In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation patterns of the field are distinguishable under a specified sensing and excitation programme. This paper develops a local information-operator framework for this purpose. Around a nominal parameter field, the parameter-to-observation map is linearized and the likelihood contribution to posterior precision is interpreted as an operator on parameter-field perturbations. For locally linearized Gaussian models with parameter-independent covariance, this operator is equivalently Fisher information, Gauss-Newton data-misfit curvature, and a noise-weighted sensitivity Gramian. The framework separates pointwise visibility from spatial identifiability. The diagonal gives a coordinate-dependent local information density, while the full kernel and metric- or prior-preconditioned spectra rank spatial patterns that are strongly visible, weakly visible, or locally invisible. Heterogeneous observation blocks are assembled in a common parameter space; information is additive only under conditional independence, whereas correlated errors require the full joint covariance. Model discrepancy, nuisance parameters, and prior information modify the same geometry through covariance inflation, Schur-complement information loss, and prior-preconditioned modes. Examples cover analytic beam kernels, two-span support coupling, static-dynamic fusion for flexural-rigidity identification, and two-dimensional damage-field reconstruction in a leading information subspace. The operator view supports interpretation of identifiability, sensor complementarity, and reduced reconstruction in distributed-parameter inverse problems.

翻译：在计算力学分布式参数反问题中，需从含噪、间接且异构的观测数据中推断空间变化场。相关可辨识性问题关注的是：在特定传感与激励方案下，何种空间扰动模式可被区分。本文为此构建了局部信息算子框架。在标称参数场附近，参数-观测映射被线性化，后验精度中的似然贡献被解释为作用于参数场扰动的算子。对于参数独立协方差的局部线性化高斯模型，该算子等价于Fisher信息、Gauss-Newton数据失配曲率及噪声加权灵敏度Gram矩阵。该框架将点态可见性与空间可辨识性分离：对角项给出坐标依赖的局部信息密度，而完整核函数及经度量或先验预条件处理后的谱可对强可见、弱可见或局部不可见的空间模式进行排序。异构观测块被汇集至共同参数空间；信息仅在条件独立假设下具有可加性，而相关误差需考虑完整联合协方差。模型偏差、冗余参数及先验信息通过协方差膨胀、Schur补信息损失及先验预条件模态修正同一几何结构。算例涵盖解析梁核函数、双跨支撑耦合、弯曲刚度识别的静动态融合以及二维损伤场在主导信息子空间中的重构。该算子视角支持对分布式参数反问题中可辨识性、传感器互补性及降阶重构的解释。