Green's Functions for Surface Waves in a Generic Velocity Structure

Tsai, Victor C.; Atiganyanun, Sarun

doi:10.1785/0120140121

Cited by 29 publications

(41 citation statements)

References 22 publications

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“…( F-6) This relation between group and phase velocity for power-law shear velocity profiles has been noted before by Tsai et al (2012) and Tsai and Atiganyanun (2014). It holds in this case because the Dix-type relation has the same frequency scaling as the exact solution in power-law shear velocity profiles (Haney and Tsai, 2015).…”

Section: Uðkþsupporting

confidence: 55%

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

Haney

Tsai

2017

GEOPHYSICS

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The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves.

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Section: Uðkþsupporting

confidence: 55%

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

Haney

Tsai

2017

GEOPHYSICS

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“…To develop a theory for Love waves, we instead consider depth models described by power-law velocity profiles, in which Love waves exist. Such models are generic and may provide a more realistic description of the shallow subsurface than a homogeneous model in many cases (Godin and Chapman, 2001;Bergamo and Socco, 2013;Tsai and Atiganyanun, 2014). Similar to the development of the theory for Rayleigh waves, equation 7.69 in Aki and Richards (1980) states that a Love-wave eigenfunction satisfies…”

Section: Fundamental-mode Love Wavesmentioning

confidence: 99%

“…Because the synthetic data are derived from a power-law model, the inversion in this case predictably does better, capturing the entire depth profile more accurately than in Figure 3b. Given the prevalence of power-law velocity profiles in unconsolidated deposits (Godin and Chapman, 2001;Bergamo and Socco, 2013;Tsai and Atiganyanun, 2014), this type of Dix-type relation should be applicable in the shallow subsurface. An interesting feature of the Rayleigh-wave inversion based on power-law velocity profiles is that the ridge of high sensitivity in Figure 3d is closer to 0.5λ than 0.63λ as shown by the black dashed line.…”

Section: Inversion With An Overparameterized Modelmentioning

confidence: 99%

“…After deriving a Dix-type relation based on a homogeneous medium, we extend the theory to include the possibility of Rayleigh or Love waves propagating in velocity-depth profiles described by power laws. In unconsolidated granular deposits, such power-law profiles constitute a more realistic model of shear wave velocity than a homogeneous model (Godin and Chapman, 2001;Bergamo and Socco, 2013;Tsai and Atiganyanun, 2014).…”

Section: Introductionmentioning

confidence: 99%

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Nonperturbational surface-wave inversion: A Dix-type relation for surface waves

Haney

Tsai

2015

GEOPHYSICS

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We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shearwave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a nearsurface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion.

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“…Finally, to retrieve the full expressions of the Rayleighwave and Love-wave Green's functions, we refer the reader to Aki and Richards (2002) and Tsai and Atiganyanun (2014) for expression relative to surface-to-surface Green's functions as well as Gimbert et al (2014) for an example of Green's function allowing non-vertical impulsive seismic sources to be taken into account.…”

Section: Signal Generation and Propagationmentioning

confidence: 99%

Seismic monitoring of torrential and fluvial processes

2016

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Abstract. In seismology, the signal is usually analysed for earthquake data, but earthquakes represent less than 1 % of continuous recording. The remaining data are considered as seismic noise and were for a long time ignored. Over the past decades, the analysis of seismic noise has constantly increased in popularity, and this has led to the development of new approaches and applications in geophysics. The study of continuous seismic records is now open to other disciplines, like geomorphology. The motion of mass at the Earth's surface generates seismic waves that are recorded by nearby seismometers and can be used to monitor mass transfer throughout the landscape. Surface processes vary in nature, mechanism, magnitude, space and time, and this variability can be observed in the seismic signals. This contribution gives an overview of the development and current opportunities for the seismic monitoring of geomorphic processes. We first describe the common principles of seismic signal monitoring and introduce time-frequency analysis for the purpose of identification and differentiation of surface processes. Second, we present techniques to detect, locate and quantify geomorphic events. Third, we review the diverse layout of seismic arrays and highlight their advantages and limitations for specific processes, like slope or channel activity. Finally, we illustrate all these characteristics with the analysis of seismic data acquired in a small debris-flow catchment where geomorphic events show interactions and feedbacks. Further developments must aim to fully understand the richness of the continuous seismic signals, to better quantify the geomorphic activity and to improve the performance of warning systems. Seismic monitoring may ultimately allow the continuous survey of erosion and transfer of sediments in the landscape on the scales of external forcing.

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Green's Functions for Surface Waves in a Generic Velocity Structure

Cited by 29 publications

References 22 publications

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

Nonperturbational surface-wave inversion: A Dix-type relation for surface waves

Seismic monitoring of torrential and fluvial processes

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