Estimation of Elastic Moduli in a Compressible Gibson Half-space by Inverting Rayleigh-wave Phase Velocity

Xia, Jianghai; Xu, Yixian; Miller, Richard D.; Chen, Chao

doi:10.1007/s10712-005-7261-3

Cited by 67 publications

(21 citation statements)

References 39 publications

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“…Near-surface S-wave velocities can be estimated by inverting phase velocities of high-frequency Rayleigh waves (XIA et al, , 2003(XIA et al, , 2006b. Near-surface quality factors (Q), which are directly related to the material damping ratio D (Q -1 = 2D) in geotechnical engineering (RIX et al, 2000), can also be determined by inverting attenuation coefficients of Rayleigh waves (XIA et al, 2002b).…”

Section: Data-resolution Matrix and Model-resolution Matrixmentioning

confidence: 99%

“…Surface-wave data would not be perfectly predicted using a damped least-squares method (XIA et al, , 2002a(XIA et al, , 2003(XIA et al, , 2006b because the generalized inverse of the solution is H = [G T G + kI] -1 G T , where G is the Jacobian matrix of the model with respect to S-wave velocity, k is a damping factor, and I is the unit matrix. The damping factor also controls the direction of iterations in model space and speed of convergence (MARQUARDT, 1965).…”

Section: Data-resolution Matrix and Model-resolution Matrixmentioning

confidence: 99%

“…Errors in S-wave velocities obtained using the MASW method are 15% or less and random when compared with direct borehole measurements (XIA et al, 2002a). Other studies include repeatability of MASW (BEATY and SCHMITT, 2003), delineation of bedrock , near-surface quality factors (Q) (XIA et al, 2002b), a pitfall using shear-wave refraction surveying (XIA et al, 2002c), detection of voids (XIA et al, 2004(XIA et al, , 2007a, the MASW method using a fast and efficient method for geophone deployment-autojuggie (STEEPLES et al, 1999;TIAN et al, 2003a b), a unified workflow for geotechnical and engineering seismology (YILMAZ et al, 2006), discussion of MASW dispersion characteristics (LIN and CHANG, 2004), optimized selection of fielddata-acquisition parameters (XU et al, 2006, XIA et al, 2006a in press), estimation of S-wave velocities for a continuous earth model (XIA et al, 2006b), generation of a dispersion image using slant stacking (XIA et al, 2007b) and a s-p transform (LUO et al, 2008b), generation of a pseudo-2D shear-wave velocity section by inversion of a series of 1D dispersion curves (LUO et al, 2008a), numerical modeling of surface waves , discussion of surface-wave inversion with a high-velocity-layer intrusion model (CALDERóN-MACíAS and LUKE, 2007), and a lowvelocity-layer intrusion model (LU et al, 2007;LIANG et al, 2008). Dispersions of ground-penetrating radar data were also inverted for the subsurface material properties (KRUK et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

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Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method

Xia

Miller²,

Xu³

2008

Pure appl. geophys.

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Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (C2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data.

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Section: Data-resolution Matrix and Model-resolution Matrixmentioning

confidence: 99%

Section: Data-resolution Matrix and Model-resolution Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method

Xia

Miller²,

Xu³

2008

Pure appl. geophys.

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“…Dispersive Rayleigh waves have been widely employed to estimate S-wave velocities in shallow layers (Nazarian and Stokoe, 1984;Xia et al, 1999Xia et al, , 2003Xia et al, , 2004Xia et al, , 2006Calderón-Macías and Luke, 2007;Luo et al, 2009a;Socco et al, 2010). Numerical modeling of Rayleigh waves has been investigated in near-surface seismology for various purposes including a study of attenuation (Carcione, 1992) and a shallow cavity investigation (Gelis et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

An improved vacuum formulation for 2D finite-difference modeling of Rayleigh waves including surface topography and internal discontinuities

et al. 2012

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Rayleigh waves are generated along the free surface and their propagation can be strongly influenced by surface topography. Modeling of Rayleigh waves in the near surface in the presence of topography is fundamental to the study of surface waves in environmental and engineering geophysics. For simulation of Rayleigh waves, the traction-free boundary condition needs to be satisfied on the free surface. A vacuum formulation naturally incorporates surface topography in finite-difference (FD) modeling by treating the surface grid nodes as the internal grid nodes. However, the conventional vacuum formulation does not completely fulfill the free-surface boundary condition and becomes unstable for modeling using high-order FD operators. We developed a stable vacuum formulation that fully satisfies the free-surface boundary condition by choosing an appropriate combination of the staggered-grid form and a parameter-averaging scheme. The elastic parameters on the topographic free surface are updated with exactly the same treatment as internal grid nodes. The improved vacuum formulation can accurately and stably simulate Rayleigh waves along the topographic surface for homogeneous and heterogeneous elastic models with high Poisson's ratios (>0.4). This method requires fewer grid points per wavelength than the stress-image-based methods. Internal discontinuities in a model can be handled without modification of the algorithm. Only minor changes are required to implement the improved vacuum formulation in existing 2D FD modeling codes.

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“…The relationship between Rayleigh-wave phase velocity and frequency has been widely utilized to estimate the S-wave velocities in shallow layers (Nazarian and Stokoe, 1984;Xia et al, 1999Xia et al, , 2003Xia et al, , 2006Calderón-Macías and Luke, 2007;Socco et al, 2010). Hence, generating synthetic records containing accurate Rayleigh-wave information is a primary objective of any near-surface seismic modeling task.…”

Section: Introductionmentioning

confidence: 99%

Application of the multiaxial perfectly matched layer (M-PML) to near-surface seismic modeling with Rayleigh waves

et al. 2011

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Perfectly matched layer (PML) absorbing boundaries are widely used to suppress spurious edge reflections in seismic modeling. When modeling Rayleigh waves with the existence of the free surface, the classical PML algorithm becomes unstable when the Poisson's ratio of the medium is high. Numerical errors can accumulate exponentially and terminate the simulation due to computational overflows. Numerical tests show that the divergence speed of the classical PML has a nonlinear relationship with the Poisson's ratio. Generally, the higher the Poisson's ratio, the faster the classical PML diverges. The multiaxial PML (M-PML) attenuates the waves in PMLs using different damping profiles that are proportional to each other in orthogonal directions. The proportion coefficients of the damping profiles usually vary with the specific model settings. If they are set appropriately, the M-PML algorithm is stable for high Poisson's ratio earth models. Through numerical tests of 40 models with Poisson's ratios that varied from 0.10 to 0.49, we found that a constant proportion coefficient of 1.0 for the x-and z-directional damping profiles is sufficient to stabilize the M-PML for all 2D isotropic elastic cases. Wavefield simulations indicate that the instability of the classical PML is strongly related to the wave phenomena near the free surface. When applying the multiaxial technique only in the corners of the PML near the free surface, the original M-PML technique can be simplified without losing its stability. The simplified M-PML works efficiently for homogeneous and heterogeneous earth models with high Poisson's ratios. The analysis in this paper is based on 2D finite difference modeling in the time domain that can easily be extended into the 3D domain with other numerical methods.

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Estimation of Elastic Moduli in a Compressible Gibson Half-space by Inverting Rayleigh-wave Phase Velocity

Cited by 67 publications

References 39 publications

Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method

Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method

An improved vacuum formulation for 2D finite-difference modeling of Rayleigh waves including surface topography and internal discontinuities

Application of the multiaxial perfectly matched layer (M-PML) to near-surface seismic modeling with Rayleigh waves

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