Misfit functions for seismic waveform inversion based on adjoint wavefield using curvilinear grid finite-difference method

The definition of misfit function takes an important part in seismic inversion which quantifies the differences between data and synthetics and evaluates the accuracy of the final model. Data coverage and different sensitivity of seismograms to different parts of earth's structure determine the seismic inversion resolution (Bozdag et al., 2011). In this case, extracting more information from seismograms becomes a key role in waveform inversion. In this study, we use the Hilbert transform in data processing, which is proposed in Bozdağ et al., (2011), to separate phase and amplitude information in time domain. This separation can lead the inverse problem from non-linear to quasi-linear (Fichtner et al., 2008). The relative adjoint sources are also defined to calculate adjoint wavefields, which is used to numerically determine Fréchet kernels with forward wavefields (Tromp et al., 2005). The 2D curvilinear grid finite difference method (Zhang & Chen, 2006), which can accurately implement topographic boundary conditions, is utilized as the numerical simulation method in the study. We use the phase and envelope misfits to construct adjoint kernels and see the kernel configurations in different structures. Due to the heterogeneities of structure, the data is always distorted and Born approximation is not adequate. With the comparison among the traditional L₂distance between data and synthetics, rms amplitude differences and cross-correlation time-shifts, the phase and envelope measurements show more robust way in determining misfit functions which can constrain different sensitivities in structure imaging.