A method providing an increased signal-to-noise (SNR) characteristic for coherent distributed acoustic sensing (DAS) systems, the method employing fiber coils (microphones) made from sections of an optical sensing fiber that collect acoustic signals and uses multiple differential pairs of the microphones for signal averaging to improve the SNR. An analysis determines complex products (beating products) for a pair of locations that are part of a fiber microphone along the length of the optical sensing fiber that are used to determine a phase change in-between locations along the length of the optical sensing fiber.