A Misfit Function For Dispersion Curve Inversion Of Rayleigh Wave Based On Improved Haskell-Thomson Algorithm

Inversion of the Rayleigh wave dispersion curve can effectively obtain the shear wave velocity and formation thickness.The traditional linearization inversion method not only depends heavily on the selection of the initial model,but also is affected by the accuracy of the Jacobian matrix.The nonlinear inversion method relaxes the requirements on the initial model.However,this type of algorithm often requires more sample models to participate in iterative operations,and the cost of calculation is large.At the same time,when the traditional objective function is used for inversion,a large number of dispersion curves must be forward-rooted,which will also significantly increase the computational complexity of nonlinear inversion,leading to slow inversion and long computation time.In addition,for the traditional misfit function,exact mode discrimination is necessary,and the misidentification of the mode may directly lead to wrong results.However,when the layer contains a complex structure such as a low-velocity weak sandwich or a highvelocity hard sandwich,Rayleigh waves may have phenomena such as “mode kissing”,“mode jumping” and “mode missing”.If the model is judged only by subjective awareness,it is very easy to cause misjudgment,and resulting in erroneous inversion results.In view of this,this thesis improved the traditional Haskell-Thomson dispersion curve forward simulation algorithm and proposed a new and effective objective function that effectively overcomes the above problems.This thesis focuses on the “A misfit function for dispersion curve inversion of Rayleigh wave based on improved Haskell-Thomson algorithm” as the core of the indepth study.First,this thesis improves the Haskell-Thomson algorithm of the classical dispersion function calculation algorithm,reduces its order of magnitude,makes the correspondence between the dispersion function surface and the dispersion curve obvious,and based on the characteristic of the dispersion function surface,a novel and effective misfit function is proposed.Then,a large number of theoretical model trials were carried out to invert the fundamental dispersion curves using the new misfit function and the shuffled complex evolution optimization algorithm.The effectiveness and application of the new inversion method for inverting the fundamental dispersion curves were tested.Secondly,using the new inversion method,a large number of theoretical models for multimode dispersion curves are calculated and compared with the inversion results of the classical misfit function,which reflects the superiority of the new misfit function and tests its effectiveness and applicability for inversion of multimode dispersion curves.Finally,the inversion of the measured data of the U.S.Wyoming area and a highway subgrade in Henan Province was conducted,and the practicality of the new misfit function for the Rayleigh wave dispersion curve inversion was examined.Main contributions of this thesis are as follows:1.Based on the improved Haskell-Thomson algorithm's surface shape characterristics,a novel and effective Rayleigh wave dispersion curve inversion misfit function is proposed.2.The shuffled complex evolution algorithm was successfully applied to the Rayleigh wave dispersion curve inversion,and the effectiveness of the algorithm was tested.3.Successfully performed a large number of theoretical model trials based on the new misfit function and shuffled complex evolution algorithm,and the effectiveness and applicability of the new inversion method for inversion of fundamental wave and multiorder wave dispersion curves were tested.4.Execution of a typical case study of the U.S.Wyoming area and the Henan highway subgrade verified the practicability of the new inversion method.5,Implemented important source code closely related to this thesis,including Rayleigh wave numerical simulation software,dispersion curve forward simulation software,dispersion curve extraction analysis software,dispersion curve inversion analysis software.The original contributions in this thesis are as follows:1.The classical Haskell-Thomson algorithm is improved to reduce the inversion speed of the classical misfit function and the wrong result caused by the mode misidentification.The magnitude of the dispersion function is reduced.And based on the shape characteristics of improved dispersion function surface,a novel and effective multimode dispersion curve inversion misift function was designed.2.When using the new misfit function to perform inversion,there is no need to assign the data points to a specific pattern,in other words,no pattern discrimination when using the new misfit function for inversion.This effectively avoids the technical problem of misidentification of the pattern that can easily occur with multimode dispersion curve inversion,and significantly improves the accuracy of inversion interpretation.3.The use of this misfit function eliminates the need for seeking rooting.Thus,the computational speed of the nonlinear global optimization inversion is significantly improved,and the calculation time is effectively saved.