An improved attenuation tomography method based on ambient noise cross-correlation
Authors: Peng Hongrui , Li Jiangtao 
Published: February 2023

In the last decade, Empirical Green&#8217;s functions (EGFs) derived from ambient noise cross-correlation have been widely and successfully applied to measure seismic velocity and its temporal variation. However, it is still pending whether the amplitude of EGFs is reliable and whether it could be utilized in attenuation tomography. From our perspective, to develop a noise interferometry-based attenuation tomography method, it is necessary to overcome difficulties from two significant aspects. Firstly, in preprocessing, the relative amplitudes between different station pairs should be preserved, which precludes standard techniques, including one-bit/running-absolute-mean normalization and spectral whitening. Secondly, in addition to the intrinsic attenuation, amplitudes are also affected by other factors, such as noise source distribution, geometric spreading, instrument response, site effect, focusing and defocusing effect, etc. To obtain precise attenuation, it is necessary to separate all those factors carefully before or during inversion.&#160;In this research, we develop a new workflow to perform attenuation tomography with ambient noise data. In preprocessing, we apply the asynchronous temporal flattening (ATF) normalization method (Zhou et al., 2020) to remove earthquake and abnormal signals in records while keeping relative amplitudes. Then we use the SNR and the symmetry of arrival times to select high-quality EGFs. Accounting focusing and defocusing effect of elastic heterogeneity, we predict it through finite-frequency theory (Zhou et al., 2004; Bao et al., 2016) and remove the effect from measured amplitudes. Finally, following the theory in (Weaver, 2013), we invert for attenuation, site effect, and wave field intensity of different incoming directions through a linear inversion. This workflow is feasible for both 1D and 2D arrays. It also delivers good results in the real data test of the Yellowstone national park region, with apparent high-attenuation anomaly beneath the Yellowstone Caldera.&#160;References:[1]L. Zhou, X. Song, and R. L. Weaver, &#8216;Retrieval of amplitude and attenuation from ambient seismic noise: synthetic data and practical considerations&#8217;, Geophysical Journal International, vol. 222, no. 1, pp. 544&#8211;559, Jul. 2020, doi: 10.1093/gji/ggaa194.[2]Y. Zhou, F. A. Dahlen, and G. Nolet, &#8216;Three-dimensional sensitivity kernels for surface wave observables&#8217;, Geophysical Journal International, vol. 158, no. 1, pp. 142&#8211;168, Jul. 2004, doi: 10.1111/j.1365-246X.2004.02324.x.[3]X. Bao, C. A. Dalton, and J. Ritsema, &#8216;Effects of elastic focusing on global models of Rayleigh wave attenuation&#8217;, Geophysical Journal International, vol. 207, no. 2, pp. 1062&#8211;1079, Nov. 2016, doi: 10.1093/gji/ggw322.[4]R. L. Weaver, &#8216;On the retrieval of attenuation and site amplifications from ambient noise on linear arrays: further numerical simulations&#8217;, Geophysical Journal International, vol. 193, no. 3, pp. 1644&#8211;1657, Jun. 2013, doi: 10.1093/gji/ggt063.