A simple buffer for a piezoelectric pickup to mixer connection
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. OP's Figure 2 has a few odities.

I have a few concerns about this circuit.


Using the op-amp output as ground is unusual. Normally the 0 V line would be considered ground. This simplifies power supply, debug and, in guitar effects units, for example, allows the battery to be connected into circuit by insertion of the jack plug.
The piezo pickup will have an extremely high input impedance. That means there is nowhere for IC1a's bias current to go. That means that the bias current will drive the + input to one supply rail or the other.








simulate this circuit

Figure 2. A more traditional approach.

The normal way to do this is to use the mid-supply as a bias for the operating point of the amplifiers. Since you have chosen a non-inverting arrangement then you need to apply the bias as shown via R3.

C2 and C3 decouple the input and output and prevent the DC being affected by external connections.