Hrvoje Tkalcic

Transdimensional inversion of receiver functions and surface wave dispersion

[1] We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade-offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South-East Australia) are jointly inverted to provide a probabilistic 1D model of shear-wave velocity beneath a given station.

The effect of D″ on PKP(AB−DF) travel time residuals and possible implications for inner core structure

Abstract The hypothesis that the deep inner core is anisotropic is based on PKP travel time observations at large distances and relies on a small number of very anomalous measurements for paths quasi-parallel to the Earth’s rotation axis. Here, we analyze a global dataset of PKP(AB−DF) travel times residuals, and discuss their significant dispersion (±2 s), and coherent large scale patterns. We show that the trends observed for quasi-equatorial paths are consistent with predictions from recent tomographic mantle models, when the latter are modified to account for strong heterogeneity at the base of the mantle under the Pacific Ocean and Africa, as documented in several recent studies. Likewise, for polar paths, we show that a large part of the signal could be explained by deep mantle structure. The effects of complex structure in the deep mantle on PKP(AB−DF) travel times should be carefully considered in order to reliably estimate the anisotropic structure of the central part of the inner core.

Transdimensional inference in the geosciences

Seismologists construct images of the Earths interior structure using observations, derived from seismograms, collected at the surface. A common approach to such inverse problems is to build a single ‘best’ Earth model, in some sense. This is despite the fact that the observations by themselves often do not require, or even allow, a single best-fit Earth model to exist. Interpretation of optimal models can be fraught with difficulties, particularly when formal uncertainty estimates become heavily dependent on the regularization imposed. Similar issues occur across the physical sciences with model construction in ill-posed problems. An alternative approach is to embrace the non-uniqueness directly and employ an inference process based on parameter space sampling. Instead of seeking a best model within an optimization framework, one seeks an ensemble of solutions and derives properties of that ensemble for inspection. While this idea has itself been employed for more than 30 years, it is now receiving increasing attention in the geosciences. Recently, it has been shown that transdimensional and hierarchical sampling methods have some considerable benefits for problems involving multiple parameter types, uncertain data errors and/or uncertain model parametrizations, as are common in seismology. Rather than being forced to make decisions on parametrization, the level of data noise and the weights between data types in advance, as is often the case in an optimization framework, the choice can be informed by the data themselves. Despite the relatively high computational burden involved, the number of areas where sampling methods are now feasible is growing rapidly. The intention of this article is to introduce concepts of transdimensional inference to a general readership and illustrate with particular seismological examples. A growing body of references provide necessary detail.

Short scale heterogeneity in the lowermost mantle: insights from PcP-P and ScS-S data

We compare lateral variations at the base of the mantle as inferred from a global dataset of PcP-P travel time residuals, measured on broadband records, and existing P and S tomographic velocity models, as well as ScS-S travel time data in some selected regions. In many regions, the PcP-P dataset implies short scale lateral variations that are not resolved by global tomographic models, except under eastern Eurasia, where data and models describe a broad region of fast velocity anomalies across which variations appear to be of thermal origin. In other regions, such as central America and southeastern Africa, correlated short scale lateral variations (several hundred kilometers) are observed in PcP and ScS, implying large but not excessive values for the ratio R =D ln Vs/D ln Vp (V2.5). On the other hand, in at least two instances, in the heart of the African Plume and on the edge of the Pacific Plume, variations in P and S velocities appear to be incompatible, implying strong lateral gradients across compositionally different domains, possibly also involving topography on the core^mantle boundary. One should be cautious in estimating R at the base of the mantle from global datasets, as different smoothing and sampling of P and S datasets may result in strong biases and meaningless results. 7 2002 Elsevier Science B.V. All rights reserved.

