The Parkfield earthquake prediction experiment (1985–2004) was designed to monitor stress accumulation in the lithosphere related to an impending earthquake on the San Andreas fault. However, no precursory signals were detected prior to the 2004 Parkfield earthquake (M6.0). In this paper we re-examine the long-term borehole strain records at Parkfield (Langbein et al., 2006). We find that they are consistent with a stationary tectonic stress field on the order of 55 MPa in the direction of the fault. This is the first measurement of far-field tectonic stresses from borehole strainmeter records. It suggests that logarithmic creep strains from boreholes can be used to interpret the state of stress in the lithosphere surrounding the San Andreas fault.
Symmetry of the experimental setup suggests conformal mapping is a useful transformation to interpret the state of stress around a cavity in a prestressed halfspace. The borehole inverts the sign of the displacement, so that compressional tectonic stresses generate extensional strains at the borehole boundary. The stress energy field is conserved under conformal transformation (Noether's theorem). This transformation facilitates recovery of the state of stress in the lithosphere from long-term Parkfield strain records. Ergodicity constrains the form of the creep function in long-term experiments as follows: