Search for direct empirical spatial correlation signatures of the critical triggering earthquake model

SUMMARY We propose a new test of the critical earthquake model based on the hypothesis that precursory earthquakes are ‘actors’ that create fluctuations in the stress field which exhibit an increasing correlation length as the critical large event becomes imminent. Our approach constitutes an attempt to build a more physically based time‐dependent indicator (cumulative scalar stress function), in the spirit of, but improving on, the cumulative Benioff strain used in previous works documenting the phenomenon of accelerating seismicity. Using a simplified scalar space and time‐dependent viscoelastic Green's function in a two‐layer model of the Earth's lithosphere, we compute spatiotemporal pseudo‐stress fluctuations induced by a series of events before four of the largest recent shocks in southern California. Through an appropriate spatial wavelet transform, we then estimate the contribution of each event in the series to the correlation properties of the simplified pseudo‐stress field around the location of the mainshock at different scales. This allows us to define a cumulative scalar pseudo‐stress function which reveals neither an acceleration of stress storage at the epicentre of the mainshock nor an increase of the spatial stress–stress correlation length similar to those observed previously for the cumulative Benioff strain. The earthquakes we studied are thus either simple ‘witnesses’ of a large‐scale tectonic organization, or are simply unrelated, and/or the Green's function describing interactions between earthquakes has a significantly longer range than predicted for standard viscoelastic media used here.