Geophys. J. Int. (2002) 151, 738–754 Multimode Rayleigh wave inversion for heterogeneity and azimuthal anisotropy of the Australian upper mantle ∗ Frederik J. Simons,1, Rob D. van der Hilst,1 Jean-Paul Montagner2 and Alet Zielhuis1 1Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. E-mail: [email protected] 2D´epartement de Sismologie, Institut de Physique du Globe, 75005 Paris, France Accepted 2002 June 10. Received 2002 May 8; in original form 2001 January 26 SUMMARY We present an azimuthally anisotropic 3-D shear-wave speed model of the Australian upper mantle obtained from the dispersion of fundamental and higher modes of Rayleigh waves. We compare two tomographic techniques to map path-average earth models into a 3-D model for heterogeneity and azimuthal anisotropy. Method I uses a rectangular surface cell parametriza- tion and depth basis functions that represent independently constrained estimates of radial earth structure. It performs an iterative inversion with norm damping and gradient regular- ization. Method II uses a direct inversion of individual depth layers constrained by Bayesian assumptions about the model covariance. We recall that Bayesian inversions and discrete reg- ularization approaches are theoretically equivalent, and with a synthetic example we show that they can give similar results. The model we present here uses the discrete regularized inversion of independent path constraints of Method I, on an equal-area grid. With the exception of westernmost Australia, we can retrieve structure on length scales of about 250 km laterally and 50 km in the radial direction, to within 0.8 per cent for the velocity, 20 per cent for the anisotropic magnitude and 20◦ for its direction. On length scales of 1000 km and longer, down to about 200 km, there is a good correlation between velocity heterogeneity and geologic age. At shorter length scales and at depths below 200 km, however, this relationship breaks down. The observed magnitude and direction of maximum anisotropy do not, in general, appear to be correlated to surface geology. The pattern of anisotropy appears to be rather complex in the upper 150 km, whereas a smoother pattern of fast axes is obtained at larger depth. If some of the deeper directions of anisotropy are aligned with the approximately N–S direc- tion of absolute plate motion, this correspondence is not everywhere obvious, despite the fast (7 cm yr−1) northward motion of the Australian plate. More research is needed to interpret our observations in terms of continental deformation. Predictions of SKS splitting times and direc- tions, an integrated measure of anisotropy, are poorly matched by observations of shear-wave birefringence. Key words: Australia, azimuthal anisotropy, heterogeneity, inversion, surface-waves, tomog- raphy. requires both the presence of anisotropic crystals and their (strain- 1 INTRODUCTION induced) preferred orientation on seismic length scales, anisotropy The Earth is heterogeneous and anisotropic on many length scales. measurements contain information about the mineralogy and dy- Polarization anisotropy (modelled by transverse isotropy with a ver- namics of the mantle (see, e.g. Silver 1996; Plomerov´a et al. 1998; tical symmetry axis) affects fundamental and higher-mode surface- Savage 1999; Kendall 2000). wave propagation. Body- and surface-wave velocities are dependent Knowledge of continental velocity heterogeneity and anisotropy on propagation azimuth. Shear-wave birefringence reflects trans- may answer a number of outstanding questions. These include the verse isotropy with a horizontal symmetry axis. Since anisotropy very definition of the base of the continental lithosphere, the rela- tion between the depth extent of the lithosphere and the age of the overlying crust, and the deformation of the continental lithospheric ∗ Now at: Princeton University, 321B Guyot Hall, Princeton, NJ 08544 mantle and the underlying asthenosphere. 738 C 2002 RAS Australian upper-mantle tomography with anisotropy 739 It has been argued that continental seismic anisotropy is best present study (Fig. 1). Waveform inversions of vertical-component explained by a combination of ‘frozen’ (subcrustal) anisotropy, de- fundamental and higher-mode Rayleigh-wave data have yielded de- veloped during major orogenic events, underlain by an actively de- tailed information on the 3-D isotropic S-wave speed variations of forming asthenosphere which displays anisotropy generated by the the continent and the adjacent oceanic areas (Zielhuis & van der subhorizontal alignment of olivine crystals by present-day mantle Hilst 1996; Simons et al. 1999; Debayle & Kennett 2000a). flow (Silver 1996). However, considerable ambiguity exists regard- The azimuthal