Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods

We present a full seismic waveform tomography for upper-mantle structure in the Australasian region. Our method is based on spectral-element simulations of seismic wave propagation in 3-D heterogeneous earth models. The accurate solution of the forward problem ensures that waveform misfits are solely due to as yet undiscovered Earth structure and imprecise source descriptions, thus leading to more realistic tomographic images and source parameter estimates. To reduce the computational costs, we implement a long-wavelength equivalent crustal model. We quantify differences between the observed and the synthetic waveforms using time-frequency (TF) misfits. Their principal advantages are the separation of phase and amplitude misfits, the exploitation of complete waveform information and a quasi-linear relation to 3-D Earth structure. Frechet kernels for the TF misfits are computed via the adjoint method. We propose a simple data compression scheme and an accuracy-adaptive time integration of the wavefields that allows us to reduce the storage requirements of the adjoint method by almost two orders of magnitude. To minimize the waveform phase misfit, we implement a pre-conditioned conjugate gradient algorithm. Amplitude information is incorporated indirectly by a restricted line search. This ensures that the cumulative envelope misfit does not increase during the inversion. An efficient pre-conditioner is found empirically through numerical experiments. It prevents the concentration of structural heterogeneity near the sources and receivers. We apply our waveform tomographic method to approximate to 1000 high-quality vertical-component seismograms, recorded in the Australasian region between 1993 and 2008. The waveforms comprise fundamental-and higher-mode surface and long-period S body waves in the period range from 50 to 200 s. To improve the convergence of the algorithm, we implement a 3-D initial model that contains the long-wavelength features of the Australasian region. Resolution tests indicate that our algorithm converges after around 10 iterations and that both long-and short-wavelength features in the uppermost mantle are well resolved. There is evidence for effects related to the non-linearity in the inversion procedure. After 11 iterations we fit the data waveforms acceptably well; with no significant further improvements to be expected. During the inversion the total fitted seismogram length increases by 46 per cent, providing a clear indication of the efficiency and consistency of the iterative optimization algorithm. The resulting SV-wave velocity model reveals structural features of the Australasian upper mantle with great detail. We confirm the existence of a pronounced low-velocity band along the eastern margin of the continent that can be clearly distinguished against Precambrian Australia and the microcontinental Lord Howe Rise. The transition from Precambrian to Phanerozoic Australia (the Tasman Line) appears to be sharp down to at least 200 km depth. It mostly occurs further east of where it is inferred from gravity and magnetic anomalies. Also clearly visible are the Archean and Proterozoic cratons, the northward continuation of the continent and anomalously low S-wave velocities in the upper mantle in central Australia. This is, to the best of our knowledge, the first application of non-linear full seismic waveform tomography to a continental-scale problem.