Earthquake source parameters and their confidence regions by a genetic algorithm with a ‘memory’

Abstract

An inverse problem is usually solved by searching for the minimum of a misfit function. However, with noisy data this solution may not be appropriate because of matching the noise and not the true signal. Therefore, it is more informative to explore the model space and to display all the solutions above some a priori selected confidence level. Usually it is not feasible to do that by a grid search; the random walk is also unsuitable due to the sparse sampling in the vicinity of the minimum. Here a simple genetic algorithm is used not only to find the point where the misfit function is a minimum, but at the same time to map the model space in its vicinity with the aim of estimating the confidence regions of the model parameters. The required diversity of the population is achieved by reasonable increases in the probability of the mutation. Here, the approach is applied to estimating earthquake source parameters, specifically to the reduction of the moment tensor rate functions (MTRFs) obtained by linear inversion of waveforms, with the aim of recovering the moment tensor, the source time function (STF), and the seismic moment. In a series of synthetic experiments, the MTRFs corresponding to 45° dip-slip double-couple sources were contaminated by random noise ranging from 10 to 50 per cent of the peak data amplitude. The STF was sampled with 10–40 points, with seven-bit resolution of the amplitude of the STF. Even at the lowest noise level, the STF appeared to be rather uncertain, while at high noise levels the resolution is lost entirely (the estimate of the 95 per cent confidence region is as large as the STF amplitude itself). However, the mechanism is retrieved very well: its orientation remains within about 10° of the true orientation. The shape of the confidence region of the mechanism may be an indicator of the complexity of the rupture process as it reflects changes of the mechanism. As an example of the method, local waveforms are processed which were generated by the volcanic tremor which occurred at Campi Flegrei, Southern Italy, 1986 September 20. A large volumetric component significant at the 95 per cent confidence level was found in the mechanism. Details of the STF seemingly indicating multiple rupturing were uncertain at the 68 per cent confidence level.