The local structures of 122-type paradium arsenides, namely BaPd$_2$As$_2$ and SrPd$_2$As$_2$, are examined by As K-edge extended x-ray absorption fine structure measurements to find a possible correlation between the variation of their superconducting transition temperature and the local structure. The local atomic distances are found to be consistent with average distances measured by diffraction techniques. The temperature dependence of mean square relative displacements reveal that, while BaPd$_2$As$_2$ is characterized by a local As-Pd soft mode, albeit with larger atomic disorder, SrPd$_2$As$_2$ shows anomalous As-Pd correlations with a kink at $sim$160 K due to hardening by raising temperature. We have discussed implications of these results and possible mechanism of differing superconducting transition temperature in relation with the structural instability.
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