Seismic Acoustic Impedance Inversion Using Mixed Second-Order Fractional ATpV Regularization

Hao Wu,Shu Li,Yingpin Chen,Yanmin He,Zhenming Peng

doi:10.1109/access.2019.2962552

Abstract

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 (MS_FATpV) 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).

Highlights

Seismic acoustic impedance (AI) plays an important role in geophysics as it can indicate rock characteristics and facilitate stratigraphic analysis [1]–[3]
To reduce the staircase and scattering effects and improve accuracy, we proposed an AI inversion method using mixed second-order fractional anisotropic total variation (MS_FATpV) regularization
We analyzed the performance of important parameters of the proposed method, including p, a, k, λ2, η2. p is the parameter of anisotropic total p-variation (ATpV) and determines the sparsity of the variants which we showed in Part 2.2

Summary

INTRODUCTION

Seismic acoustic impedance (AI) plays an important role in geophysics as it can indicate rock characteristics and facilitate stratigraphic analysis [1]–[3]. H. Wu et al.: Seismic AI Inversion Using Mixed Second-Order Fractional ATpV Regularization which can improve the accuracy by utilizing the sparsity of rock properties [22]–[24]. To reduce the staircase and scattering effects and improve accuracy, we proposed an AI inversion method using mixed second-order fractional anisotropic total variation (MS_FATpV) regularization. REGULARIZATION CONSTRAINT The fractional difference can reduce the scattering effect by enhancing the texture details in the smooth areas and avoiding large oscillations in edges We used it to replace the integer difference in ATpV. ADMM algorithm is used in the proposed method to solve the objective function Based on this algorithm, we introduced matrix Lax, Lay, Laxx, Layy, Laxyto represent LDax, DayL, LDaxDax, DayDayL, DayLDax, respectively. We obtained the inversion framework and displayed by Algorithm 1

EXPERIMENTS

2: Calculate the matrices of difference

MODEL DATA

Findings

CONCLUSION