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Australian Journal of Earth Sciences (2011) 58, ( ) Seismic wave attenuation beneath the Australasian region B. L. N. KENNETT* AND A. ABDULLAH { Research School of Earth Sciences, The Australian

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Australian Journal of Earth Sciences (2011) 58, ( ) Seismic wave attenuation beneath the Australasian region B. L. N. KENNETT* AND A. ABDULLAH { Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia The attenuation of seismic waves is strongly influenced by temperature and rheological changes, and so provides an important supplement to information from seismic wavespeeds. Differential attenuation measurements are made for seismic waves refracted through the mantle beneath the Australasian region and are then used to construct 3D images of the attenuation of shear and compressional waves. The differential attenuation between different seismic phases is estimated using a spectral ratio method in the frequency band Hz using a multi-taper method. Over this band the attenuation is nearly independent of frequency so that the logarithmic spectral ratio is a linear function of frequency. Differential measurements are made either between P and S phases on the same record or between stations for P and S waves separately. Images of seismic attenuation for the Australasian region are produced using a tomographic inversion, with the fast marching method employed to trace ray paths in an initial 3-D model derived from surface wave tomography. There is a deep seated horizontal contrast between central Australia and the eastern seaboard. The crustal and lithospheric mantle beneath the Archean and Proterozoic rocks in the west and in the middle of the continent have low seismic attenuation, whereas the Phanerozoic material in the east is more attenuative. Regions with recent volcanism, most likely associated with hot spots such as near Bass Strait and the Coral Sea, display high seismic attenuation anomalies. There is a strong contrast in attenuation between the relatively low loss lithosphere and the high loss asthenosphere beneath with a change by a factor of Anisotropy in attenuation is slight even though some would be expected from the radial anisotropy seen in shear wavespeed in the lithosphere. KEY WORDS: seismic waves, attenuation, tomography, Australian continent, lithosphere, asthenosphere. INTRODUCTION Over the last two decades, a wide range of studies have been used to understand the 3-D structure in the mantle beneath the Australian continent by exploiting different aspects of seismograms. Many different methods have been employed (see e.g. Kennett 2003; Fichtner et al. 2010) with most attention directed to understanding the distribution of seismic wavespeeds. Most work has been carried out using the techniques of seismic tomography, either exploiting the seismic waveforms for the large amplitude surface waves that travel nearly horizontally, or using the travel times of body waves along thousands of propagation paths in which case, the sampling is closer to vertical. Knowledge of the pattern of seismic attenuation in the Australian region is still limited. Seismic attenuation is important because it is particularly sensitive to temperature and rheological processes (see e.g. Jackson 2000), with a rapid increase in attenuation as the solidus is approached. Studies on seismic attenuation of the Australasian region were initiated by Gudmundsson et al. (1994) who presented an attenuation profile of the upper mantle beneath the north of the continent. This work indicated the presence of a zone of strong attenuation below the lithosphere under northern Australia but with a limited number of events, was not able to localise the behaviour. Subsequently Cheng (2000) studied Australian attenuation structure using the spectral ratio between P and S phases for nearly 2000 three-component seismograms for paths refracted back from the upper mantle recorded between 1993 and The differential attenuation data were organised into azimuthal corridors across the continent and then inverted for 1-D attenuation structure using the Neighbourhood Algorithm (Sambridge 1999). A quasi 3-D attenuation model at fixed frequency was then constructed by combining the set of 1-D attenuation profiles weighted by ray density. The results clearly delineate major contrasts in seismic attenuation between the cratonic structures in the centre and west of Australia and the younger eastern zone where attenuation is much stronger. The continuing sequence of deployments of portable broadband seismic stations across Australia has significantly increased the number of propagation paths providing suitable sampling of the region. In this work nearly 6500 seismograms recorded in the period from *Corresponding author: { Present address: ExxonMobil Oil Indonesia Inc., Jakarta, 10210, Indonesia. ISSN print/issn online Ó 2011 Geological Society of Australia DOI: / 286 B. L. N. Kennett and A. Abdullah are exploited to provide differential