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Application of spectral decomposition of Green's function to linear inverse problem

机译：Green函数谱分解在线性反问题中的应用

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An inverse analysis method using the spectral decomposition of Green's function is proposed for linear inverse problems of identifying inner sources from data of surface responses. It is assumed that Green's function of the corresponding physical problem is given. Applying the spectral decomposition, Green's function is discretized as a sum of eigen-values and eigen-functions. From the comparison of the measurement accuracy with the eigen-values, it is shown that responses which can be actually measured are given as a linear combination of eigen-functions corresponding to larger eigen-values. Such responses are found by determining coefficients of the eigen-functions from the measured data, and then sources which are predictable are determined just by calculating their coefficients for the eigen-functions. Without any ambiguity, the proposed method can determine the predictable inner sources from the data which are measured with the limited accuracy. A numerical simulation of solving a simple example problem is carried out to demonstrate the usefulness of the proposed inverse analysis method, and the results are discussed.
机译：提出了一种利用格林函数谱分解的逆分析方法，用于从表面响应数据中识别内部源的线性逆问题。假设给出了相应物理问题的格林函数。应用频谱分解，格林函数被离散为特征值和特征函数之和。通过将测量精度与特征值进行比较，可以看出，可以实际测量的响应是对应于较大特征值的特征函数的线性组合给出的。通过从所测量的数据确定本征函数的系数来找到这种响应，然后仅通过计算其本征函数的系数就可以确定可预测的源。没有任何歧义，所提出的方法可以从数据中确定可预测的内部源，这些数据以有限的精度进行测量。进行了求解一个简单示例问题的数值模拟，以证明所提出的反分析方法的有效性，并对结果进行了讨论。

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