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

Abstract

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. Copyright 2007 by the American Geophysical Union.