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反演问题的时空间分辨率或称时空分辨长度是评估模型精细程度的重要参数,决定了该模型应用的范围和价值,但是分辨长度估算却是比反演更复杂和麻烦的数学问题。除了层析成像中广泛利用理论模型恢复试验定性提取空间分辨长度外,通过求解分辨率矩阵可定量获得分辨长度。通过矩阵操作给出的分辨率矩阵包括三类:直接分辨率矩阵、正则化分辨率矩阵和混合分辨率矩阵。这三类矩阵包含了反演本身不同侧面的信息,因此在一个反演应用中,同时提供这三类分辨率矩阵可更全面地评估反演模型分辨率分布。最近An(2012)提出了从大量随机理论模型及其解中统计出分辨率矩阵的方法。这种分辨率矩阵是从模拟真实反演实验的输入和输出模型中通过反演得到的,因此这种分辨率矩阵更能反映整个反演所涉及到的更多因素和过程;同时由于这种分辨率矩阵计算过程无需进行矩阵操作且不依赖于具体正演和反演方法,因此可以被应用于更普遍的反演问题。实际应用证明统计分辨率分析方法适用于对二维和三维层析成像反演模型进行分辨率分析。
The time-space resolution or spatial-temporal resolution of the inversion problem is an important parameter to evaluate the fineness of the model. It determines the scope and value of the model’s application. However, the resolution length estimation is a more complicated and troublesome mathematical problem than the inversion. In addition to the extensive use of theoretical model recovery experiments to qualitatively extract the spatial resolution length in tomography, the resolution length can be obtained quantitatively by solving the resolution matrix. The resolution matrix given by matrix operation includes three categories: direct resolution matrix, regularized resolution matrix, and mixed resolution matrix. These three types of matrices contain information on different aspects of the inversion itself. Therefore, in an inversion application, providing these three types of resolution matrices provides a more complete assessment of the resolution distribution of the inversion models. Recently, An (2012) proposed a method to calculate the resolution matrix from a large number of stochastic theoretical models and their solutions. This resolution matrix is obtained from inversion of the input and output models that simulate real inversion experiments so that this resolution matrix better reflects more of the factors and processes involved in the overall inversion; The resolution matrix calculation process does not require matrix operations and does not depend on specific forward and inversion methods, so it can be applied to the more general inversion problems. The practical application shows that the statistical resolution analysis method is suitable for the resolution analysis of two-dimensional and three-dimensional tomography inversion models.