The Inversion Of Damping Least Square Method Of Rayleigh Wave With Weighting Matrix Based On The Singular Value Decomposition Technique

Rayleigh wave prospecting is a new method of engineering geophysical exploration. It has been used widely in production and scientific research, since it has many advantages such as fast detection speed, simple testing equipment, high resolution, no damage to the environment and so on. In recent years, more and more researchers have been devoted to exploiting and utilizing Rayleigh wave. It will become one of the most powerful approaches in shallow geophysical survey and engineering quality inspection.Inversion of Rayleigh wave dispersion curves is the most important aspect in Rayleigh wave exploration technique because the shear-wave velocity can be obtained, which is an important geotechnical parameters, and the stratum can be divided. So we can know more geotechnical parameters so as to solve the geological problems. Currently many approaches can be used to invert the Rayleigh wave dispersion curve, but the linear inversion method can be used widely since it is simple and fast. In this paper, the weighted damped least square is used for the inversion of Rayleigh wave dispersion curve. However, the coefficient matrix will always be the "sick" situation when we solve the equation of Rayleigh wave inversion. It is due to the special nature of geophysical problems. The use of singular value decomposition technique can effectively improve the equation pathological level to avoid the coefficient matrix is singular. The condition number of coefficient matrix can be effectively improved by weight matrix and the damping factor. This paper designs two of the most common model which are the model of increasing velocity and the model of layered media with weak interlayer, using the fast vector-transfer algorithm for forwarding the model and using the improved damping least square method for the inversion of the two models to verify the effect of inversion. The results show that this algorithm is fast, high accuracy and stability. Finally, using this algorithm to inverse the measured dispersion curve, we can obtain correct results. It verifies that the algorithm is practical.