Insights on surface wave dispersion and HVSR: Joint analysis via Pareto optimality

Abstract Surface Wave (SW) dispersion and Horizontal-to-Vertical Spectral Ratio (HVSR) are known as tools able to provide possibly complementary information useful to depict the vertical shear-wave velocity profile. Their joint analysis might then be able to overcome the limits which inevitably affect such methodologies when they are singularly considered. When a problem involves the optimization (i.e. the inversion) of two or more objectives, the standard practice is represented by a normalized summation able to account for the typically different nature and magnitude of the considered phenomena (thus objective functions). This way, a single cost function is obtained and the optimization problem is performed through standard solvers. This approach is often problematic not only because of the mathematically and physically inelegant summation of quantities with different magnitudes and units of measurements. The critical point is indeed represented by the inaccurate performances necessarily obtained while dealing with problems characterized by several local minima and the impossibility of a rigorous assessment of the goodness and meaning of the final result. In the present paper joint analysis of both synthetic and field SW dispersion curves and HVSR datasets is performed via the Pareto front analysis. Results show the relevance of Pareto's criterion not only as ranking system to proceed in heuristic optimization (Evolutionary Algorithms) but also as a tool able to provide some insights about the characteristics of the analyzed signals and the overall congruency of data interpretation and inversion. Possible asymmetry of the final Pareto front models is discussed in the light of relative non-uniqueness of the two considered objective functions.

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