S. Pilia 1,
∗
, N. Rawlinson 2 , R. A. Cayley 3 , T. Bodin 4 , R. Musgrave 5 , A. M. Reading 6 ,
N. G. Direen 6 , and M. K. Young 7
1 Research School of Earth Sciences, Australian National University, Canberra 0200,
Australia
2 School of Geosciences, University of Aberdeen, Aberdeen AB24 3UE, Scotland
3 Geological Survey of Victoria, Department of State Development, Business and
Innovation, GPO Box 4509 Melbourne, Victoria 3001, Australia
4 Berkeley Seismological Lab, University of California Berkeley, California, USA
5 Geological Survey of New South Wales, NSW Trade & Investment, 516 High Street,
Maitland, New South Wales 2320, Australia
6 School of Earth Sciences, Institute for Marine and Antarctic Studies and CODES
Centre of Excellence, University of Tasmania, Hobart, Tasmania, 7001, Australia
7 DownUnder GeoSolutions Pty Ltd, 76 Kings Park Rd., Perth, Western Australia,
6005, Australia
∗
Correspondence should be addressed to S.P. ( simone.pilia@anu.edu.au
)
S1
Rayleigh wave Green’s functions
In order to obtain the Rayleigh wave Green’s functions we employ the scheme developed by Arroucau et al 1 ., which is based on processing procedures described by Bensen et al 2 . The day-long seismic records are divided up into approximately 54 minute segments with 400 seconds of overlap. Segments that
1

contain anomalously large amplitudes, either from earthquake signals or instrument errors, are removed prior to applying a bandpass-filter between 0.01 and 2.0 Hz. Subsequently, the vertical-component is cross-correlated and stacked for all possible station pairs that ultimately produces the empirical
Green's functions (EGFs) of the Rayleigh wave component of the wavefield
(Figure S1). Thereafter, the fundamental mode Rayleigh wave group velocities are calculated (Figure S2) using the frequency - time analysis method of Levshin et al 3 . Before applying our Bayesian inversion approach, we firstly map the velocity information by using an efficient iterative, non-linear tomographic inversion scheme to evaluate the reliability of the group velocity measurements and yield bent rays through a robust grid-based eikonal solver, known as the fast marching method or FMM 4 .
S2 – Transdimensional Bayesian Inversion scheme
To better constrain the structures present in continental accretionary margins of this kind, we extract structural information from seismic noise data using a novel and robust transdimensional, hierarchical, Bayesian-driven tomographic approach. Modern statistical methods, coupled with fast, parallel computing architectures, allow us to perform robust, non-linear tomographic inversion, in this case via the reversible-jump Markov Chain Monte Carlo 5,6,7,8 (rj-MCMC) algorithm, which yields considerable improvements in crustal information compared to conventional methods. Key attributes of this approach include: i) the number, spatial distribution and value of parameters, as well as the level of noise, are unknowns in the inversion and implicitly controlled by the data; ii) solution represented by a large ensemble of data-fitting models that are
2

statistically distributed according to the posterior probability density function
(Bayesian inference). The final solution is therefore probabilistic and allow us to correctly propagate data noise into model uncertainties; iii) the inversion scheme is based on a parameter search and is fully non-linear. In this way, the function relating the seismic model to observations does not need to be linearized and the final solution does not depend on an initial model chosen by the user. We provide a very brief description of the method below, further details can be found in Bodin et al.
7,8,9 and Young et al.
10 .
The fundamentals of this approach are based on Bayes’ theorem 11 , in which a transdimensional posterior probability distribution is sought by combining prior information on the model m with the observed data d , according to the following expression: posterior
likelihood
prior which can be expressed as: p ( m | d obs
)
p ( d obs
| m )
p ( m ) where p ( m | d obs
) is the a posteriori probability distribution of the unknown model parameter m conditional on the observed data d obs
. The likelihood function, inferred by the expression p ( d obs
| m ) , is regarded as the probability of reproducing d obs
given a particular model m . Our knowledge about the model before using the data is incorporated in the a priori probability density p ( m ) , provided that it can be defined as a probability distribution. Any conclusion we make on the posterior distribution is relative to the prior information, which in our case corresponds to what we understand about the velocity field of the area. In order to minimise the influence on the results and rigorously follow the Bayesian
3

