A method is provided of inspecting a nested multi-layer structure including a first and second electrically conductive layer and a third layer disposed behind the second conductive layer. The method includes deploying a sensor device including an electromagnetic acoustic transducer to a borehole location proximate to the structure, generating a drive signal including a plurality of frequencies, applying an electrical current signal to the sensor device based on the drive signal and inducing currents in the first conductive layer that induce currents generating acoustic signals having the plurality of frequencies, detecting a first set of resonant frequencies based on received electromagnetic signals, detecting a second set of resonant frequencies based on received acoustic signals, estimating a property of the first and/or the second conductive layer based on the first set of resonant frequencies, and estimating a property of the third layer based on the second set of resonant frequencies.