Dominant seismic noise sources in the Southern Ocean and West Pacific, 2000–2012, recorded at the Warramunga Seismic Array, Australia

Seismic noise is important in determining Earth structure and also provides an insight into ocean wave patterns and long-term trends in storm activity and global climate. We present a long-duration study of seismic noise focused on the Southern Ocean using recordings from the Warramunga Seismic Array, Northern Territory, Australia. Using high-resolution analysis, we determine the seismic slowness and back azimuth of observed seismic noise, microseisms, at hourly intervals through over a decade (2000–2012). We identify three dominant sources of body wave ( P ) noise in the Southern Ocean which we interpret to originate from a South Atlantic source propagating as PP waves, and Kerguelen Island and Philippine Sea sources propagating as P waves. We also identify surface waves from around the Australian coast. All sources show distinct seasonality and a low, but discernable, interannual variability.

Complex inner core of the Earth: The last frontier of global seismology

The days when the Earths inner core (IC) was viewed as a homogeneous solid sphere surrounded by the liquid outer core (OC) are now behind us. Due to a limited number of data sampling the IC and a lack of experimentally controlled conditions in the deep Earth studies, it has been difficult to scrutinize competitive hypotheses in this active area of research. However, a number of new concepts linking IC structure and dynamics has been proposed lately to explain different types of seismological observations. A common denominator of recent observational work on the IC is increased complexity seen in IC physical properties such as its isotropic and anisotropic structure, attenuation, inner core boundary (ICB) topography, and its rotational dynamics. For example, small-scale features have been observed to exist as a widespread phenomenon in the uppermost inner core, probably superimposed on much longer-scale features. The characterization of small-scale features sheds light on the nature of the solidification process and helps in understanding seismologically observed hemispherical dichotomy of the IC. The existence of variations in the rate and level of solidification is a plausible physical outcome in an environment where vigorous compositional convection in the OC and variations in heat exchange across the ICB may control the process of crystal growth. However, further progress is hindered by the fact that the current traveltime data of PKIKP waves traversing the IC do not allow discriminating between variations in isotropic P wave velocity and velocity anisotropy. Future studies of attenuation in the IC might provide crucial information about IC structure, although another trade-off exists—that of the relative contribution of scattering versus viscoelastic attenuation and the connection with the material properties. Future installations of dense arrays, cross paths of waves that sample the IC, and corresponding array studies will be a powerful tool to image and clearly distinguish between viscoelastic and scattering attenuation, and isotropic- and anisotropic-heterogeneity related effects on traveltimes of core-sensitive body waves. This will then inevitably contribute to a better understanding of what the IC is made of, how it solidifies and how it contributes to the generation and dynamics of the geomagnetic field.

Structure of the Tasmanian lithosphere from 3D seismic tomography

Seismic data from three separate experiments, a marine active source survey with land-based stations, and two teleseismic arrays deployed to record distant earthquakes, are combined in a joint inversion for the 3D seismic structure of the Tasmanian lithosphere. In total, travel-time information from nearly 14 000 source–receiver paths are used to constrain a detailed model of crustal velocity, Moho geometry and upper mantle velocity beneath the entire island. Synthetic reconstruction tests show good resolution beneath most of Tasmania with the exception of the southwest, where data coverage is sparse. The final model exhibits a number of well-constrained features that have important ramifications for the interpretation of Tasmanian tectonic history. The most prominent of these is a marked easterly transition from lower velocity crust to higher velocity crust which extends from the north coast, northeast of the Tamar River, down to the east coast. Other significant anomalies include elevated crustal velocities beneath the Mt Read Volcanics and Forth Metamorphic Complex; thickened crust beneath the Port Sorell and Badger Head Blocks in central northern Tasmania; and distinctly thinner, higher velocity crust beneath the Rocky Cape Block in northwest Tasmania. Combined with existing evidence from field mapping, potential-field surveys and geochemical data, the new results support the contention that east and west Tasmania were once passively joined as far back as the Ordovician, with the transition from lithosphere of Proterozoic continental origin to Phanerozoic oceanic origin occurring some 50 km east of the Tamar River; that the southeast margin of the Rocky Cape Block may have been a former site of subduction in the Cambrian; and that the Badger Head and Port Sorell Blocks were considerably shortened and thickened during the Cambrian Tyennan and Middle Devonian Tabberabberan Orogenies.

