基于L1范数正则化的三维多震源最小二乘逆时偏移

3D multi-source least-squares reverse time migration based on L1 norm regularization

关键词:  最小二乘逆时偏移  L1范数正则化  三维多震源  一阶速度-应力方程

Key words:  least-squares reverse time migration (LSRTM)  L1 norm regularization  3D multi-source  first-order velocity-stress equation

摘要:

与常规偏移相比,最小二乘偏移在振幅保真性、提高分辨率、压制偏移噪音等方面具有较大优势。交错网格下基于一阶波动方程的最小二乘逆时偏移能够考虑介质密度的影响,且在压制数值频散方面有一定的优势,但该方法目前主要应用于二维介质中。为了拓展方法的适用范围,将该算法推广到三维情形下。同时,考虑到多震源方法会引入串扰噪声,在目标泛函中引入L1范数的稀疏正则化约束,并给出一种快速有效的解法。结果表明,相位编码算法可显著降低计算量,提高计算效率,但会引入高频的串扰噪音,而L1范数正则化由于加入稀疏约束,可有效地压制成像结果中的低频和高频噪音,显著提升成像分辨率,较大程度地改善成像质量,且线性Bergman解法降低反演结果对参数的依赖度,适用于实际资料的处理。

Abstract:

Compared with the conventional migration method,least-squares reverse time migration (LSRTM)has many advantages including, for example, higher imaging resolution, amplitude preservation and amplitude balance. LSRTM algorithm based onfirst order velocity-stress wave equation is able to handle the medium with variable density and has certain advantages in suppressing numerical dispersion, but is mainly applied to two-dimensional media.In order to extend the scope of the method, the first-order velocity stress equation LSRTM algorithm is extended to three-dimensional.Giventhat multi-source method will introduce high frequency crosstalk noise, L1 norm sparse regularization constraintsare used to suppress the crosstalk noise caused by phase encoding. Numerical tests on synthetic data demonstrate that the phase encoding algorithm can significantly reduce the computational effort and at the same time improve the computational efficiency. The L1 norm regularization can effectively suppress the low and high frequency noise, improving imaging resolution and the image quality. Lastly, the linear Bergman solution reduces the dependence of the inversion results on model parameters and is therefore suitable for processing of field data.