Time-series analysis of diffusion interferometry data and its application to Bayesian inversion of synthetic borehole pressure data

Abstract

Interferometry methods in exploration geophysics are premised on a powerful theoretical foundation in which the ambient noise observed at discrete locations can be manipulated through either crosscorrelation or convolution to yield the response of a virtual “active source” experiment (i.e., the empirical Green’s function, abbreviated as EGF) without the actual deployment of physical sources. Sources of the ambient background may be either naturally occurring or engineered. Regardless, the theory for diffusive systems requires them to be volumetrically distributed over an infinite domain. The central question is then, “What region for the ambient sources matters most for good EGF estimation?” Here, we build on previous work in frequency domain EGF estimation by extending the analysis to the time domain where the broadband response is driven by the continuum of diffusive length scales therein. Analysis of the double half-space diffusion model (simulating a lithologic contact) demonstrates that sources between the two receiver locations have the most impact on EGF accuracy, and that when either of the receivers is close to the lithologic contact, the sources must also extend more deeply, into the high-diffusivity side to maintain accuracy. We further examine the suitability for inversion of EGF signals built with the limited and finite ambient source distributions expected in actual exploration scenarios. One-dimensional Bayesian inversion of singlewell and crosswell configurations of a three-layered system simulating a reservoir layer between two impermeable layers revealed that transient EGF signals were reliably invertible when sources were constrained to the middle reservoir layer. In production monitoring settings, natural sources originating from pumping and subsequent flow-related physics (pressure diffusion, electrochemical and seismoelectric effects, etc.), this result suggests that EGF signals may be a useful measure of reservoir properties.