principles, we impose a prior that is as broad as possible by assigning two plausible bounds to the velocity distribution. Hence, the velocity is a uniform distribution allowed to vary from plus to minus 1 km/s, centred on the average group velocity for a particular period of interest (Figure S2).
The parameter space is explored with a random sampler (Markov chain), which is a generalization of the well-known Metropolis-Hasting algorithm 6 . The first step in a chain requires a randomly generated starting model, after which subsequent proposed models within the same chain will be drawn as a perturbation from the last, driven by a proposal probability distribution. The first strand of models produced after a certain number of iterations are tagged as trial and must be discarded as “burn-in” iterations. Thereafter, the random walk is assumed to have converged to a stable configuration, and the algorithm evolves by sampling the model space from the posterior distribution. In this study we perform a total of 310,000 iterations (taking approximately two weeks to accomplish), 80 thousan d of which were discarded during the “burn-in” period. This was carried out by exploiting 80 simultaneous and non-communicating Markov chains running in parallel on a cluster. One example of the Voroni cell distribution, along with the relative path coverage map, is shown in Figure S3.
Each iteration (i.e., a step in the Markov chain) requires the crucial decision of whether to replace the current model with the proposed model (conditional only on the current model), according to an acceptance probability distribution (see
Bodin et al.
7,8 for more details). It is important to note that the proposal function plays an important role in sampling the model. For instance, limited variations in the proposal function will lead to an undue level of acceptance and consequently the sampler will move slowly around the model space. In contrast, relatively
4

large jumps in the model space will result in a high rejection rate, with the risk of hampering the sampler 12 .
When the required number of iterations is complete, we extract the desired information from the ensemble of solutions to produce a naturally smoothed final model (Figure S4). Typically, a spatially averaged model is determined from the ensemble along with a statistical measure of uncertainty, such as standard deviation via a grid discretization, which in our study corresponds to a regular grid spacing of 15 km in both latitude and longitude (finer sampling was found to produce ultimately the same level of detail).
Practically, the algorithm has to be tuned as to the number of iterations, with parti cular care as to the number of “burn-in” iterations, the proposal function and the thinning of the chain. Furthermore, depending on the grade of resolution we are after, a grid spacing distance has to be provided for extraction of the final model. However, although such user-provided variables are in general not desirable, we find, as do previous users of the method, that the final results are generally invariant across a wide-range of sensibly-chosen input parameters.
In order to represent 3-D seismic structure beneath southeastern Australia, we sample the period-dependent group velocity field - obtained using the above procedure - at each point of a 2-D grid to generate 1-D group velocity dispersion curves, which will be subsequently inverted for 1-D shear wavespeed profiles.
The forward operation of predicting theoretical dispersion curves used in the inversion step is accomplished by using the software DISPER80, developed by
Saito 13 . Here, we assume that the number, position and velocity of the layers are all unknown during the inversion; the posterior is then a transdimensional
5

function and can be sampled with the rj-McMC algorithm used for the inversion of 2-D group velocity maps. However, instead of parameterizing the model by using 2-D Voronoi cells, we employ a variable number of layers with variable thickness of the layers through the 1-D inversion. The prior knowledge on shear wave velocity was set to vary between 2 and 5 km/s, while the uppermost 30 km of the crust is described by between 2 and 25 layers. We inverted a total of 5413 group dispersion curves, each of which provides a 1-D shear velocity model.
Each 1-D model is obtained by averaging an ensemble of 60,000 models, after
40,000 were discarded during t he “burn-in” period.
S3
– Resolution test and uncertainty maps
The reliability of our Bayesian inversion method has been verified by performing a resolution test based on synthetic data. Gaussian noise with a standard deviation equal to 1 s is added to the synthetic traveltimes to simulate uncertainties associated with the observational dataset. Due to the demanding computational requirements for partition modelling tomography, we carried out the resolution test for only one specific period (Figure S5).
Overall, the probabilistic approach applied here, although computationally expensive, faithfully recovers the input structures significantly better than the standard linearized inversion scheme. This is despite the fact that the underlying grid spacing of the linearized scheme is identical to that used to describe the synthetic model, which strongly preconditions the inversion towards the correct region of model space. In the case of the optimum linearized inversion solution, the exact level of noise is assumed known and the damping and smoothing are adjusted accordingly. By contrast the transdimensional scheme is provided with
6

