Generation of a pseudo-2D shear-wave velocity section by inversion of a series of 1D dispersion curves
Introduction
The shear (S)-wave velocity (vS) 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 vS structure with its lateral dimension smaller than this will not be properly resolved in the final vS 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).
Section snippets
Resolution analysis
Seismic resolution defines to what extent detail of vertical and lateral changes in the earth can be obtained from seismic data. Horizontal resolution determines the ability to distinguish events that are laterally displaced from each other (e.g., Yilmaz, 1987, Hokstad et al., 2001). The term “horizontal resolution” in this paper refers to the lateral interval of S-wave velocities inverted from surface waves. The main task of the resolution analysis is to study relative errors of calculated
The method
We first introduce the method of cross-correlation with phase-shift scanning and then present the scheme illustrating the processing flow of obtaining pseudo-2D S-wave velocity sections.
synthetic example
A shot gather (the vertical component, Fig. 4) from a 2D model (Fig. 5) was computed using a finite difference method (Xu et al., 2007). In this model, a corner edge was designed to simulate a vertical fault at a shallow depth. In the finite difference method, the spatial grid size was 1 m with time step of 0.1 ms, source is described by the first-order derivative of Gaussian function t · exp(− at2) with controlling parameter a = 3000, and the nearest shot-geophone offset was selected as 6 m with a
A real-world example
Real-world data (Miller et al., 1999) were employed to study the feasibility of the scheme using a pair of traces to estimate S-wave velocity sections. The depth of interest ranged from about 1 to 10 m below the ground surface. Improving the bedrock surface map and delineating any potential contaminant pathways on or into bedrock were the primary objectives of this survey. Standard CMP roll-along techniques were used to record data with a 1.2-m shot interval. Forty-eight channel surface data
Conclusions
The main motivation of the present work lies in the observation that improving horizontal resolution of S-wave velocities by the MASW method is a very hard task. Horizontal resolution of an S-wave velocity profile is determined by the receiver spread length and the acquisition interval. We present a scheme to generate a high-resolution pseudo-2D S-wave velocity section by inverting a series of dispersion curves that were generated by a pair of traces. In this scheme, a pair of traces is chosen
Acknowledgments
This study is partly supported by the National Science Foundation of China (No. 40474025) and Excellent Young Teacher Foundation of China University of Geosciences (No. CUGQNL0524). The authors appreciate the efforts of Marla Adkins-Heljeson and Mary Brohammer of the Kansas Geological Survey in editing of the manuscript.
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2016, Journal of Applied GeophysicsCitation Excerpt :Grandjean and Bitri (2006) extended the SASW method with a multifold acquisition for processing dispersion images in highly laterally contrasted media, while Lin and Lin (2007) proposed a high lateral resolution method based on walk-away survey and phase-seaming procedure. Based on the assumption of a mildly horizontal S-wave velocity variation, Luo et al. (2008a) present a scheme to generate a pseudo-2D S-wave velocity section by inverting high-frequency surface-wave dispersion curves calculated by consecutive two traces within a multichannel record. Although this method possesses potential to improve horizontal resolution of high-frequency surface-wave methods to some degree, it is difficult to distinguish a minor anomalous body due to the inaccuracy of dispersion curves generated from two traces with a smaller receiver spacing.
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2012, Journal of Applied GeophysicsCitation Excerpt :This approach makes it possible to retrieve the dispersion curve approximately corresponding to the soil below the centre of the acquisition receivers. On the one hand, SASW has high horizontal resolution: it involves only two receivers and hence the lateral resolution is equal to the receiver spacing (Luo et al., 2008); on the other hand, SASW is very sensitive to random and coherent noise (higher modes, body waves, and others) and individual geophone coupling. Multi-channel analysis of surface waves (MASW – Park et al., 1999; Socco and Strobbia, 2004) was developed to overcome these problems.
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2011, Journal of Applied GeophysicsCitation Excerpt :The inverted S-wave velocity can be considered a horizontally averaged value from the underground area beneath the receiver spread (Luo et al., 2009a). To obtain a 2D distribution of S-wave velocities, a standard common depth point (CDP) roll-along acquisition format (Mayne, 1962) is usually used to produce multiple shot gathers so that a pseudo 2D S-wave velocity section can be inverted from a set of dispersion curves (Luo et al., 2008; Xia et al., 2004). The accuracy and horizontal resolution of this pseudo 2D S-wave velocity section depends on the length of the receiver spread and the degree of lateral heterogeneity of underground materials.
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2011, Journal of Applied GeophysicsCitation Excerpt :Near-surface shear (S)-wave velocity structure is important in ground-motion amplification and site response in sedimentary basins (Borcherdt, 1970; Stephenson et al., 2005). The Multichannel Analysis of Surface Waves (MASW) method is an efficient tool to obtain the vertical S-wave profile using the dispersive characteristic of Rayleigh waves (Calderón-Macías and Luke, 2007; Luo et al., 2007, 2008a, 2008b, 2009a, 2009b, 2009c; Song et al., 1989; Xia et al., 1999, 2002a, 2004, 2006a). Recent studies associated with Rayleigh-wave data analysis and applications include: bedrock mapping (Miller et al., 1999); near-surface quality factors (Q) (Xia et al., 2002b); inversion with the incorporation of higher mode data (Beaty et al., 2002; Luo et al., 2007; Xia et al., 2003); cavern detection (Xia et al., 2004); numerical modeling (Mittet, 2002; Xu et al., 2007); joint inversion of P-wave velocities and surface wave phase velocities (Dal Moro and Pipan, 2007; Ivanov et al., 2006); discussion on resolution of surface-wave data (Xia et al., 2005); a non-layered-earth model (Gibson half-space, Xia et al., 2006a); the nearest offset and cutoff frequencies and their applications (Xia et al., 2006b; Xu et al., 2006, 2009); discussion of Rayleigh-wave inversion with a high-velocity-layer intrusion model (Calderón-Macías and Luke, 2007); a low-velocity-layer intrusion model (Liang et al., 2008; Lu et al., 2007); dispersive imaging (Luo et al., 2008a; Xia et al., 2007); mode separation (Luo et al., 2009a); and assessment of inverted models (Xia et al., 2010).