Metapyroxenite in the mantle transition zone revealed from majorite inclusions in diamonds

The transition zone of the Earth’s mantle (the depth interval between two major seismic discontinuities at 410 km and 660 km) is critical to understanding our planet’s evolution. Some diamonds are thought to have originated in the transition zone and the inclusions found in them are the only samples of material directly extracted from this depth range. By comparing natural majorite garnet inclusions in diamonds with the compositions of experimentally crystallized majorite garnets, we determine two major compositional trends, the pure metabasitic (or eclogitic) trend and the combined metaperidotitic and metapyroxenitic trend, that are strongly correlated with their preferred substitution mechanisms during majorite formation. Based on these trends, we demonstrate that the majority of the reported majorite inclusions in natural diamonds formed neither in a pure metabasite nor in a metaperidotite lithology, but in fact crystallized from a wide range of compositions intermediate between conventional basaltic and peridotitic, referred to here as metapyroxenitic. Given the dominance of metapyroxenite-type majorite diamond inclusions and their inferred syngenetic origin, we argue that a significant fraction of metapyroxenite rock is present within Earth’s transition zone and is important in the diamond-forming process. This is in agreement with recent self-consistent seismological and/or mineral physics studies that support models of a lithologically heterogeneous transition zone. From trace element and carbon isotope features, we infer a crustal origin for these rocks.

The frequency dependence and locations of short period microseisms generated in the Southern Ocean and west Pacific

The origin of the microseismic wavefield is associated with deep ocean and coastal regions where, under certain conditions, ocean waves can excite seismic waves that propagate as surface and body waves. Given that the characteristics of seismic signals generally vary with frequency, here we explore the frequency and azimuth dependent properties of microseisms recorded at a medium aperture (25 km) array in Australia. We examine the frequency dependent properties of the wavefield, and its temporal variation, over two decades (1991–2012), with a focus on relatively high-frequency microseisms (0.325–0.725 Hz) recorded at the Warramunga Array (WRA), which has good slowness resolution capabilities in this frequency range. The analysis is carried out using the Incoherently Averaged Signal (IAS) Capon beamforming, which gives robust estimates of slowness and backazimuth, and is able to resolve multiple wave arrivals within a single time window. For surface waves, we find that fundamental mode Rayleigh waves (Rg) dominate for lower frequencies ( 0.55 Hz) show a transition to higher mode surface waves (Lg). For body waves, source locations are identified in deep ocean regions for lower frequencies and in shallow waters for higher frequencies. We further examine the association between surface wave arrivals and a WAVEWATCH III ocean wave hindcast. Correlations with the ocean wave hindcast show that secondary microseisms in the lower frequency band are generated mainly by ocean swell, while higher frequency bands are generated by the wind sea, i.e. local wind conditions.

The Puzzle of the 1996 Bárdarbunga, Iceland, Earthquake: No Volumetric Component in the Source Mechanism

A volcanic earthquake with M w 5.6 occurred beneath the Bardarbunga caldera in Iceland on 29 September 1996. This earthquake is one of a decade-long sequence of ![Graphic][1] events at Bardarbunga with non-double-couple mechanisms in the Global Centroid Moment Tensor catalog. Fortunately, it was recorded well by the regional-scale Iceland Hotspot Project seismic experiment. We investigated the event with a complete moment tensor inversion method using regional long-period seismic waveforms and a composite structural model. The moment tensor inversion using data from stations of the Iceland Hotspot Project yields a non-double-couple solution with a 67% vertically oriented compensated linear vector dipole component, a 32% double-couple component, and a statistically insignificant (2%) volumetric (isotropic) contraction. This indicates the absence of a net volumetric component, which is puzzling in the case of a large volcanic earthquake that apparently is not explained by shear slip on a planar fault. A possible volcanic mechanism that can produce an earthquake without a volumetric component involves two offset sources with similar but opposite volume changes. We show that although such a model cannot be ruled out, the circumstances under which it could happen are rare. [1]: /embed/inline-graphic-1.gif