attenuation measurements that are then used to produce seismic attenuation images beneath the Australasian region using a tomographic technique. The resulting images of attenuation structure provide further insights into the lithospheric and asthenospheric structure and temperature distribution beneath the Australian continent and its surroundings. ATTENUATION STRUCTURE The mineral assemblages in the crust and mantle have a very complex rheology; although in the short time span associated with the passage of a seismic wave the behaviour is nearly elastic, some energy is lost through anelastic processes, such as dislocation motion and defect movement. A convenient measure of the rate of energy dissipation is provided by the loss factor Q 71, the ratio of the energy loss in a wave cycle to the elastic energy in the oscillation (see e.g. Kennett 2001). An alternative representation of the cumulative attenuation along a propagation path is provided by the quantity t ¼ R ds Q 1 =v, where the integral is taken along the path with a local propagation wavespeed v. We here exploit differential t* between different seismic phases extracted using logarithmic spectral ratios in the frequency domain. We use either P and S phases on the same station, or a set of P or S phases from the same event recorded at multiple stations. Because interpretation of the attenuation results depends on knowledge of the seismic wavespeed we need also to construct a suitable model for the wavespeed distribution. Seismic data Thousands of seismic events from the Australasian region have been archived since 1992 by the Research School of Earth Sciences, Australian National University, from a major program of deployment of portable broadband seismic stations across Australia in experiments primarily designed to improve knowledge of the 3-D structure of the region. The data coverage exploited in this work is presented in Figure 1, which shows the location of both events and receivers and the great-circle paths between them (in grey). Seismic events with body wave magnitudes between 5.0 and 7.0 with epicentral distances out to 408 were selected over the Figure 1 Seismic ray paths exploited in the attenuation study with epicentral distances out to 408. The great-circle paths from event to receivers are indicated in grey. The portable broadband stations are shown by black triangles. The seismic events are colour coded for depth and the symbol size depends on magnitude mb (between 5.0 and 7.0); mb 0.0 is used where a magnitude is not provided. Seismic attenuation beneath Australasia 287 Figure 2 Example of implementation of the spectral ratio method using a graphical user interface (Matlab) for an event near Halmahera at a depth of 70 km recorded at station TL13. The background noise and the signal spectra for both P and S are estimated using the Multitaper method. The differential attenuation is extracted from the slope of natural logarithm of spectral ratio between S and P spectra over the frequency range from 0.25 to 1.00 Hz. The upper panel displays the seismic traces and the windows used for analysis: Z vertical component, R, T radial and transverse components to the path, H horizontal ground speed. The lower panels show the spectra in each window compared to the preceding noise, and the behaviour of the logarithmic spectral ratios as a function of frequency. period The hypocentral parameters were taken from the reprocessed catalogue of Engdahl et al. (1998) and its subsequent updates. The depth range of the events lies between 3 and 670 km, as indicated by the colour coding. The majority of events in the useful distance range of to stations in Australia are located to the north and to the east of Australia in Indonesia, New Guinea, New Caledonia, Tonga to New Zealand, and the Philippines. There are only a limited number of events to the south mainly on the mid-oceanic ridge between Australia and Antarctica; nevertheless, these events still provide valuable information. The northern part of the continent has a good coverage of seismic data except for the Great Sandy Desert area in the northwest, where there are major logistical difficulties for the deployment of portable stations. Attenuation measurements As in the work of Gudmundsson et al. (1994), the differential attenuation is estimated using a spectral ratio method. In the frequency domain at angular frequency o, the spectrum of a recorded seismic phase for epicentral distance r, at an azimuth y from the source can be expressed as: uðo; rþ ¼ SðoÞBðÞC y s ðoþmðo; rþc r ðo; rþiðoþ where S(o) is the source spectrum, B(y) is the source radiation pattern, C s (o) is the crustal contribution at the source, M(o, r) is the mantle contribution, and C r (o, r)isthe contribution from the receiver crust. The spectrum imparted by the source is modulated by the instrumental response I(o). The main component arising from the mantle ð1þ 288 B. L. N. Kennett and A. Abdullah will be a geometrical spreading factor g(r) and an exponential amplitude loss associated with attenuation: