Analysis of Surface-Wave Data Including Higher Modes Using the Genetic Algorithm

Abstract

Analysis of surface wave data generally assumes that a dispersion curve mainly consists of a fundamental mode. Higher modes may dominate in several types of velocity structures, such as a model in which a high-velocity layer overlays on a low-velocity layer or a model in which a high-velocity layer is embedded in lowvelocity layers. In these types of complex velocity structures, higher modes may dominate in particular frequency range and observed dispersion curves look very complex. It is generally difficult to separate the fundamental mode and the higher modes correctly and traditional inversion methods based on the Jacobiam matrix cannot be applied. In order to overcome these difficulties, we have developed a new inversion method using a genetic algorithm (GA). In this new method, phase velocities and relative amplitude for the fundamental and higher modes are calculated. For each frequency, residual between observed and theoretical phase velocities is defined as the difference of an observed phase velocity and a synthetic phase velocity that has maximum relative amplitude in all modes. The GA is applied to obtain a velocity model that provides minimum residual. In this paper, we describe typical examples of dispersion curves in which higher modes dominate. Secondly, the theory of the new inversion method and numerical examples are shown. Finally, application of the new method to an engineering site investigation is demonstrated.

Full-wavefield inversion of surface waves for mapping embedded low-velocity zones in permafrost

“…To reduce the risk of mode misidentification, modal-curve methods incorporating amplitude responses use modal amplitude responses to aid in identifying individual modes. This method facilitates inversion for irregularly dispersive media (Lu and Zhang, 2006;Lu et al, 2007;Hayashi, 2012;Ikeda et al, 2012); a highly relevant example is the study of Tsuji et al (2012), which identifies unfrozen zones enclosed in glacial sediments by using this method. However, two limitations are worth noting: First, this technique becomes inapplicable in situations in which modal curves cannot be unambiguously separated, and second, it does not consider the effect of data acquisition and processing procedures, even though these factors affect the modal amplitudes measured from the dispersion spectra.…”

“…Among the commonly used derivative-free methods, stochastic global-search algorithms are widely applied in surface-wave literature, including Monte Carlo methods (Socco and Boiero, 2008;, genetic algorithms (Lu and Zhang, 2006;Lu et al, 2007;Hayashi, 2012;Ikeda et al, 2012;Tsuji et al, 2012), simulated annealing (Beaty et al, 2002;Ryden and Park, 2006), and the neighborhood algorithm (Wathelet et al, 2004;Douma and Haney, 2013). By contrast, the use of deterministic algorithms is not yet as common among surface-wave applications.…”

Multimodal Layered Transdimensional Inversion of Seismic Dispersion Curves With Depth Constraints

“…By deriving material‐layer boundaries we are able to fix the Vp and density appropriately in each layer according to the material expected. This is an improvement from models that have no defined layers with Vp and density fixed as constants throughout the model space (Hayashi, ). However, a development of the algorithm would be, at increased computational cost, to also consider resolving Vp and density in each layer.…”

“…At this point, the Markov chain is presumed independent of the initial condition and statistics of the chain are recorded from then on. This technique therefore differs fundamentally from techniques such as the Genetic Algorithm which relies on an initial reference model to start the inversion process (Hayashi, ). On completion, all diagnostics must be checked to ensure sufficient iterations have been taken to achieve convergence.…”