Finite‐Frequency Inversion of Cross‐Correlation Amplitudes for Ambient Noise Source Directivity Estimation

Abstract

We present a new method for determining the azimuthal variation of ambient noise sources, which combines the computational speed and simplicity of traditional approaches with the rigor of waveform-inversion-based approaches to noise source estimation. This method is based on a previously developed theoretical framework of sensitivity kernels for cross-correlation amplitudes. It performs a tomographic inversion for ambient noise sources on the Earth's surface and is suitable for small-(local-) scale studies. We apply the method to passive seismic data acquired in an exploration context and account for azimuth-dependent uncertainties in observed cross-correlation amplitudes. Our inversion results correlate well with the azimuthal distribution of noise sources suggested by signal-to-noise ratio analysis of noise cross-correlation functions.

noisi: A Python tool for ambient noise cross-correlation modeling and noise source inversion

“…power spectral densities of seismic noise, can be modeled for arbitrary noise source distributions. Finally, it can be utilized for noise source inversion when no updates to the Earth structure model are required, similar to the pioneering study by Nishida and Fukao (2007), who inverted observed cross-correlations for source distribution of the Earth's hum, and as performed by Ermert et al (2017); Xu et al (2018Xu et al ( , 2019 and Datta et al (2019).…”

“…CC BY 4.0 License. pre-calculated Green's functions have recently been applied to a variety of seismological problems, such as source inversion of earthquakes (Dahm et al, 2018;Fichtner and Simutė, 2018), landslides (Gualtieri and Ekström, 2018) and ambient noise (Ermert et al, 2017;Datta et al, 2019). Although the generation of such databases themselves often requires HPC resources, they can be shared to provide access to the results of costly wave propagation simulations to users without access to those resources.…”

“…To deal with sources of unknown, stochastic phase, it is commonly assumed that they are spatially uncorrelated when averaged over a sufficiently long observation span, or that their correlation length is far below observational resolution (e.g. Snieder, 2004;Nishida and Fukao, 2007;Tromp et al, 2010;Stutzmann et al, 2012;Hanasoge, 2013b;Farra et al, 2016;Xu et al, 2018;Datta et al, 2019). Upon this assumption, the noise sources can be described by their location-dependent power spectral density (PSD):…”

“…While the number of applications based on the Green's function assumption is large and rapidly increasing (Nakata et al, 2019), only a modest number of studies have presented models of ambient noise crosscorrelations themselves, i.e. numerical evaluations of cross-correlations due to distributed noise sources, rather than models of Green's functions (e.g., Nishida and Fukao, 2007;Tromp et al, 2010;Hanasoge, 2013a;Basini et al, 2013;Ermert et al, 2017;Sager et al, 2018b;Datta et al, 2019;Xu et al, 2018Xu et al, , 2019Sager et al, 2020).…”

Introducing noisi: a Python tool for ambient noise cross-correlation modeling and noise source inversion

“…Numerical models of noise auto-and crosscorrelations allow us to probe this assumption and eventually circumvent it (Halliday and Curtis, 2008;Fan andSnieder, 1598 L. Ermert et al: Noise modeling andinversion 2009;Cupillard and Capdeville, 2010;Kimman and Trampert, 2010;Fichtner, 2014;Stehly and Boué, 2017;Delaney et al, 2017). While the number of applications based on the Green's function assumption is large and rapidly increasing (Nakata et al, 2019), only a modest number of studies have presented models of ambient noise cross-correlations themselves, i.e., numerical evaluations of cross-correlations due to distributed noise sources rather than models of Green's functions (e.g., Nishida and Fukao, 2007;Tromp et al, 2010;Hanasoge, 2013a;Basini et al, 2013;Ermert et al, 2017;Sager et al, 2018bSager et al, , 2020Datta et al, 2019;Xu et al, 2018Xu et al, , 2019.…”