Mðo; rþ ¼gr ðþexp o Z dr ð2þ 2 Qðo; rþvr ðþ For the same event, the spectral ratio between two seismic phases such as P and S cancels most of the effects of the source and instrumental functions. When the phases have similar propagation paths, the crustal effects and radiation pattern also largely cancel. The logarithmic spectral ratio then takes the form: ln uðoþ Z Z S uðoþ ¼ o dr dr þ ln g S ðþ r P 2 S Q S V S P Q P V P ln g P ðþþf r ðo; rþ ð3þ where f(o, r) is a very weakly varying function of frequency associated with imperfect cancellation of crustal effects in the narrow band of frequencies employed. The geometrical spreading is independent of frequency and so the dominant frequency-dependent contribution is the effect of attenuation. Equation (3) can therefore be expressed as: ln uðoþ S uðoþ ¼ o P 2 ðt S t P Þþc ¼ pfðt S t P Þþc The logarithmic spectral amplitude ratio thus has a linear dependence on frequency f with a slope determined by the differential attenuation DtSP ¼ðt S t PÞ between the S and P arrivals. This enables estimates of differential attenuation to be extracted by linear regression over the seismic frequency band ( Hz) for which the attenuation is not expected to vary significantly with frequency. A similar treatment can be made for the same seismic phase from a single event recorded at two different stations to determine differential attenuation ð4þ factors DtPP, Dt SS. When an event is recorded by a number of stations it is convenient to designate one as a reference and carry out the differential attenuation measurements with respect to that station. Differential attenuation measurements have been made from nearly 6500 high-quality three component seismograms using a graphical user interface implemented in the Matlab computer programming environment (Figure 2). Spectra for the P phase are extracted from the vertical component (Z) and S phase spectra from the transverse (T) and radial component (R), after rotation to the great-circle between source and receiver. In addition, the horizontal ground speed H, Ö(R 2 þ T 2 ), is constructed from the R and T traces; the quantity H has the advantage of not depending on the orientation of the path. The spectra are calculated for a time window of between 25 and 45s and compared with the noise in the immediately preceding window. The location of the phase windows are predicted using the ak135 model of Kennett et al. (1995), and then adjusted by hand picking to obtain a more accurate estimate. The spectral windows start 1 s before the estimated P arrival time and 3 s before the S pick. The travel times for the P and S phases are used to build the 3-D velocity structure necessary to interpret the differential attenuation measurements. Figure 2 illustrates the measurement of the differential attenuation between S and P waves (DtSP ) for an event near Halmahera at a depth of 70 km. The station lies at an epicentral distance of 208 from the station TL13 in southern Australia. No filtering has been applied to the velocity seismograms. The time windows used to estimate the spectra for signal and background noise for both P and S waves are 40 s long. All the spectra are estimated using the multitaper method (Percival & Walden 1993), which provides a stable spectral estimate. As would be expected the spectrum for the S phase spectrum decays more rapidly than that for the P phase, but both show a similar character with frequency. The Figure 3 Summary of the differential attenuation between S and P waves (DtSP ) estimated from over 6000 paths. The three panels represent different ranges of epicentral distance D: (a) dominantly lithospheric propagation (b) returns form the mantle transition zone waves turning below the 660 km discontinuity. The great-circle paths for the DtSP measurements are colour coded by the value of DtSP, with a line thickness inversely proportional to the error in the Dt SP estimation, ranging from 0.1 to 1.0, so that emphasis is given to the best determined results. The red lines represent plate-tectonic boundaries. Seismic attenuation beneath Australasia 289 differential attenuation (DtSP ) is extracted from the slope of the natural logarithm of the spectral ratio between the S and P phases over the restricted frequency range from 0.25 to 1.00 Hz. Figure 3 provides a summary of the Dt* SP differential attenuation results for the Australian seismic dataset. The great-circle paths between source and receiver are plotted and colour coded by the value of Dt* SP for three Figure 4 Chequer-board test of the recovery of velocity structure from tomographic inversion at , and km depth with different cell sizes: (a d) 98 and (e h) 68. The panels (b d) and (f h) represent the recovered images for each tomographic inversion. (a) and (e) are the input structure where the anomalies have maximal perturbations of +2% relative to the ak135 model. 