Appropriate model of an unknown sonar piezo
A simplified model of a piezo resonator is similar to the model of a crystal (the ones used in crystal oscillators).

The circuit for both are the same but the component values are different.

This is an example of a model for a piezo element:



Note how Cm is much smaller (500 times smaller) in value than Co. This makes it somewhat difficult to determine the values of the LCR series circuit.

The issue is this: the LCR series circuit resonates at a certain frequency (in the circuit above this is at 17 kHz). At lower and higher frequencies that this resonance frequency the circuit will just measure as if it is only the capacitor Co (13 nF). Additional to that the frequency band for which you will see that resonance is very narrow, possibly only a few Hz so it can be quite a challenge to "find" that resonance and even when you find it you will need an extremely frequency stable signal generator to be able to do accurate measurements.

Professionals would use a "network analyzer" for this. I have used these in the past and with these it is just a matter of selecting the circuit topology (so I select a circuit similar to the one shown above) and setting the right frequency sweep. Then the Network analyzer will determine the circuit's component values. Unfortunately Network analyzers are in the range of: if you have to ask what it costs, you cannot afford it.

I suggest you read this question and answer and also this article about models of crystals.