Locating Spatial Changes of Seismic Scattering Property by Sparse Modeling of Seismic Ambient Noise Cross‐Correlation Functions: Application to the 2008 Iwate‐Miyagi Nairiku ( M w 6.9), Japan, Earthquake

Locating change regions of seismic velocities and seismic scattering properties associated with volcanic activities and earthquakes is important for structural monitoring. To increase such applications, we propose to use sparse modeling to estimate spatial distributions of seismic scattering property changes. The sparse modeling is an inversion technique that enables us to estimate model parameters from a small data set with sparsity condition such as ℓ 1 norm regularization. We apply this technique to seismic ambient noise cross‐correlation functions from 17 Hi‐net stations around the epicenter of the 2008 Iwate‐Miyagi Nairiku, Japan, earthquake ( M w =6.9). We compute waveform decoherences at the 0.5–1 Hz band and invert the waveform decoherences for the spatial distributions of seismic scattering property changes. Just after the main shock, the largest change occurred at the south of the epicenter, and the maximum change of the scattering coefficient in this region is estimated to be 0.032 km −1 . The result from an ordinary linear least squares inversion with the ℓ 2 norm regularization is almost consistent with that from the sparse modeling. Moreover, we confirm the superiority of sparse modeling in imaging with smaller data sets. Only five seismic stations that are deployed near the epicenter so as to surround the change regions are necessary to retrieve the result from 17 stations. On the other hand, in the case of the ℓ 2 norm regularization, we need at least 15 stations. The sparse modeling will be helpful to estimate the spatial distribution of seismic scattering property changes from a small data set.