Spatial Filter for the Pseudo-spectral Implementation of Fractional Derivative Wave Equation

As a high-precision parameter inversion method, visco-acoustic full waveform inversion (QFWI) is widely used in the inversion of parameters such as velocity and quality factor Q in visco-acoustic media. Conventional QFWI, using the L2 norm as the objective function, is susceptible to face the cycle-skipping problem, especially with inaccurate initial models. Lately, adopting the optimal transportation (OT) distance as the objective function in QFWI (OT-QFWI) has become one of the most promising solutions. In OT-QFWI, converting oscillatory seismic data into a probability distribution that satisfies equal-mass and nonnegativity conditions is essential. However, seismic data in visco-acoustic media face challenges in meeting the equal-mass assumption, primarily due to the attenuation effect (amplitude attenuation and phase distortion) associated with the quality factor Q. Unbalanced optimal transportation (UOT) has shown potential in solving equal-mass assumption. It offers the advantage of relaxing equal-mass requirements through entropy regularization. Due to this advantage, UOT can mitigate the attenuation effect caused by inaccurate quality factor Q during the inversion. Simultaneously, the Sinkhorn algorithm can quickly solve the UOT distance through CUDA programming. Accordingly, we propose a UOT-based QFWI (UOT-QFWI) method to improve the accuracy of two-parameter inversion. The proposed method mitigates the impact of inaccurate quality factor Q by introducing UOT distance to calculate the objective function, thereby helping to obtain more accurate inverted parameters. Experimental tests on the 1D Ricker wavelet and 2D synthetic model are used to validate the effectiveness and robustness of our proposed method.

show abstract

Viscoacoustic least-squares reverse-time migration using the L1-2 norm sparsity constraint

Zhang,

Wang,

Chen

et al. 2023

Journal of Geophysics and Engineering

View full text Add to dashboard Cite

Least-squares reverse-time migration (LSRTM) has become an advanced technique for complex structures imaging of the subsurface, as it can provide a higher resolution and more balanced amplitude migrated image than conventional reverse-time migration (RTM). However, the intrinsic attenuation of subsurface introduces amplitude attenuation and phase dispersion of seismic wavefield, which leads to the inverted image kinematically and dynamically inexactitude. Moreover, the imperfect geometry, limited bandwidth of seismic data, and inappropriate modeling kernel etc., would inevitably introduce two side-effects in migrated image, resulting in degradation of LSRTM imaging potential. To alleviate above issues, we present a data-domain sparsity constraint viscoacoustic least-squares reverse-time migration algorithm in this paper. In particular, we utilize the decoupled constant Q fractional Laplacians (DFLs) viscoacoustic wave equation as the modeling kernel to describe the attenuation effects of the subsurface, while a model constraint constructed in the misfit function via L1-2 norm is carried out to clear the migrated artefacts and boost the imaging resolution. Thanks to the excellent performance in sparsity, the drawbacks of unconstraint LSRTM can be effectively mitigated by the L1-2 norm-based regularization. In this paper, we adopt the alternating direction of multipliers method (ADMM) to iteratively address the constrained L1-2 minimization problem by implementing a proximal operator, and three synthetic examples are hired to evaluate the effectiveness and practicability of the proposed strategy. Migration results prove that the proposed scheme can effectively compensate the attenuation effects, improve the resolution, and suppress the migration artifacts of inverted images even in the complex imaging situations.

show abstract

Spatial Filter for the Pseudo-spectral Implementation of Fractional Derivative Wave Equation

Cited by 5 publications

References 26 publications

Simulation and modeling of grinding surface topography based on fractional derivatives

Simulation and modeling of grinding surface topography based on fractional derivatives

Unbalanced optimal transport for full waveform inversion in visco-acoustic media

Viscoacoustic least-squares reverse-time migration using the L1-2 norm sparsity constraint

Contact Info

Product

Resources

About