Abstract
In seismic waveform analysis and inversion, data functionals can be used to quantify the misfit between observed and model-predicted (synthetic) seismograms. The generalized seismological data functionals (GSDF) of Gee & Jordan quantify waveform differences using frequency-dependent phase-delay times and amplitude-reduction times measured on time-localized arrivals and have been successfully applied to tomographic inversions at different geographic scales as well as to inversions for earthquake source parameters. The seismogram perturbation kernel is defined as the Fréchet kernel of the data functional with respect to the seismic waveform from which the data functional is derived. The data sensitivity kernel, which is the Fréchet kernel of the data functional with respect to structural model parameters, can be obtained by composing the seismogram perturbation kernel with the Born kernel through the chain rule. In this paper, we extend GSDF analysis to broad-band waveforms by removing constraints on two control parameters defined in Gee & Jordan and derive the seismogram perturbation kernels for the modified GSDF analysis. The modifications given in this paper are consistent with the original GSDF theory in Gee & Jordan around the centre frequency and improve the stability of GSDF analysis towards the edges of the passband. We also present numerical examples of perturbation kernels for the modified GSDF analysis and their data sensitivity kernels using a homogenous half-space structure model and a complex 3-D structure model.
Highlights
Advances in parallel computing technology and numerical methods have made large-scale, 3-D numerical simulations of seismic wavefields much more affordable and they open up the possibility of ‘full 3-D tomography’ (F3DT), in which the starting model as well as the derived model perturbation is 3-D in space and the Frechet kernel is computed using the full physics of 3-D wave propagation
Two physically equivalent but computationally distinct approaches to F3DT (Chen et al 2007a) have been developed, the scattering-integral (SI) method, which sets up the inverse problem by calculating and storing the Frechet kernels for individual misfit measurements (Zhao et al 2005) and the adjoint-wavefield method, which constructs the gradient of the objective function through correlating the forward wavefield from the source and the adjoint-wavefield from the receivers (Tarantola 1986; Tromp et al 2005)
We extend generalized seismological data functionals (GSDF) analysis to broad-band waveforms by removing constraints on two control parameters defined in Gee & Jordan (1992): the pre-filtering parameter ξ0 and the frequency-shift parameter ξ3
Summary
Advances in parallel computing technology and numerical methods have made large-scale, 3-D numerical simulations of seismic wavefields much more affordable and they open up the possibility of ‘full 3-D tomography’ (F3DT), in which the starting model as well as the derived model perturbation is 3-D in space and the Frechet kernel is computed using the full physics of 3-D wave propagation. C 2010 The Authors Geophysical Journal International C 2010 RAS to image the crustal structure in Southern California using waveform data from local earthquakes and Fichtner et al (2009) has adapted the adjoint-wavefield method to continental-scale tomography and inverted for upper-mantle structure in the Australasian region. In these successful F3DT applications, time- and frequencydependent phase and amplitude anomalies were used to quantify the misfit between synthetic and observed seismograms. The formulation given in this paper has been successfully applied in the F3DT for the Los Angeles Basin region in Chen et al (2007b)
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