Determining Hydraulic Diffusivity from Ambient Noise in Subsurface Flow Rate and Temperature Data

Summary Determining the properties that control fluid flow and pressure migration through rocks is essential for understanding groundwater, energy reservoirs, and fault zones. However, direct measurements of these properties underground generally require expensive and invasive processes such as pumping large volumes of water in or out of the ground. These conventional methods may change the structure that they are trying to measure and do not resolve variations in space without complex, multiple experiments. Here we capitalize on the existing, natural fluctuations of pore pressure, flow and temperature that are always present underground, likely driven by tides, seismic waves and other noise in the Earth. We develop the theoretical framework to utilize these noises to determine hydrogeologic structure. We begin with prior work demonstrating a connection between cross-correlation and Green's functions for diffusive processes and illustrate how the existing theory could be used specifically for the case of inferring hydraulic diffusivity from closely spaced observations of pore pressure. We extend the current theory to include a capability for inferring Green's functions from closely spaced flow rate measurements, rather than pore pressure data. We then note that closely spaced temperature measurements are much more practical as an observational system, however, diffusive transport is likely not the dominant cause of high-frequency fluctuations of temperature in the Earth. Advective transport is a more plausible controlling factor and thus we need to incorporate advection into the theory and model the corresponding response functions. We therefore develop a semi-analytical method that includes advection and numerically compute the corresponding response function. We use these synthetics to illustrate how cross-correlation of ambient noise in subsurface temperature measurements carries information about hydraulic structure and show that it is possible to constrain hydraulic diffusivity values from cross-correlation of closely spaced continuous temperature measurements. This new method opens up the possibility of passive determination of reservoir properties with high spatial resolution from closely-spaced, continuous temperature data, which is a realistic deployment strategy that could be used in a wide variety of settings.