  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.