no prior knowledge about structure nor the level of data noise, but still yields superior results. One characteristic that can be clearly inferred from the linearized recovered models is the tendency to smear out velocity anomalies.
This is not surprising given the well-known sensitivity of this approach to dominant raypath directions, something that is far less pronounced in the
Bayesian output. It can also be seen that the process of averaging the spatially varying Voronoi cells over many models produces a parsimonious smoothness that is directly controlled by the data. When compared to the linearized outputs, where the imposed smooth variations are applied globally to the velocity model, the transdimensional output is clearly superior when it comes to the recovery of sharp velocity discontinuities. It should be noted, however, that areas of strong velocity contrast or discontinuities exhibit larger standard deviations (Figure S6), indicating that their location may be uncertain. This is a not surprising consequence of the partition modelling approach that is used; the full posterior probability is expected to show a bi-modal distribution in such a scenario and the average model is a poor summary of this distribution. In such cases, if we were to extract the maximum or median of the posterior distribution, they would be closer to the true model. For more details see Bodin et al.
14 .
Clearly, the Bayesian inversion approach produces the most robust results, while the use of conventional ad hoc regularisation (damping and smoothing in this case) can strongly influence the results and yield patterns of anomalies that are more dictated by the restrictions of the method than the information contained in the data.
7

S4
– Tilt-filtered total magnetic intensity map
Variable thicknesses of post-Palaeozoic cover, which exceeds 5 km in parts of the Darling Basin and 10 km in Bass Strait, make upper crustal structure difficult to recognize in conventional presentations of aeromagnetic data. The tilt filter is a phase filter in which the first vertical derivative is normalised by the first horizontal derivative 15 . When applied to total magnetic intensity (TMI), it yields imagery that traces geological structure over a wide range in dynamic signal and depth of source 16 . The background image of Figure 1 shows tilt-filtered TMI as a color scale, using data from the 2010 compilation of Australian aeromagnetic data provided by Geoscience Australia, decimated to a 250 m grid.
8

Figure S1 - Crosscorrelation of ambient seismic noise
Crosscorrelograms calculated from one subarray in mainland Australia
(reference station E1D4), Tasmania (reference station TSM2) and Bass Strait
(reference stations BA01 and BA02). The characteristic move-out pattern of emergent Rayleigh waves can be clearly observed among the three examples.
9

Figure S2 - Group velocity measurements
Average group velocity measurements for each period examined for the arrays in mainland Australia, Bass Strait and Tasmania. Blue error bars represent the standard deviation of the dispersion of velocities.
10

Figure S3 - Raypath distribution and transdimensional parameterisation
Left Raypath coverage showing the irregular spatial distribution of data among the three main deployments. Right – One example of Voronoi cell distribution extracted from the inversion procedure after the “burn-in” period.
The plots make use of 8 s period data.
11

Figure S4 - Group velocity maps from 2 to 20 s
Group velocity maps of southeastern Australia for different periods, obtained by using a partition modelling inversion scheme. Below 6 s period, little coherent energy coupled with wavefield complexity such as multipathing, degrade the ability of tomography to recover accurate information, particularly where inter-station distance is relatively large (e.g., Bass Strait).
12

Figure S5 - Synthetic tests: Comparison of inversion methods applied
Resolution synthetic test for the 2-D Bayesian inversion method and linearized inversion with different regularization values applied. Gaussian noise with a standard deviation of 1 s was added to the synthetic traveltimes.
Yellow circles represent seismic stations.
13

Figure S6 - Uncertainty maps
Accompanying uncertainty maps (showing standard deviation values across the study area) for Figure S5.
14

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