Seismic structure of Sri Lanka using receiver function analysis: A comparison with other high-grade Gondwana terrains

Modeling of receiver functions computed using data from the IRIS broadband station PALK in Sri Lanka reveals a simple crust with a thickness of 34 km. The crust appears to be more felsic with dominance of quartzite, as evidenced by a low Poisson's ratio of 0.25 compared to the global average for Precambrian shields. An overview of crustal composition of the high-grade terrains of Gondwana land reveals that Poisson's ratios mostly lie in the range of 0.24–0.26. These lower than global average values from both Archean and Proterozoic shields, including the metamorphic regions appear to be characteristic of Precambrian shields consistent with the average continental crust composition estimates showing 59% silica content. The two principal mantle discontinuities beneath PALK are found at 418 and 678 km, respectively, which are both deeper than the global averages, suggesting a hotter upper mantle.     

Lithospheric structure of the continent–continent collision zone: eastern Turkey

We infer the lithospheric structure in eastern Turkey using teleseismic and regional events recorded by 29 broad-band stations from the Eastern Turkey Seismic Experiment (ETSE). We combine the surface wave group velocities (Rayleigh and Love) with telesesimic receiver functions to jointly invert for the S -wave velocity structure, Moho depth and mantle-lid (lithospheric mantle) thickness. We also estimated the transverse anisotropy due to Love and Rayleigh velocity discrepancies. We found anomalously low shear wave velocities underneath the Anatolian Plateau. Average crustal thickness is 36 km in the Arabian Plate, 44 km in Anatolian Block and 48 km in the Anatolian Plateau. We observe very low shear wave velocities at the crustal portion (30–38 km) of the northeastern part of the Anatolian Plateau. The lithospheric mantle thickness is either not thick enough to resolve it or it is completely removed underneath the Anatolian Plateau. The shear velocities and anisotropy down to 100 km depth suggest that the average lithosphere–asthenosphere boundary in the Arabian Plate is about 90 and 70 km in Anatolian block. Adding the surface waves to the receiver functions is necessary to constrain the trade-off between velocity and the thickness. We find slower velocities than with the receiver function data alone. The study reveals three different lithospheric structures in eastern Turkey: the Anatolian plateau (east of Karliova Triple Junction), the Anatolian block and the northernmost portion of the Arabian plate. The boundary of lithospheric structure differences coincides with the major tectonic boundaries.     

New approach in the kinematic k−2 source model for generating physical slip velocity functions

In an attempt to improve the ground motion modelling, the characteristics of the slip velocity functions (SVF) generated using the kinematic k ⁻² source are investigated and compared to the dynamic solutions proposed in the literature. Several numerical simulations were performed to test the influence of the model parameters on the SVF modelling. Overall, the shapes of SVF are very complex and exhibit a large variability in time and space. However, we found out that the mean SVF is a simple boxcar with duration equal to the largest rise time value. In the areas of weak slip, the SVFs are characterized by the existence of negative values, whereas in large slip areas, the SVF is more impulsive. Overall, on the examples investigated, the SVFs modelled with this k ⁻² source model are different from a typical Kostrov's solution. The critical analysis of the kinematic k ⁻² source led us to identify the Fourier decomposition of the slip to be responsible for these difficulties, and to propose a new recombination scheme. It consists of adding a positive correction to the Fourier slip components. The slip is described as the sum of positive contributions at various scales. The SVFs modelled using this new scheme are greatly improved. Moreover, through several parametrical analyses performed to qualify this new approach, we show that the SVF are corrected while preserving the essential quality of the k ⁻² modelling, that is, the ω² spectral shape and C _d apparent directivity of the synthetic accelerograms. Strong ground motion modelling in the near-fault region was made and numerical ground motion parameters were compared to the empirical relationships. We show that predicted peak ground motion is consistent with near-source attenuation laws.     

