Generation of a pseudo-2D shear-wave velocity section by inversion of a series of 1D dispersion curves

Abstract

Multichannel Analysis of Surface Waves utilizes a multichannel recording system to estimate near-surface shear (S)-wave velocities from high-frequency Rayleigh waves. A pseudo-2D S-wave velocity (v_S) section is constructed by aligning 1D models at the midpoint of each receiver spread and using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. The receiver spread length sets the theoretical lower limit and any v_S structure with its lateral dimension smaller than this length will not be properly resolved in the final v_S section. A source interval smaller than the spread length will not improve the horizontal resolution because spatial smearing has already been introduced by the receiver spread.

In this paper, we first analyze the horizontal resolution of a pair of synthetic traces. Resolution analysis shows that (1) a pair of traces with a smaller receiver spacing achieves higher horizontal resolution of inverted S-wave velocities but results in a larger relative error; (2) the relative error of the phase velocity at a high frequency is smaller than at a low frequency; and (3) a relative error of the inverted S-wave velocity is affected by the signal-to-noise ratio of data. These results provide us with a guideline to balance the trade-off between receiver spacing (horizontal resolution) and accuracy of the inverted S-wave velocity. We then present a scheme to generate a pseudo-2D S-wave velocity section with high horizontal resolution using multichannel records by inverting high-frequency surface-wave dispersion curves calculated through cross-correlation combined with a phase-shift scanning method. This method chooses only a pair of consecutive traces within a shot gather to calculate a dispersion curve. We finally invert surface-wave dispersion curves of synthetic and real-world data. Inversion results of both synthetic and real-world data demonstrate that inverting high-frequency surface-wave dispersion curves – by a pair of traces through cross-correlation with phase-shift scanning method and with the damped least-square method and the singular-value decomposition technique – can feasibly achieve a reliable pseudo-2D S-wave velocity section with relatively high horizontal resolution.

Introduction

The shear (S)-wave velocity (v_S) of near-surface materials (soil, rocks, and pavement) and its effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Multichannel Analysis of Surface Waves (MASW) analysis is an efficient tool to obtain a vertical S-wave velocity profile (Song et al., 1989, Park et al., 1999, Xia et al., 1999, Xia et al., 2002a, Xia et al., 2002b, Xia et al., 2006, Calderón-Macías and Luke, 2007, Luo et al., 2007). The large amplitude of surface waves allows an accurate reconstruction of shallow structures in a noisy environment by inversion of observed dispersion curves. Smoothed S-wave velocity sections can be reconstructed by considering successive shots. MASW techniques, therefore, have been applied to determine near-surface S-wave velocity (Park et al., 1999, Xia et al., 1999, Xia et al., 2002a, Xia et al., 2002b) and near-surface attenuation parameters (Xia et al., 2002c), bedrock mapping (Xia et al., 1998, Miller et al., 1999), cavern detection (Xia et al., 2004, Xia et al., 2007a), joint inversion of P-wave velocities and surface-wave phase velocities (Ivanov et al., 2006a), and other nondestructive detection projects (Lai et al., 2002, Yilmaz and Eser, 2002, Tian et al., 2003a, Tian et al., 2003b, Ivanov et al., 2006b).

The MASW method utilizes a multichannel recording system to estimate near-surface S-wave velocity from high-frequency Rayleigh waves. A pseudo-2D S-wave velocity section is constructed by aligning 1D models at each spread midpoint and using a spatial interpolation scheme. This technique consists of (1) acquisition of wide-band, high-frequency ground roll using a multichannel recording system (e.g., Song et al., 1989, Park et al., 1999); (2) creation of efficient and accurate algorithms organized in a straightforward data-processing sequence designed to extract and analyze 1D Rayleigh-wave dispersion curves (e.g., McMechan and Yedlin, 1981, Yilmaz, 1987, Park et al., 1998, Xia et al., 2007b); (3) development of stable and efficient inversion algorithms to obtain S-wave velocity profiles (e.g., Xia et al., 1999), and (4) construction of the 2D S-wave velocity field (Xia et al., 1998, Miller et al., 1999). The horizontal resolution of the section is therefore most influenced by the receiver spread length (the distance between the first and last receivers) and the acquisition interval (the distance of the same source–receiver configuration moved). The receiver spread length sets the theoretical lower limit, and any v_S structure with its lateral dimension smaller than this will not be properly resolved in the final v_S section. An acquisition interval smaller than the spread length will not improve this limitation because spatial smearing has already been introduced by the receiver spread (Park, 2005).

Dal Moro et al. (2003) evaluated the effectiveness of three schemes for phase velocity computation based on F–K spectrum, Tau–p transform, and phase shift. They concluded that the phase-shift approach is insensitive to data processing and performs very well even when a limited number of traces are considered. Xia et al. (2005) discussed the resolving power of the MASW technique and resolution of S-wave velocity and presented a lateral unblurring processing by generalized inversion and pointed out that the ultimate goal of Rayleigh-wave techniques is to extract accurate dispersion curves from a record with a short geophone spread.

An appealing alternative solution to generate pseudo-2D S-wave velocity sections can be obtained by inversion of dispersion curves calculated through a cross-correlation method (Guo and Liu, 1999, Liu et al., 2003). The cross-correlation method chooses only a pair of consecutive receivers in the multichannel record to calculate dispersion curves. This method can greatly improve the horizontal resolution of pseudo-2D sections without having to acquire redundant field data. This method, however, is sensitive to noise in data and unrealistic results will be generated if the data have a very low signal-to-noise (S/N) ratio.

In this paper, we first analyze the feasibility of generating dispersion curves with a pair of traces with a selected trace interval. Then we present a scheme to generate a pseudo-2D S-velocity section with high horizontal resolution using multichannel records by inverting high-frequency surface-wave dispersion curves calculated through a combined method of cross-correlation and phase-shift scanning that uses simply two consecutive traces in a multichannel record to calculate the dispersion curve. The purpose of the combined method is to obtain high reliable dispersion curves with the highest horizontal resolution possible. In the end, we invert surface-wave dispersion curves of both a theoretical model and a real-world example to demonstrate the feasibility of the scheme to estimate S-wave velocity sections using a damped least-square method and the singular-value decomposition (SVD) technique (Xia et al., 1999).