilize the spatial information of seismic data. Sparsity and nonlocal self-similarity are important prior information. However, there is no seismic denoising method using both of them. To jointly use the sparsity and nonlocal self-similarity of seismic data, we propose a seismic denoising method using sparsity and low-rank regularization (called SD-SpaLR). Experimental results showed that the SD-SpaLR method has better performance than the conventional wavelet denoising and total variation denoising. This is because both the sparsity and the nonlocal self-similarity of seismic data are utilized in seismic denoising. This study is of significance for designing new seismic data analysis, processing and inversion methods.