anisotropy measured by Debayle (1999) and ing the amount and location of anisotropy inferred from body waves. Debayle & Kennett (2000a) changes from a regime with fast- Surface-wave waveform tomography allows the delineation of changing directions in the upper 150 km to smoother North-South lateral heterogeneities in the upper mantle with better radial reso- patterns below 150 km, and an analysis of Love and Rayleigh waves lution than body-wave traveltime tomography. A variety of meth- by Debayle & Kennett (2000b) shows polarization anisotropy ex- ods has been developed to extract the variation of wave speed with tending down to about 200–250 km. depth from surface waves, (e.g. Nolet et al. 1986; Cara & Lev´ equeˆ In this paper, we present a new model for the Australian upper 1987), and a number of tomographic methods to invert for aspher- mantle that takes into account both wave-speed heterogeneity and ical structure exist (e.g. Montagner 1986; Nolet 1990). Inversions azimuthal anisotropy. We quantify resolution and uncertainty by of surface waves for heterogeneity have traditionally been restricted means of synthetic tests, trade-off estimates, and an exact calcu- to fundamental modes but more recent models have incorporated lation of the horizontal resolution matrix. While there is a general higher-mode measurements, thereby enhancing the resolution down agreement between the long-wavelength structures imaged in our to depths of about 400 km. Inversions for both heterogeneity and present model and the one by Debayle & Kennett (2000a) (here- azimuthal anisotropy have been made using fundamental modes after: DK2000), there are substantial differences in heterogeneity (e.g. Montagner & Jobert 1988; Nishimura & Forsyth 1989) and and anisotropic structure at wavelengths smaller than about 500 km multimode waves (Lev´ equeˆ et al. 1998; Debayle & Kennett 2000a). even in regions for which both groups claim good resolution. Local measurements of the seismic structure of the Australian Like DK2000, in this paper we attempt to invert for 3-D struc- upper mantle have indicated the presence of a high-velocity litho- ture starting from path-average models. The validity of the approx- spheric lid down to ∼200 km in Northern Australia (e.g. Dey et al. imation of independent propagation of the individual modes of the 1993; Kennett et al. 1994), and to ∼300 km in Central Australia seismogram has been explored theoretically (Kennett & Nolet 1990; (Gaherty & Jordan 1995; Gaherty et al. 1999). Seismic anisotropy Kennett 1995; Meier & Malischewsky 2000) and been found to be has been proposed for the upper mantle under Central Australia subject to certain frequency limitations, to which we adhere. As down to 200–300 km (Gaherty et al. 1999), and between 210 and the frequency bounds for uncoupled mode propagation presume a 410 km depth under Northern Australia (Tong et al. 1994). Girardin scale length of lateral heterogeneity, DK2000 conclude one should & Farra (1998) report evidence for two-layer anisotropy in southeast be wary of comparing differences in our and their model on lat- Australia. The conflicting results of different shear-wave birefrin- eral length scales shorter than 300 km. DK2000 report noticeable gence studies (Clitheroe & van der Hilst 1998; Ozalaybey¨ & Chen differences from great-circle propagation through their model at fre- 1999) indicate that the anisotropy of the Australian continental man- quencies >25 mHz. In the present paper, the higher-mode window tle is complex and not yet well understood. of the waveforms is fit up to 50 mHz where possible. Ideally, the The SKIPPY experiment (van der Hilst et al. 1994) has produced a capability of our models to explain the observed waveforms needs unique broad-band data set of seismic waves propagating all across to be tested with 3-D wave propagation techniques (e.g. Komatitsch the Australian lithosphere, resulting in the path coverage used in the & Tromp 1999). Figure 1. Path coverage. About 2250 vertical-component seismograms provided waveforms which were fitted to obtain the model presented in this paper. The stations belong to the SKIPPY, KIMBA, AGSO, IRIS and GEOSCOPE arrays. We used earthquake locations from Engdahl et al. (1998). C 2002 RAS, GJI, 151, 738–754 740 F.J. Simons et al. In addition to differences in the waveform inversion technique, Clitheroe et al. 2000a,b). This is arguably the most accurate crustal the tomographic inversion method used to obtain the model pre- model to date of the Australian continent. sented in this paper differs from the one used by DK2000. They use a form of the regionalized inversion method due to Montagner (1986), while we use the discretely parametrized, regularized inver- sion method introduced