Retrieving electric resistivity data from self‐potential measurements by cross‐correlation

[1] We show that the two‐point cross‐correlation of self‐ potential field recordings is equal to the electric resistivity between the two points. This holds under the condition that spatially and temporally uncorrelated noise sources exist throughout the volume. These sources should have a known amplitude spectrum and their correlated strengths should be proportional to the dissipative medium property function. Natural fluctuations, such as thermal noise, may occur that satisfy the necessary conditions. When these fluctuations are random deviations from a state of thermal equilibrium, the fluctuation‐dissipation theorem can be used to describe these sources. Other types of sources may exist, such as the ones creating the self‐potential field through coupling with fluctuations in pressure, temperature and chemical potential gradients. Citation: Slob, E., R. Snieder, and A. Revil (2010), Retrieving electric resistivity data from self‐ potential measurements by cross‐correlation, Geophys. Res. Lett., 37, L04308, doi:10.1029/2009GL042247.