Modern inversion workflow of the multimodal surface wave dispersion curves: staging strategy and Pattern search with embedded Kuhn–Munkres algorithm

Abstract

SUMMARY The dispersive information of the higher surface wave modes is beneficial for improving the resolution of the inverted S-wave velocity structure, increasing the penetration depth and enhancing the robustness of the inversion. The recently proposed frequency-Bessel (F-J) transformation can achieve the relatively stable measurement of the higher-mode surface waves. However, sometimes the phenomena of the mode losses and aliases would appear in the dispersion energy image of the seismic records, which may lead to the mode misidentification. And the wrong mode identification is likely to cause the negative impacts on the dispersion inversion and geological interpretation about the survey site. In view of this, we recommend a staging strategy for the inversion of multimodal surface wave dispersion curves. The pattern search (PS) is used to invert the reliable segment of the fundamental-mode surface wave phase velocities for the first stage. For the second stage, the inverted result of the first stage is set as the initial model, the PS with embedded Kuhn–Munkres (PSEKM) algorithm is adopted for inverting the observed phase velocities of all modes. And for each frequency, a weighted bipartite graph is established between the observed values with no-explicitly specified-mode-order (NESMO) and predicted values of the model m during the inversion, then the maximum match is determined by the KM algorithm for calculating the minimum distance between the observed and predicted data sets. The mode-order information of the observed phase velocities with NESMO would be dynamically evaluated for each model m occurred in the inversion process. The synthetic reconstruction tests have confirmed the effectiveness of the novel workflow. Also, the performance of the preconditioned steepest-descent algorithm of local optimization methods and influence of the mode misidentification on the inversion result are also clarified in the synthesis tests. The comparison results show that the proposed workflow can realize the nice data fitting and model reconstruction without the time-consuming manual mode-identification for the higher-mode surface waves. Then, the new workflow is applied to the analysis of the actual surface wave data sets collected on two roadbeds, which is still satisfactory. Finally, we discuss the role of the staging strategy of the workflow.