Identification of surface wave higher modes using a methodology based on seismic noise and coda waves

Abstract

Dispersion analysis of Rayleigh waves is performed to assess the velocity of complex structures such as sedimentary basins. At short periods several modes of the Rayleigh waves are often exited. To perform a reliable inversion of the velocity structure an identification of these modes is thus required. We propose a novel method to identify the modes of surface waves. We use the spectral ratio of the ground velocity for the horizontal components over the vertical component (H/V) measured on seismic coda. We then compare the observed values with the theoretical H/V ratio for velocity models deduced from surface wave dispersion when assuming a particular mode. We first invert the Rayleigh wave measurements retrieved from ambient noise cross-correlation with the assumptions that (1) the fundamental mode and (2) the first overtone are excited. Then we use these different velocity models to predict theoretical spectral ratios of the ground velocity for the horizontal components over the vertical component (H/V). These H/V ratios are computed under the hypothesis of equipartition of a diffuse field in a layered medium. Finally we discriminate between fundamental and higher modes by comparing the theoretical H/V ratio with the H/V ratio measured on seismic coda. In an application, we reconstruct Rayleigh waves from cross-correlations of ambient seismic noise recorded at seven broad-band stations in the Valley of Mexico. For paths within the soft quaternary sediments basin, the maximum energy is observed at velocities higher than expected for the fundamental mode. We identify that the dominant mode is the first higher mode, which suggests the importance of higher modes as the main vectors of energy in such complex structures.

The inversion of spectral ratio H/V in a layered system using the diffuse field assumption (DFA)

“…They appear explicitly in formulae (5) and can be selected as desired to obtain theoretical H/V a la carte in order to identify the wave types that are effectively in the data (see Rivet et al 2015).…”

“…In fact, the H/V ratio considering only the body waves contributions (see figure 4-a) is very similar to the transfer function for vertical S waves, in partial agreement with Nakamura's (1989) interpretation. Finally, when all the wave types are considered (Spica et al 2015;Rivet et al 2015García-Jerez et al 2016, the H/V ratio is usually dominated by surface wave contributions for frequencies higher than the first maximum, whereas it is dominated by body waves below that frequency (see figure 4-a) .…”

Constraining on the Stationarity of Signal with Time-Frequency Surrogates to Enhance the Reliability of Singularity Spectrum Attributes of Random Seismic Noise Wavefield

“…around the maxima of spectrum, ℎ 0 ( ), Shimizu et al, (2002) proposed an excellent tool for experimentally visualizing 15 the shape of multi-fractal spectrum. By extrapolating curves to zero, the width of the spectrum can be defined as…”

“…where the width of the spectrum is zero for a mono-fractal series (Shimizu et al, 2002;Telesca et al, 2004;Telesca et al, 2015). For q = 1, (ℎ) can be interpreted as a fractal dimension, while q = 2 and q = 3 represents the information dimension and the correlation dimension of a time series, respectively.…”

“…generating source and an ample image of the subsurface, nonetheless, trapped incoherent waves, arisen from randomly distributed scatterers or from a finite medium with an irregular bounding surface, due to the repeatedly sampling of medium, can be used in both imaging and monitoring purposes (Snieder, 2006). For propagation distances typically less than the mean free path, defined as the distance between two successive scattering anomalies, the coherent part is dominance over the incoherent part, while for times more than the mean free time, waves bounce on several heterogeneities and enter into the 5 multiple scattering regime (Hillers et al, 2012(Hillers et al, , 2013Galluzzo et al, 2015).…”