Full Waveform Reflectivity For Inversion Of Surface Wave Dispersion In Shallow Site Investigations

Dominant higher modes of surface waves are generated in sites with large stiffness contrasts and/or reversals between layers. A multichannel simulation employing full-waveform reflectivity properly models dispersion curve discontinuities and allows inversion for shear velocity structure. A fundamental mode assumption causes low-velocity layers to be undetected and high-velocity layers to be interpreted both too deep and thick. Dominant higher modes are observed and inverted at a mine site over weathered sandstone and a compacted waste dump. Stacking dispersion curves provides a more unique dispersion for inversion. Introduction Surface waves have long been known to be affected by vertical variations in elastic parameters. Since the propagation of surface waves is dominated by the stiffness of the solid medium within a wavelength from the interface, in a layered system different frequency components travel at different velocity. The variation with frequency of phase or group velocity, the dispersion relationship, is the key property when modelling and interpreting surface wave data for shear velocity structure, which is an important parameter in geotechnical engineering (Whiteley 1990). In civil engineering applications (upper tens of metres), in situ imaging of shear velocity can be accomplished quickly through the inversion of surface wave dispersion (Cuellar 1997) and its use has become very common in recent years (Forbriger 2003a; Foti 2000). Conventional surface wave surveying comprises three stages: acquisition, processing, and inversion (Gabriels et al. 1987). Seismograms acquired in the field are processed to extract the ‘groundroll’ dispersion, the dominant component being surface waves. The inversion of the dispersion curve is conventionally based on a 1D plane-wave propagator matrix model (Buchen and Ben-Hador 1996). Differences between calculated and observed ‘modal’ dispersion curves are minimised for the mode of interest, based on an Earth model consisting of horizontal layers. Although all layer elastic parameters (compressional and shear velocities and density) and thicknesses may be unknown, dispersion is most sensitive to shear wave velocity, so it is this parameter which is sought (Beaty et al. 2002). A major problem is that commonly used inversion methods may not provide reliable results in engineering cases where large stiffness contrasts and/or reversals occur, for example: caprock (laterite or calcarenite), soft layers (peats and clays) and shallow hard horizons (secondary cemented sediments or crystalline rock). Caprocks and buried hard horizons, in particular, can be problematic from both safety (onshore and offshore engineering foundation) and economic (mining overburden rippability) aspects. In these sites, an ‘apparent’ or ‘effective’ dispersion is observed, since a continuous, fundamental mode is not measured, but rather several modes combined into a discontinuous curve (Lai and Rix 1999; Tokimatsu et al. 1992). While comparisons to invasive methods are generally good in ‘normally dispersive’ sites (Xia et al. 2002), discrepancies occur in more severely ‘irregularly’ and ‘inversely dispersive’ sites, due to the restriction to continuous, modal phase velocity dispersion observation and modelling (Brown et al. 2002). Mode mis-identification can also occur if the observed surface wavefield is assumed to be dominated by the fundamental mode. The following section introduces effective dispersion curves generated in synthetic cases, employing the new modelling procedure. Dispersion modeling methods Plane-wave dispersion modeling The conventional method for modelling dispersion curves is based on plane-wave propagator matrices (Buchen and Ben-Hador 1996). Since surface waves only propagate with specific wavenumbers, the roots of an implicit function in phase velocity–frequency space are the modal dispersion curves. The ‘Fast Surface Wave’ code (Schwab and Knopoff 1972) has been employed by other researchers in theoretical and field studies (Xia et al. l999). However, it will be used in this paper (hereafter called the FSW method) to illustrate how plane-wave modal dispersion is unsuitable for inverting surface wavefields with dominant higher modes. Full-waveform dispersion modeling The new modelling method is a simulation of the multichannel analysis of surface waves (MASW) employed in modern field surveys. It comprises full-waveform shot gather generation followed by standard multichannel dispersion measurement, hereafter called the PSV method. It will be described starting with synthetic examples, the three shear velocity cases of Tokimatsu et al. (1992), shown in Figure 1. Case 1 is normally dispersive while Cases 2 and 3 are irregularly dispersive. In Case 2, the second layer is a low velocity layer (LVL) and in Case 3 it is a high velocity layer (HVL). The kernel of the new method employs the reflectivity method (Muller 1985), which belongs to the class of wavenumber or slowness integration methods for generating synthetic seismograms. Although the integrand is based on plane-wave matrices, and is still restricted to flat isotropic layering, summation of nearand far-field responses of all internal multiples over a well defined slowness range provides an accurate simulation of all P-SV wavefields. This allows modelling of Rayleigh waves, which are coupled P-SV interface waves, along with all other body wavefields (direct, refracted, reflected and guided). The synthetic shot gathers for a surface impact source for the models of Figure 1 are shown in Figure 2. These are trace-normalised, as is usual for displaying surface waves. To extract dispersion curves from multichannel data, the frequency-slowness (f-p) method is used (McMechan and Yedlin 1981), with some practical aspects outlined in Louie (2001). Plane-wave transformation of the shot gather into the τ–p domain followed by FFT down the τ–axis, creates a dispersion image, shown in Figure 3. An equivalent procedure is to use a f-k transform (Gabriels et al. 1987). 0 100 200 300 400 0 2 4 6 8 10 12 14 16 18 20 Shear velocity (m/s) D ep th ( m ) (0.46)