Regional gravity modeling in terms of spherical base functions

This article provides a survey on modern methods of regional gravity field modeling on the sphere. Starting with the classical theory of spherical harmonics, we outline the transition towards space-localizing methods such as spherical splines and wavelets. Special emphasis is given to the relations among these methods, which all involve radial base functions. Moreover, we provide extensive applications of these methods and numerical results from real space-borne data of recent satellite gravity missions, namely the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE). We also derive high-resolution gravity field models by effectively combining space-borne and surface measurements using a new weighted level-combination concept. In addition, we outline and apply a strategy for constructing spatio-temporal fields from regional data sets spanning different observation periods.     

Turbulent velocity distributions and implied trajectory models

Well-mixed, first-order Lagrangian stochastic (LS) particle trajectory models are derived from several idealized (“toy”) turbulent velocity distributions, and their performance is compared against the observations of Project Prairie Grass, i.e., the case of a continuous point source of tracer near the ground, in the horizontally homogeneous and neutrally stratified surface layer. Although in a context of limited information a Gaussian distribution is the preferred choice, and although the Gaussian corresponds to the simplest of this set of LS models (namely, the Langevin equation), models stemming from other velocity distributions give similar, albeit distinguishable, predictions.     

A note on the top-down and bottom-up gradient functions over a forested site

The dimensionless bottom-up and top-down gradient functions in the convective boundary layer (CBL) are evaluated utilizing long-term well-calibrated carbon dioxide mixing ratio and flux measurements from multiple levels of a 447-m tall tower over a forested area in northern Wisconsin, USA. The estimated bottom-up and top-down functions are qualitatively consistent with those from large-eddy simulation (LES) results and theoretical expectations. Newly fitted gradient functions are proposed based on observations for this forested site. The integrated bottom-up function over the lowest 4% of the CBL depth estimated from the tower data is about five times larger than that from LES results for a ‘with-canopy’ case, and is smaller than that from LES results for a ‘no-canopy’ case by a factor of 0.7. We discuss the uncertainty in the evaluated gradient functions due to stability, wind direction, and uncertainty in the entrainment flux and show that while all of these have a significant impact on the gradient functions, none can explain the differences between the modelled and observed functions. The effects of canopy features and atmospheric stability may need to be considered in the gradient function relations.     

Topological vector spaces of harmonic functions and the trace operator

Many problems in physical geodesy can be formulated in terms of boundary-value problems (BVPs) for the gravitational potential; many of them can be ultimately formulated as a Dirichlet problem. For this reason, there is a flourishing literature of geodetic contributions to potential theory. In this paper, the authors pick up some classical arguments from the mathematical analysis of BVPs and show, by using only Hilbert spaces of harmonic functions, how they can be systematically cast into a functional scheme clarifying the role of duality when dealing with the harmonic subspaces of classical Sobolev spaces, of any real order. The analysis is here restricted to the case of functions harmonic in spherical domains to make the results transparent and more readable by geodesists. A further step is then taken showing how to generalize the Dirichlet problem for the space of all the functions that are harmonic outside a sphere, which exploits the more general theory of Fréchet topological spaces. Basically, the result is that any functions harmonic in the exterior of a sphere can be uniquely identified by a suitably defined trace on the sphere. The paper concludes with comments and discussion of future work.     

New relations among associated Legendre functions and spherical harmonics

Several new relations among associated Legendre functions (ALFs) are derived, most of which relate a product of an ALF with trigonometric functions to a weighted summation over ALFs, where the weights only depend on the degree and order of the ALF. These relations are, for example, useful in applications such as the computation of geopotential coefficients and computation of ellipsoidal corrections in geoid modelling. The main relations are presented in both their unnormalised and fully normalised (4π-normalised) form. Several approaches to compute the weights involved are discussed, and it is shown that the relations can also be applied in the case of first- and second-order derivatives of ALFs, which may be of use in analysis of satellite gradiometry data. Finally, the derived relations are combined to provide new identities among ALFs, which contain no dependency on the colatitudinal coordinate other than that in the ALFs themselves.