We have been able to demonstrate the feasibility of 3-D full waveform inversion on continental scales. Our approach rests on the interplay of several components that have specifically been designed for this purpose: a spectral-element solver that combines accuracy, speed and algorithmic simplicity; long-wavelength equiv- alent crustal models that allow us to increase the numerical grid size; an accuracy-adaptive integration scheme for the regular and adjoint wavefields; time-frequency misfits that extract as much useful informa- tion as possible and a rapidly converging conjugate-gradient algorithm with an empirical pre-conditioner. The numerical solution of the elastic wave ensures that the tomographic images are free from artefacts that can be introduced by simplifying approximations of seismic wave propagation in strongly heterogeneous media. Our results agree with earlier studies on length scales greater than500 km. Both long and short wavelength structures can be interpreted in terms of regional tectonic processes.
While full waveform tomography is now in principle feasible, there are several important problems that need to be solved in the years to come: Most importantly, we need to develop strategies to better assess the resolution of non-linear tomographic problems that are too expensive to be solved probabilistically.
Closely related are questions concerning the still somewhat conjectural higher resolution of full waveform inversion as compared to classical ray tomography. We must furthermore find quantitative estimates of waveform errors in order to evaluate the robustness of the full waveform tomographic images. To ensure that waveform differences are solely due to structure, inversions for potentially finite sources will need to be incorporated into future full waveform tomographies.
We finally wish to note that full waveform inversion is not an automatic procedure, and certainly not a black box that can be applied at will. From our experience with real-data applications, semi-automatic waveform inversions are likely to result in unreasonable Earth models, a slow convergence of the optimisa- tion scheme or both. A successful application requires a balancing of different types of waveforms based on physical insight, careful inspection of waveform differences after each iteration and intelligent guidance of the inversion scheme. In this sense, the optimisation algorithm described in section 8.3.3 should not be taken as a dogma from which no deviations through human intervention are allowed.
9
Full waveform inversion for radially anisotropic
structure: New insights into present and past states of
the Australasian upper mantle
In the previous chapter we derived a 3D tomographic model of the Australasian upper mantle from vertical- component waveforms. While the results are encouraging, the neglect of horizontal-component waveforms is contradictory to the philosophy of full waveform tomography: We wish to exploit as much waveform information as is possible or as is physically reasonable.
Including horizontal-component waveforms in our inversion scheme is, in principle, straightforward. It requires us, however, to allow for radial anisotropy, because three-component data can rarely be explained with an isotropic model.
The inference of radial anisotropy opens new perspectives for the interpretation of the tomographic images. This is because radially anisotropy is at least partly due to the lattice preferred orientation (LPO) of strongly anisotropic upper-mantle minerals such as olivine and orthopyroxene. Since large-scale LPO results from large-scale strain patterns, we can link radial anisotropy to deformation. Knowledge of anisotropic structure thus complements knowledge of isotropic structure from which we infer the thermochamical state of the upper mantle.
In the following paragraphs, we thus extend the methodology described in the previous chapters to include horizontal-component data. Our method allows us to explain 30 s waveforms in detail, and it yields tomographic images with unprecedented resolution. In the course of19conjugate-gradient iterations the total number of exploited waveforms increases from2200 to nearly 3000. The final model, AMSAN.19, therefore explains many data that were not initially included in the inversion. This is strong evidence for the effectiveness of the inversion scheme and the physical consistency of the tomographic model.
AMSAN.19 confirms long-wavelength heterogeneities found in previous studies, and it allows us to draw the following inferences concerning the past and present states of the Australian upper mantle and the formation of seismic anisotropy: (1) Small-scale neutral to low-velocity patches beneath central Australia are likely to be related to localised Paleozoic intraplate deformation. (2) Increasing seismic velocities between the Moho and150km depth are found beneath parts of Proterozoic Australia, suggesting thermochemical variations related to the formation and fragmentation of a Centralian Superbasin. (3) Radial anisotropy above150
depth reveals a clear ocean-continent dichotomy: We find strongvSH> vSVbeneath the Coral and Tasman
Seas. The anisotropy is strongest at the top of the inferred asthenospheric flow channel, where strain is expected to be largest. Radial anisotropy beneath the continent is weaker but more variable. Localised patches withvSH< vSVappear, in accord with small-scale intraplate deformation. (4) The ocean-continent
dichotomy disappears gradually between150−250 km depth, where the continental lithospheric mantle and the oceanic asthenosphere pass into the underlying convecting mantle. (5) Significant anisotropy exists below250km depth. Its character can be explained by sublithospheric small-scale convection and a change in olivine’s dominant glide system.
Figure 9.1: Comparison of three-component recordings at station CAN for an event that occurred near the island of Sumbawa. Observed waveforms are shown as black lines and synthetic waveforms as red lines. The synthetic waveforms were computed using model AMSV.11, that was derived from vertical-component data only. While the vertical-component waveform can be explained well, the horizontal-component synthetics arrive about10s too late.
9.1 The need for radial anisotropy: Observation of the Love-
Rayleigh discrepancy
Before we introduce radial anisotropy in our model of the Australasian upper mantle, we need to justify that it is indeed required. For this we consider figure 9.1. It shows a comparison of three-component recordings at station CAN for an earthquake that occurred near the island of Sumbawa. The synthetics were computed using model AMSV.11, that was derived from vertical-component data only. While the vertical-component seismogram can be explained well, the horizontal-component synthetics arrive about
10 s too late. This is one example for the very general observation that the SV model AMSV.11 can not explain horizontal-component data. Horizontal-component synthetics computed with AMSV.11 arrive almost always too late, indicating that the model is too slow. Increasing the S wave velocity in AMSV.11 could improve the fit of the horizontal-component waveforms, at the prize, however, of a significantly reduced fit to the vertical-component waveforms.
The observation that one single S velocity model can not explain three-component seismograms is com- monly referred to as Love-Rayleigh discrepancy. It can be resolved by introducing anisotropy with a radial symmetry axis. This type of anisotropy is also known as polarisation anisotropy or under the unfortunate name transverse isotropy.
A medium with radial anisotropy is fully described by 5 elastic parameters, and it allows for distinct SV and SH velocities. Based on our observation from figure 9.1, we can already anticipate that the SH wave speed,vSH, will almost always be larger than the SV wave speed,vSV.