Imaging of crustal heterogeneous structures using a slowness‐weighted back‐projection with effects of scattering modes: 1. Theory

This is the first paper in a two‐part series on a newly developed imaging approach for small‐scale heterogeneities (<1 km) in the crust with effects of scattering modes. To obtain a reliable crustal heterogeneous structure, we follow the six major steps: (1) removing overall complex propagation effects, including anelastic attenuation, by using a statistical technique with the use of the Akaike Information Criterion (AIC), (2) obtaining high‐resolution frequency‐wave number ( f ‐ k ) power spectra and slowness vectors of spectral peaks in the time‐frequency domain, based on a stationary autoregressive model, (3) estimating polarization vectors of the scattered waves identified in step 2 with a stationary multivariate autoregressive model, (4) determining scattering modes (i.e., P or S wave arrival) from the angle between the slowness and polarization vectors obtained in steps 2 and 3, respectively, (5) correcting effects of seismic‐source radiation and surface geology by a coda‐normalization approach, and finally (6) mapping the f ‐ k power spectra into small blocks in a model space as scattering coefficients, using a slowness‐weighted back‐projection. We can incorporate scattering modes as well as propagation effects such as anelastic attenuation factors in the background medium, with the AIC based amplitude recovery technique. The resolution in f ‐ k spectrograms and the accuracy of polarization estimates are significantly improved through the present approach, so that not only more scattered phases are clearly identified but also their spatial three‐dimensional locations are pinpointed more precisely and stably than previous approaches in imaging based on scattering theory.