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 A Python framework for efficient use of pre-computed Green's functions in seismological and other physical forward and inverse source problems

Solid Earth ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 1921-1935 ◽  
Author(s):  
Sebastian Heimann ◽  
Hannes Vasyura-Bathke ◽  
Henriette Sudhaus ◽  
Marius Paul Isken ◽  
Marius Kriegerowski ◽  
...  
Keyword(s):  
Green's Functions ◽  
Heterogeneous Media ◽  
Green’S Functions ◽  
Application Programming Interface ◽  
Earth Model ◽  
Forward Modelling ◽  
Field Equations ◽  
Wide Range ◽  
Geophysical Processes ◽  
Numerical Calculation Method

Abstract. The finite physical source problem is usually studied with the concept of volume and time integrals over Green's functions (GFs), representing delta-impulse solutions to the governing partial differential field equations. In seismology, the use of realistic Earth models requires the calculation of numerical or synthetic GFs, as analytical solutions are rarely available. The computation of such synthetic GFs is computationally and operationally demanding. As a consequence, the on-the-fly recalculation of synthetic GFs in each iteration of an optimisation is time-consuming and impractical. Therefore, the pre-calculation and efficient storage of synthetic GFs on a dense grid of source to receiver combinations enables the efficient lookup and utilisation of GFs in time-critical scenarios. We present a Python-based framework and toolkit – Pyrocko-GF – that enables the pre-calculation of synthetic GF stores, which are independent of their numerical calculation method and GF transfer function. The framework aids in the creation of such GF stores by interfacing a suite of established numerical forward modelling codes in seismology (computational back ends). So far, interfaces to back ends for layered Earth model cases have been provided; however, the architecture of Pyrocko-GF is designed to cover back ends for other geometries (e.g. full 3-D heterogeneous media) and other physical quantities (e.g. gravity, pressure, tilt). Therefore, Pyrocko-GF defines an extensible GF storage format suitable for a wide range of GF types, especially handling elasticity and wave propagation problems. The framework assists with visualisations, quality control, and the exchange of GF stores, which is supported through an online platform that provides many pre-calculated GF stores for local, regional, and global studies. The Pyrocko-GF toolkit comes with a well-documented application programming interface (API) for the Python programming language to efficiently facilitate forward modelling of geophysical processes, e.g. synthetic waveforms or static displacements for a wide range of source models.

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.

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