The improved first-arrival traveltime tomography based on the adjoint-state method
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摘要:
目前，有关伴随状态法初至波走时层析成像方法的文献，基本上都是基于面积分来定义目标函数，由此得到的伴随方程也都依赖于地表的法向量.这样，一方面会因为伴随变量计算的不准确而造成梯度的不合理，另一方面也无法合理地处理井中观测问题.本文从理论或数值试验角度指出了这些问题，并提出了不依赖地表法向量的改进的伴随状态法走时层析成像方法.主要改进包括：(1)采用体积分定义目标函数，避免了传统方法不能较好处理井中观测数据的缺陷，可以适应任意地表或井中观测系统.(2)采用摄动法得到了新的伴随方程，克服了传统方法中伴随场计算需要依赖于地表法向量的缺陷，使得检波点处的走时残差可以正确地反传播至地下，进而得到更加合理的速度修正方向，提高了速度反演的精度.
Abstract:In the currently-used first-arrival traveltime tomography based on adjoint state method,the boundary normal vectors of the computational domain must be used to compute the adjoint field. As one result,it will get inaccurate gradients and produce unreasonable inversion results in the situation with complex topography. On the other hand,it cannot correctly deal with the problems for borehole observations. These limitations are discussed in this paper by theoretical analysis and numerical experiments. Furthermore,an improved adjoint state based first-arrival traveltime tomography method is proposed. Major improvements include: (1) The data of any observation geometry can be processed by this improved method,including surface and borehole observations simultaneously. (2) New adjoint equation is derived by perturbation method. It does not depend on the boundary normal vector so that the traveltime residuals of the receivers can be correctly back-propagated to the underground and a correct gradient can be obtained. As a result,the velocity inversion accuracy can be increased.
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Key words:
- First-arrival /
- Traveltime tomography /
- Adjoint-state method /
- Adjoint equation /
- Objective function /
- Eikonal equation
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图 1
不同地表法向量的对称接收点试验的真实模型
Figure 1.
The true velocity model with two symmetrical receivers but different surface normal vectors
图 3
传统AST方法得到的归一化后的伴随场分布
Figure 3.
The normalized adjoint field distribution by the conventional AST method
图 6
改进的AST方法计算的归一化后的梯度分布
Figure 6.
The normalized gradient obtained by the improved AST method
图 7
简单起伏地表速度模型及改进前后AST反演结果
Figure 7.
The simple topographic velocity model and the AST inversion results
图 8
传统与改进的AST方法不同迭代次数的归一化梯度
Figure 8.
The normalized gradients of different iterations for the conventional and the improved AST methods From top to bottom show the gradients corresponding to 1, 20, 100 and 300 iterations.
图 14
第80代反演结果地表下不同深度的速度剖面对比
Figure 14.
The inverted lateral velocity slices with depth of (a) 20 m, (b) 30 m, (c) 40 m and (d) 50 m below the surface for the 80th iteration
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