Predicting earthquakes by analyzing accelerating precursory seismic activity

Abstract

During 11 sequences of earthquakes that in retrospect can be classed as foreshocks, the accelerating rate at which seismic moment is released follows, at least in part, a simple equation. This equation (1) is$d(\Sigma \sqrt {M_0 } )/dt = C/(t_f - t)^n$,where$\Sigma \sqrt {M_0 }$ is the cumulative sum until time,t, of the square roots of seismic moments of individual foreshocks computed from reported magnitudes;C andn are constants; andt _fis a limiting time at which the rate of seismic moment accumulation becomes infinite. The possible time of a major foreshock or main shock,t _f,is found by the best fit of equation (1), or its integral, to step-like plots of$\Sigma \sqrt {M_0 }$ versus time using successive estimates oft _fin linearized regressions until the maximum coefficient of determination,r ²,is obtained. Analyzed examples include sequences preceding earthquakes at Cremasta, Greece, 2/5/66; Haicheng, China 2/4/75; Oaxaca, Mexico, 11/29/78; Petatlan, Mexico, 3/14/79; and Central Chile, 3/3/85. In 29 estimates of main-shock time, made as the sequences developed, the errors in 20 were less than one-half and in 9 less than one tenth the time remaining between the time of the last data used and the main shock. Some precursory sequences, or parts of them, yield no solution. Two sequences appear to include in their first parts the aftershocks of a previous event; plots using the integral of equation (1) show that the sequences are easily separable into aftershock and foreshock segments. Synthetic seismic sequences of shocks at equal time intervals were constructed to follow equation (1), using four values ofn. In each series the resulting distributions of magnitudes closely follow the linear Gutenberg-Richter relation logN=a−bM, and the productn timesb for each series is the same constant. In various forms and for decades, equation (1) has been used successfully to predict failure times of stressed metals and ceramics, landslides in soil and rock slopes, and volcanic eruptions. Results of more recent experiments and theoretical studies on crack propagation, fault mechanics, and acoustic emission can be closely reproduced by equation (1). Rate-process theory and continuum damage mechanics offer leads toward understanding the physical processes.