We consider the rate-distortion problem for recording a Gaussian acoustic field with an array of sensors equipped with microphones. Our analysis is based on the field's spatiotemporal correlation structure, which is induced by the physics of sound propagation. Under certain assumptions about the spectrum of the wave kernel, we determine the rate-distortion functions for various distributed source coding schemes and sampling lattices. Our results also include an answer to the multiterminal rate-distortion problem for the setup considered in the paper.