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本文基于重力梯度张量密度反演基本理论,建立了模型约束正则化密度反演矩阵方程.分析了代数重构算法(ART)中迭代初始值、松弛因子和终止条件三个关键参数的影响;与最小二乘求逆法对应比较分析了算法的时间和精度.结果表明:在地震、地质等地球物理手段提供初值、边界等约束较多的情况下,ART可以克服方程的不适定进行直接求解,并且合理的松弛因子和终止条件可有效提高反演效率.当初始信息不足时,添加光滑假设、深度加权等模型约束,正则化方程可以提高反演结果的可靠性.ART的行迭代可有效避免观测误差的积累和矩阵求逆的计算,从而使计算精度和速度提高数倍.最后基于GOCE地球重力场模型所得重力梯度,以地震层析成像所得速度模型为约束,对华北克拉通密度结构进行了反演,并与该区已有密度研究结果进行了对比.结果表明:利用GOCE重力场系数计算重力梯度扰动,以速度模型为约束,基于代数重构算法进行重力梯度反演所得密度模型与重力-地震联合反演所得密度模型具有很好的对应性.ART算法为重力梯度张量反演中大规模复杂问题的快速计算提供了又一种有效手段.
In this paper, based on the basic theory of gravity gradient tensor density inversion, a model constrained regularized density inversion matrix equation is established, and the influence of three key parameters of iterative initial value, relaxation factor and termination condition in algebraic reconstruction algorithm (ART) The results show that ART can overcome the ill-posedness of the equation when there are more constraints such as initial value and boundary in geophysical methods such as seismic and geology. And the reasonable relaxation factor and termination condition can effectively improve the inversion efficiency.When the initial information is not enough, the model constraints such as the smooth hypothesis and the depth weighting can be added and the regularization equation can improve the reliability of the inversion results. Effectively avoiding the accumulation of observational errors and the calculation of matrix inversion, which can improve the calculation accuracy and speed several times.Finally, based on the gravitational gradient obtained from the GOCE Earth Gravity Model and the velocity model obtained from seismic tomography as the constraint, The results are compared with the results of the existing density studies in this area. The results show that using GOCE gravity field coefficient The gravitational gradient perturbation is based on the velocity model, and the density model derived from the gravity gradient inversion based on the algebraic reconstruction algorithm has good correspondence with the density model derived from the gravity-seismic inversion.ART algorithm is the gravity gradient tensor inversion The rapid calculation of large-scale complex problems provides another effective means.