Improved Holistic Analysis of Rayleigh Waves for Single- and Multi-Offset Data: Joint Inversion of Rayleigh-Wave Particle Motion and Vertical- and Radial-Component Velocity Spectra

Pure Appl. Geophys. Ó 2017 The Author(s) This article is an open access publication DOI 10.1007/s00024-017-1694-8 Pure and Applied Geophysics Improved Holistic Analysis of Rayleigh Waves for Single- and Multi-Offset Data: Joint Inversion of Rayleigh-Wave Particle Motion and Vertical- and Radial-Component Velocity Spectra GIANCARLO DAL MORO,1 SAYED S. R. MOUSTAFA,2 and NASSIR S. AL-ARIFI2 Abstract—Rayleigh waves often propagate according to complex mode excitation so that the proper identification and separation of specific modes can be quite difficult or, in some cases, just impossible. Furthermore, the analysis of a single component (i.e., an inversion procedure based on just one objective function) necessarily prevents solving the problems related to the non-uniqueness of the solution. To overcome these issues and define a holistic analysis of Rayleigh waves, we implemented a procedure to acquire data that are useful to define and efficiently invert the three objective functions defined from the three following ‘‘objects’’: the velocity spectra of the vertical- and radialcomponents and the Rayleigh-wave particle motion (RPM) frequency-offset data. Two possible implementations are presented. In the first case we consider classical multi-offset (and multi-component) data, while in a second possible approach we exploit the data recorded by a single three-component geophone at a fixed offset from the source. Given the simple field procedures, the method could be particularly useful for the unambiguous geotechnical exploration of large areas, where more complex acquisition procedures, based on the joint acquisition of Rayleigh and Love waves, would not be economically viable. After illustrating the different kinds of data acquisition and the data processing, the results of the proposed methodology are illustrated in a case study. Finally, a series of theoretical and practical aspects are discussed to clarify some issues involved in the overall procedure (data acquisition and processing). Key words: Surface wave dispersion, joint inversion of seismic data, Rayleigh waves, holistic analysis of surface waves, Pareto optimality, Rayleigh-wave Particle Motion (RPM) curve, Rayleigh-wave Prograde motion. 1 Institute of Rock Structure and Mechanics, Academy of Sciences of the Czech Republic, V Holešovičkách 94/41, 18209 Prague 8, Czech Republic. E-mail: 2 Geology and Geophysics Department, Faculty of Sciences, King Saud University, King Saud Street, Riyadh 11451, Saudi Arabia. 1. Introduction The exploitation of surface-wave propagation for the determination of the vertical shear-wave velocity (VS) profile is nowadays routinely adopted for a number of seismological and geotechnical applications (e.g., Poggi and Fäh 2010; Luo et al. 2011; O’Connell and Turner 2011; Boxberger et al. 2011; Zhang et al. 2017). A number of active and passive techniques aimed at retrieving the dispersive properties of the investigated site have been proposed (for an overview, see Dal Moro 2014; Foti et al. 2014) but we should highlight that the way we then invert the obtained dispersive properties is a different issue. Surface-wave analysis is in fact typically accomplished in two steps: 1. determination of the dispersive properties of the site; 2. their inversion (aimed at determining the subsurface VS model). The multi-channel analysis of surface waves (MASW) is a very well known acronym typically used to indicate the classical approach to determine the dispersive properties from multi-channel (multioffset) active data. A series of equally spaced geophones is deployed and the acquired seismic traces are used to define the phase velocity spectrum (Xia et al. 1999; Dal Moro et al. 2003). Typically, only the vertical-component of Rayleigh waves is considered and the obtained velocity spectrum (which represents the dispersive properties of the site) is interpreted in terms of modal curves G. Dal Moro et al. which are then inverted (Xia et al. 1999; Ryden et al. 2003). It must be emphasized that such approach (the interpretation of the modal dispersion curves of the vertical-component of Rayleigh waves, their picking and final inversion) is not the only possible and, actually, it can be highly problematic because it involves a personal (i.e., subjective) interpretation of a single velocity spectrum (see Zhang and Chan 2003; Dal Moro 2014; Dal Moro et al. 2015a, b, c). With the aim of illustrating how complex and counterintuitive a phase velocity spectrum can actually be, in Fig. 1 we present and comment a synthetic dataset computed according to Carcione (1992). The Pure Appl. Geophys. computed phase velocity spectrum reported in Fig. 1c is apparently continuous and seemingly simple (no jump or weird features). In spite of this, once we plot the theoretical dispersion curves of the first two modes (Fig. 1d), we realize that the signal that dominates the velocity spectrum is actually the combination of the fundamental mode for frequencies higher than 40 Hz and of the first higher mode for lower frequencies. Because the signal in the velocity spectrum is continuous (Fig. 1c), it is clear that in case this kind of dataset would be interpreted in terms of modal dispersion curves, it would be inevitably misinterpreted and, consequently, an erroneous subsurface Figure 1 Complex (counterintuitive) phase velocity spectrum for a synthetic dataset (MASW data): a subsurface model (the numbers are the adopted Poisson’s values); b synthetic seismic traces of the vertical-component computed according to Carcione (1992); c phase velocity spectrum of the computed synthetic traces; d phase velocity spectrum and theoretical modal dispersion curves of the first two modes (the white and green lines indicate the fundamental and first higher mode, respectively). Because the signal in the velocity spectrum is continuous (see plot c), it is impossible to separate the two modes. Consequently, any kind of analysis based on the identification and inversion of the modal dispersion curves will necessarily fail Improved Holistic Analysis of Rayleigh Waves for Single- and Multi-Offset Data: Joint model would be obtained. Since the velocity spectrum would be likely interpreted as expression of the fundamental mode only, the obtained VS values would be clearly overestimated. In Dal Moro et al. (2015a, b, 2016), we introduced a series of procedures aimed at the joint analysis of multi-component data with the final goal of obtaining a subsurface model free from significant ambiguities both because we analyze multi-component data, both because we do not consider an approach based on the analysis of picked (i.e., subjectively interpreted) modal dispersion curves. One of the goals of the present work is to further improve the analysis of Rayleigh waves and, therefore, give the MASW acronym a more comprehensive meaning. In fact, several points should be addressed when dealing with surface-wave analysis: 1. How many and wha (...truncated)