290 B. L. N. Kennett and A. Abdullah groups of epicentral distances D: sampling the lithosphere, with waves returned from the transition zone in the upper mantle, and with arrivals turning below the 660 km discontinuity. The Dt* SP values represent the average for the path between source and receiver. At first sight negative values for Dt* SP may seem surprising, but the variation in the v p /v s ratio with depth mean that P and S waves do not have the same propagation paths. It is thus possible for P waves to sample the lower Q asthenosphere while S waves remain within the higher Q lithosphere with less loss. This feature is seen in the cratonic areas of northern and western Australia that have a relatively thick lithosphere. Tomographic inversion In a similar way to the travel times of P and S waves, the differential attenuation measurements for DtSP represent an integral along the propagation path. For the P and S phases, the differential measurements DtPP and DtSS represent the difference of two path integrals. We are therefore able to employ the attenuation results in a two-stage tomographic inversion based on the treatment of Rawlinson & Sambridge (2003). First, we exploit the arrival times of the P and S wave arrivals for all the paths illustrated in Figure 1 to develop a 3-D model for the seismic wavespeeds in the upper mantle. Then, we are able to invert for the 3-D distribution of the loss factor Q 71, by calculating the requisite path integrals in a proposed model and then comparing the results to the observations. We employ a cellular model to represent both the seismic wavespeed and the attenuation structure, with uniform properties in each cell. To ensure stability in the tomographic inversion we employ regularisation through a combination of damping towards a background model and constraints on gradients to produce a smoothly varying model. The station distribution across the continent has some holes and the regularisation provides a means of interpolation across such data gaps. The model volume encompasses the region of interest around Australia: from latitude 228N to 658S, longitude 788 to 1898E and from 0 to 1240 km in depth. The lithosphere and the mantle are divided into 10 layers with layer thicknesses ranging from 35 to 100 km in the lithosphere and upper mantle and from 100 to 200 km in the transition zone and upper mantle. We use a uniform grid of constant velocity and attenuation cells with horizontal size Several cell sizes were examined (18618, and 38638), and we found that the best balance between resolution and ray sampling was Figure 5 Misfit function (w 2 ) for the inversion, for attenuation from DtSP, as a function of the number of iterations, with the corresponding attenuation images for the depth interval from km. As the number of iterations increases, smaller scale features become prominent. Seismic attenuation beneath Australasia 291 achieved with cells. With this model parameterisation, the total number of unknowns to be extracted from the tomographic inversion is about 11,100. Chequer-board tests Before producing tomographic images from the inversion of the Australian data set, a set of chequer-board tests were carried out to evaluate the model parameterisations and the inversion method. We examine how well artificial wave-speed anomalies are recovered upon inversion using the actual geometry of sources and receivers. The 3-D ray-tracing is undertaken using the fast-marching method (Rawlinson & Sambridge 2003) that provides a stable means of tracking wavefronts through complex structures (Rawlinson & Sambridge 2004). In this chequer-board test, a set of synthetic models are divided into alternating regions of high and low wavespeed with patch sizes of or The input model is a simple structure of S wave perturbation with the anomalies having maximum perturbations of +2% relative to the ak135 model (Kennett et al. 1995) as illustrated in Figure 4a, e. Figures 4b d and 4f h show the results from the inversions for these imposed structures for particular depth slices. The quality of the inversion can be judged by the extent of the recovery of the original chequer-board pattern. The recovery of structure is quite good in the northern part of Australia where the raypath density is high. Although the southern margin of the continent has limited ray sampling, the chequer-board tests still show a reasonable result. Parts of the structure show some degree of streaking associated with the dominant directions of wave propagation. As is inevitable with limited sampling there is some loss in the amplitude of the patterns recovered in the tomographic inversion. Attenuation models The initial model used for 3-D ray tracing was derived from the shear wavespeed results of Fishwick et al. (2005) from surface wave tomography. The ray tracing was carried out using the fast-marching method of Rawlinson & Sambridge (2003). Wavespeed inversion is then applied to determine the deviations from the initial model, and then the resulting velocity field is used in the inversion of the differential attenuation results (DtSP ; Dt PP and Dt SS ) to produce shear (transverse and radial) and compressional a

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