GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.2 ___ GNGTS 2023 Figure 1. a) 1D plane-parallel structure characterized by aspect ratio h/w → 0 and undistinguishable horizontal main axes. b) idealized 2D basin (the longitudinal extension is infinite) characterized by aspect ratio h/w ≠ 0 and longitudinal (L), transversal (T) and vertical (V) principal directions. c) ‘Real’ 3D basin. d) Longitudinal (L1, L2, L3), transversal (T1, T2), torsional (TX) and vertical (V1) mode shapes for a basin of infinite length and sinusoidal cross-section. The red color indicates the maximum displacement and the arrows the direction of motion. In this study we focus on idealized 2D sediment-filled basins, with symmetric and homogenous cross sections, over rigid bedrock. By means of extensive numerical models and analytical derivations, we show that the ratios between their modal frequencies are almost purely shape-dependent, and poorly sensitivity to the Poisson’s coefficient, within the common values that apply to geological materials (Figure 1d). Thus, we provide a set of relations between the modal frequency ratios and the aspect ratio of the basins (h/w), for different idealized shapes. We show that when a basin geometry is not known, but its modal frequencies have been experimentally assessed, the proposed relations offer a quick estimate of its aspect ratio, maximum depth and equivalent shear wave velocity of the sedimentary filling. The size of uncertainty is linked to the wavelength involved in the modal frequency assessment. The most important relation that can be used to infer information about a sediment-filled basin is the ratio between the first transversal (T1) and the first longitudinal (L1) modal frequencies (Figure 2). The T1/L1 frequency ratio, as known from the mechanics of solid materials, is related to the geometrical stiffness in the two directions. It increases monotonically with increasing aspect ratio. Clearly, for h/w → 0 (that is on 1D plain conditions or in the case of outcropping bedrock), T1 ≈ L1.