The Canterbury Earthquake Sequence 2010-2011 (CES) induced widespread liquefaction in many parts of Christchurch city. Liquefaction was more commonly observed in the eastern suburbs and along the Avon River where the soils were characterised by thick sandy deposits with a shallow water table. On the other hand, suburbs to the north, west and south of the CBD (e.g. Riccarton, Papanui) exhibited less severe to no liquefaction. These soils were more commonly characterised by inter-layered liquefiable and non-liquefiable deposits. As part of a related large-scale study of the performance of Christchurch soils during the CES, detailed borehole data including CPT, Vs and Vp have been collected for 55 sites in Christchurch. For this subset of Christchurch sites, predictions of liquefaction triggering using the simplified method (Boulanger & Idriss, 2014) indicated that liquefaction was over-predicted for 94% of sites that did not manifest liquefaction during the CES, and under-predicted for 50% of sites that did manifest liquefaction. The focus of this study was to investigate these discrepancies between prediction and observation. To assess if these discrepancies were due to soil-layer interaction and to determine the effect that soil stratification has on the develop-ment of liquefaction and the system response of soil deposits.
In this paper we apply Full waveform tomography (FWT) based on the Adjoint-Wavefield (AW) method to iteratively invert a 3-D geophysical velocity model for the Canterbury region (Lee, 2017) from a simple initial model. The seismic wavefields was generated using numerical solution of the 3-D elastodynamic/ visco- elastodynamic equations (EMOD3D was adopted (Graves, 1996)), and through the AW method, gradients of model parameters (compression and shear wave velocity) were computed by implementing the cross-adjoint of forward and backward wavefields. The reversed-in-time displacement residual was utilized as the adjoint source. For inversion, we also account for the near source/ station effects, gradient precondition, smoothening (Gaussian filter in spatial domain) and optimal step length. Simulation-to-observation misfit measurements based on 191 sources at 78 seismic stations in the Canterbury region (Figure 1) were used into our inversion. The inversion process includes multiple frequency bands, starting from 0-0.05Hz, and advancing to higher frequency bands (0-0.1Hz and 0-0.2Hz). Each frequency band was used for up to 10 iterations or no optimal step length found. After 3 FWT inversion runs, the simulated seismograms computed using our final model show a good matching with the observed seismograms at frequencies from 0 - 0.2 Hz and the normalized least-squared misfit error has been significantly reduced. Over all, the synthetic study of FWT shows a good application to improve the crustal velocity models from the existed geological models and the seismic data of the different earthquake events happened in the Canterbury region.
