An Improved Method for Computing Broadband Green’s Functions of Surface Sources and Its Application to Inverting the Processes of the 2017 Xinmo Landslide

2021 ◽  
Author(s):  
Yunyi Qian ◽  
Zhengbo Li ◽  
Xiaofei Chen
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Complex Surface ◽  
Dominant Frequency ◽  
Improved Method ◽  
Transmission Method ◽  
Surface Source ◽  
Near Surface ◽  
Xinmo Landslide ◽  
Initiation Stage

Abstract Landslides are dramatic and complex surface processes that can result in extensive casualties and property damage. The broadband seismic signals generated by landslides provide datasets essential for understanding time-dependent sliding processes. However, traditional methods for computing Green’s functions based on wavenumber integration converge very slowly for surface sources, especially at high frequencies. Usually, long-period synthetic waves with a cutoff k-integral for an approximated near-surface source are adopted for landslide studies, which may lead to artifacts. Thus, the development of efficient methods for computing the broadband Green’s functions of surface sources is important. The generalized reflection and transmission method with the peak-trough averaging technique can overcome the difficulties in wavenumber integration for surface sources, quickly converging even for high-frequency calculations. We use this improved method to compute Green’s functions for surface single-force sources and invert the force histories of the 2017 devastating Xinmo landslide in different frequency bands. The results indicate that the complex sliding process of this drastic event can be revealed by broadband signals (0.02–0.5 Hz), and that the initiation stage of this event shows a dominant frequency up to 0.2 Hz.

Sensitivity kernels for seismic Fresnel volume tomography

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. U35-U46 ◽  
Author(s):  
Yuzhu Liu ◽  
Liangguo Dong ◽  
Yuwei Wang ◽  
Jinping Zhu ◽  
Zaitian Ma
Keyword(s):  
Green's Functions ◽  
Heterogeneous Media ◽  
Green’S Functions ◽  
Dominant Frequency ◽  
Sensitivity Kernel ◽  
Distribution Ranges ◽  
Band Limited ◽  
Homogeneous Media ◽  
Limited Sensitivity ◽  
Fresnel Volume Tomography

Fresnel volume tomography (FVT) offers higher resolution and better accuracy than conventional seismic raypath tomography. A key problem in FVT is the sensitivity kernel. We propose amplitude and traveltime sensitivity kernels expressed directly with Green’s functions for transmitted waves for 2D/3D homogeneous/heterogeneous media. The Green’s functions are calculated with a finite-difference operator of the full wave equation in the frequency-space domain. In the special case of homogeneous media, we analyze the properties of the sensitivity kernels extensively and gain new insight into these properties. According to the constructive interference of waves, the spatial distribution ranges of the monochromatic sensitivity kernels in FVT differ from each other greatly and are [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] periods of seismic waves, respectively, for 2D amplitude, 3D amplitude, 2D traveltime, and 3D traveltime conditions. We also have a new understanding of the relationship between raypath tomography and FVT. Within the first Fresnel volume of the dominant frequency, the band-limited sensitivity kernels of FVT in homogeneous media or smoothly heterogeneous media are very close to those of the dominant frequency. Thus, it is practical to replace the band-limited sensitivity kernel with a few selected frequencies or even the single dominant frequency to save computation when performing band-limited FVT. The numerical experiment proves that FVT using our sensitivity kernels can achieve more accurate results than traditional raypath tomography.

scholarly journals Validation of a fast semi-analytic method for surface-wave propagation in layered media

2019 ◽  
Vol 219 (2) ◽  
pp. 1405-1420 ◽  
Author(s):  
Quentin Brissaud ◽  
Victor C Tsai
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Power Law ◽  
Green's Functions ◽  
Green’S Functions ◽  
Shear Velocity ◽  
Surface Velocity ◽  
Near Surface ◽  
Phase Velocities ◽  
Surface Wave Propagation

SUMMARY Green’s functions provide an efficient way to model surface-wave propagation and estimate physical quantities for near-surface processes. Several surface-wave Green’s function approximations (far-field, no mode conversions and no higher mode surface waves) have been employed for numerous applications such as estimating sediment flux in rivers, determining the properties of landslides, identifying the seismic signature of debris flows or to study seismic noise through cross-correlations. Based on those approximations, simple empirical scalings exist to derive phase velocities and amplitudes for pure power-law velocity structures providing an exact relationship between the velocity model and the Green’s functions. However, no quantitative estimates of the accuracy of these simple scalings have been reported for impulsive sources in complex velocity structures. In this paper, we address this gap by comparing the theoretical predictions to high-order numerical solutions for the vertical component of the wavefield. The Green’s functions computation shows that attenuation-induced dispersion of phase and group velocity plays an important role and should be carefully taken into account to correctly describe how surface-wave amplitudes decay with distance. The comparisons confirm the general reliability of the semi-analytic model for power-law and realistic shear velocity structures to describe fundamental-mode Rayleigh waves in terms of characteristic frequencies, amplitudes and envelopes. At short distances from the source, and for large near-surface velocity gradients or high Q values, the low-frequency energy can be dominated by higher mode surface waves that can be captured by introducing additional higher mode Rayleigh-wave power-law scalings. We also find that the energy spectral density for realistic shear-velocity models close to piecewise power-law models can be accurately modelled using the same non-dimensional scalings. The frequency range of validity of each power-law scaling can be derived from the corresponding phase velocities. Finally, highly discontinuous near-surface velocity profiles can also be approximated by a combination of power-law scalings. Analytical Green’s functions derived from the non-dimensionalization provide a good estimate of the amplitude and variations of the energy distribution, although the predictions are quite poor around the frequency bounds of each power-law scaling.

Impact of Geometric Effects on Near-Surface Green's Functions

2013 ◽  
Vol 103 (6) ◽  
pp. 3289-3304 ◽  
Author(s):  
F. De Martin ◽  
S. Matsushima ◽  
H. Kawase
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Near Surface ◽  
Geometric Effects
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