Inversion Of Rayleigh Wave Dispersion Curve With Logarithmic Spiral-Lévy Firefly Algorithm

Rayleigh wave method is an important geophysical exploration technique,which has been widely used in geotechnical engineering and geological hazard detection because of its advantages of fast and simple,strong anti-interference ability and high resolution.The technique utilizes the dispersion characteristics of Rayleigh waves in layered media,and the inversion of Rayleigh wave dispersion curves can effectively construct the transverse velocity model of the stratum.Linear and nonlinear inversions are the most commonly used methods in Rayleigh wave dispersion curve inversion.Although the linear algorithm performs well in terms of computational speed and iterative convergence,it has high requirements on the initial model and is prone to fall into local extremes.The nonlinear algorithm is exemplified by the Firefly Algorithm(FA),which has a strong global search capability and relies less on the initial model,but the FA operation is less stable and tends to converge too early when encountering complex problems.The Rayleigh wave dispersion curve inversion has the characteristics of multi-parameter,multi-polarity and non-linearity,and the traditional method is difficult to accurately invert and reconstruct the transverse velocity and thickness of the stratum in the face of the Rayleigh wave information processing in complex geological situations.To this end,this paper applies the Adaptive Logarithmic Spiral-Lévy Firefly Algorithm(ALSL-FA)to the inversion of Rayleigh wave dispersion curves.ALSL-FA incorporates the advantages of Lévy Flying Firefly Algorithm(LF-FA),which has a strong global search capability,and adds the logarithmic spiral path movement to enhance the local exploitation capability.In addition,ALSL-FA uses adaptive switching factor to balance global search and local development in the search process,which effectively solves the shortcomings of the FA that is more focused on exploration and less on development.In this paper,we conduct a number of experimental researches based on "Inversion of Rayleigh wave dispersion curve with logarithmic Spiral-Lévy firefly algorithm".Firstly,the performance of the three algorithms is preliminarily evaluated by comparing the accuracy of ALSL-FA,LF-FA and FA in solving Rastrigin function,Beale function,Ackley function and Sphere function.Then,the theoretical model of velocity increment,the theoretical model of high-speed interlayer and the theoretical model of low-speed interlayer are established.The ALSL-FA is used to invert the Rayleigh wave dispersion curve of the theoretical model with base order,high order and noise.The validity and applicability of ALSL-FA in the inversion of Rayleigh wave dispersion curve under different conditions are analyzed,and ALSL-FA is applied to a set of actual seismic data processing to verify the correctness of the method.Finally,the inversion results of ALSL-FA,LF-FA,FA and Artificial Bee Colony algorithm(ABC)on the above geological models are compared to further analyze the advantages of ALSL-FA in the inversion of Rayleigh wave dispersion curve.The results show that this method is suitable for Rayleigh wave dispersion curve inversion,which can further improve the accuracy and stability of inversion,and has excellent anti-noise performance.