引用本文: 张灵莉, 任玉晓, 刘斌, 王凯, 许新骥, 陈磊. 2022. 基于垂直构造梯度优化的全波形反演方法. 地球物理学报, 65(4): 1425-1438, doi: 10.6038/cjg2022P0179

伴随状态法是全波形反演的主流梯度计算方法, 该方法对水平构造反演效果较好, 但是不易反演垂直构造.对此, 本文以有效反演垂直构造为目标, 提出了一种基于垂直构造梯度优化的全波形反演方法.首先基于波场传播特征, 分析了伴随状态法在垂直构造梯度计算方面的局限性.在此基础上, 通过构建模拟数据和观测数据之间残差逆传波场的自相关项, 实现了垂直构造位置处的梯度补偿; 并将其以自相关梯度项能量最大值为归一准则与伴随状态法所得梯度相结合, 以保证在有效反演垂直构造的同时兼顾水平构造反演效果.单层、双层阶梯模型测试表明本方法可以有效反演垂直构造, 同时提升水平构造反演效果; 局部Marmousi模型测试证明了本方法同样可以改善倾斜构造的反演效果.

全波形反演 伴随状态法 残差逆传波场自相关 Abstract:

Adjoint-state method is the mainstream gradient calculation method of full waveform inversion. Although adjoint-state method can realize accurate inversion of horizontal structures, it has limitations on vertical structure inversion. In order to effectively invert the vertical structure, a full waveform inversion method based on vertical structure gradient optimization is proposed. On the basis of the principle of adjoint-state method gradient calculation as well as the characteristics of the source-wavefield forward-time propagation and the residual-wavefield reverse-time propagation, the limitations of adjoint state method in calculating the gradient at the position of the vertical structure is first analyzed. Then, by constructing the autocorrelation term of the residual wavefield of the simulated and the observed data, the gradient obtained by adjoint-state method is compensated at the vertical structure position. Taking the maximum energy of autocorrelation gradient term as the normalization criterion, the weighting factor is introduced to realize the combination of autocorrelation term mentioned above and cross-correlation term calculated by adjoint-state method, to improve the inversion effect of vertical structure and retain the inversion effect of horizontal structure at the same time. The inversion results of single-layered and double-layered ladder model show that the proposed method not only effectively inverts the vertical structures, but also improves the inversion effect of horizontal structures. The inversion results of the main part of Marmousi model prove that the proposed method is also applicable to the inclined structure.

Key words: Full waveform inversion Adjoint-state method Gradient Vertical structure Autocorrelation term of residual reverse wavefield Figure 9.

(a) Local Marmousi model; (b) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (a); (c) Initial velocity model; (d) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (c); (e) Result of conventional adjoint-state method; (f) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (e); (g) Result of our improved method; (h) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (e). i, ii, iii denote the key fault in the model space; a, b denote the trace we focus on. A and B are the starting points of faults a and b in the solid frame area respectively

董良国, 迟本鑫, 陶纪霞等. 2013. 声波全波形反演目标函数性态. 地球物理学报, 56(10): 3445-3460, doi: 10.6038/cjg20131020 . http://www.geophy.cn/article/doi/10.6038/cjg20131020 王义, 董良国. 2015. 基于截断牛顿法的VTI介质声波多参数全波形反演. 地球物理学报, 58(8): 2873-2885, doi: 10.6038/cjg20150821 . http://www.geophy.cn/article/doi/10.6038/cjg20150821 杨积忠, 刘玉柱, 董良国. 2014. 变密度声波方程多参数全波形反演策略. 地球物理学报, 57(2): 628-643, doi: 10.6038/cjg20140226 . http://www.geophy.cn/article/doi/10.6038/cjg20140226 Figure 1.

(a) Single-layered ladder model; (b) The initial velocity model; (c) The result of full waveform inversion applying traditional adjoint-state method

Figure 2.

Schematic diagram of wave propagation (single layered ladder model) when source located (a) above the sharp angle of the vertical, (b) on the left side of the vertical structure, (c) on the right side of the vertical structure

Figure 3.

(a) Gradient of the traditional adjoint-state method; (b) The autocorrelation of the residual wavefield; (c) The autocorrelation of the residual wavefield after adding the directional control factor; (d) Applying the grad calculating method of this paper

Figure 4.

The scheme of full waveform inversion method based on vertical structural gradient optimization

Figure 5.

Single-layered ladder model inversion result by applying (a) equation (9) and (b) equation (7)

Figure 6.

The viration figure of the objective-function value following iteration times of the single-layered ladder model

Figure 7.

(a) Two-layered ladder model; (b) Initial velocity model; (c) Inversion result of conventional adjoint-state method; (d) Inversion result of our method

Figure 8.

The viration figure of the objective-function value following iteration times (double layered model)

Figure 9.

(a) Local Marmousi model; (b) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (a); (c) Initial velocity model; (d) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (c); (e) Result of conventional adjoint-state method; (f) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (e); (g) Result of our improved method; (h) Partial enlarged drawing of the area denoted by the solid line rectangular frame in figure (e). i, ii, iii denote the key fault in the model space; a, b denote the trace we focus on. A and B are the starting points of faults a and b in the solid frame area respectively

Figure 10.

Velocity fitting diagram of channel along (a) line a and (b) line B in Fig. 9

Figure 11.

(a) Initial velocity model; (b) Inversion result of conventional adjoint-state method; (c) Inversion result of our method at small offset; (d) Initial velocity model; (e) Inversion result of conventional adjoint-state method; (f) Inversion result of our method at large offset

Figure 12.

Single-layered ladder model inversion result by applying (a) equation (13) and (b) equation (14)