Combinations of the simplex and weighted distance-based grey wolf algorithms for the seismic source parameter inversion with GPS measurements

Objectives:  With the improvement of geodetic observation accuracy, higher requirements are put forward for the seismic inversion algorithm.   Methods:  In view of this problem, we successfully develop a novel Grey Wolf Optimization (GWO) algorithm to invert the seismic source parameters. The weighted distance Grey Wolf Optimization (wdGWO) algorithm with the strategy of the nonlinear decreasing convergence factor based on the cosine law is proposed to instead that of the original linear decreasing. Subsequently, a combination approach with the improved wdGWO algorithm and the Simplex algorithm is configured and the introduction of the latter algorithm is to stabilize the performance of the proposed wdGWO algorithm. Thus, the combination algorithm has better advantages for both convergence and stability. Finally, we achieve synthetic tests to evaluate the performance of the basic wdGWO algorithm, the genetic algorithm and the combination algorithm.   Results:  The simulated experimental results show that the estimation of seismic source parameters via the proposed algorithm is superior to the wdGWO algorithm, which expresses excellent stability and accuracy. On the other hand, the stability of seismic source parameters is validated between the combination algorithm and the genetic algorithm, and we find the superiority of the combination algorithm. Furthermore, the availability of the combination algorithm is tested by the 2014 Napa earthquake and the 2017 Bodrum-Kos earthquake. The results show that the combination algorithm can achieve the inversion precision of genetic algorithm, and exhibit better parameters stability.   Conclusions:  Considering the accuracy and stability of the inversion results is particularly important for the accurate determination of seismic source parameters, the combination algorithm has potential applications in the inversion of seismic source parameters.