ALBERT

Description: Differences between 3-D numerical predictions of earthquake ground motion in the Mygdonian basin near Thessaloniki, Greece, led us to define four canonical stringent models derived from the complex realistic 3-D model of the Mygdonian basin. Sediments atop an elastic bedrock are modelled in the 1D-sharp and 1D-smooth models using three homogeneous layers and smooth velocity distribution, respectively. The 2D-sharp and 2D-smooth models are extensions of the 1-D models to an asymmetric sedimentary valley. In all cases, 3-D wavefields include strongly dispersive surface waves in the sediments. We compared simulations by the Fourier pseudo-spectral method (FPSM), the Legendre spectral-element method (SEM) and two formulations of the finite-difference method (FDM-S and FDM-C) up to 4 Hz. The accuracy of individual solutions and level of agreement between solutions vary with type of seismic waves and depend on the smoothness of the velocity model. The level of accuracy is high for the body waves in all solutions. However, it strongly depends on the discrete representation of the material interfaces (at which material parameters change discontinuously) for the surface waves in the sharp models. An improper discrete representation of the interfaces can cause inaccurate numerical modelling of surface waves. For all the numerical methods considered, except SEM with mesh of elements following the interfaces, a proper implementation of interfaces requires definition of an effective medium consistent with the interface boundary conditions. An orthorhombic effective medium is shown to significantly improve accuracy and preserve the computational efficiency of modelling. The conclusions drawn from the analysis of the results of the canonical cases greatly help to explain differences between numerical predictions of ground motion in realistic models of the Mygdonian basin. We recommend that any numerical method and code that is intended for numerical prediction of earthquake ground motion should be verified through stringent models that would make it possible to test the most important aspects of accuracy.

Description: Simulating seismic waves with uniform grid in heterogeneous high-velocity contrast media requires small-grid spacing determined by the global minimal velocity, which leads to huge number of grid points and small time step. To reduce the computational cost, discontinuous grids that use a finer grid at the shallow low-velocity region and a coarser grid at high-velocity regions are needed. In this paper, we present a discontinuous grid implementation for the collocated-grid finite-difference (FD) methods to increase the efficiency of seismic wave modelling. The grid spacing ratio n could be an arbitrary integer n  ≥ 2. To downsample the wavefield from the finer grid to the coarser grid, our implementation can simply take the values on the finer grid without employing a downsampling filter for grid spacing ratio n  = 2 to achieve stable results for long-time simulation. For grid spacing ratio n  ≥ 3, the Gaussian filter should be used as the downsampling filter to get a stable simulation. To interpolate the wavefield from the coarse grid to the finer grid, the trilinear interpolation is used. Combining the efficiency of discontinuous grid with the flexibility of collocated-grid FD method on curvilinear grids, our method can simulate large-scale high-frequency strong ground motion of real earthquake with consideration of surface topography.

Description: In this study, we present a new method for simulating the 3-D dynamic rupture process occurring on a non-planar fault. The method is based on the curved-grid finite-difference method (CG-FDM) proposed by Zhang & Chen and Zhang et al. to simulate the propagation of seismic waves in media with arbitrary irregular surface topography. While keeping the advantages of conventional FDM, that is computational efficiency and easy implementation, the CG-FDM also is flexible in modelling the complex fault model by using general curvilinear grids, and thus is able to model the rupture dynamics of a fault with complex geometry, such as oblique dipping fault, non-planar fault, fault with step-over, fault branching, even if irregular topography exists. The accuracy and robustness of this new method have been validated by comparing with the previous results of Day et al. , and benchmarks for rupture dynamics simulations. Finally, two simulations of rupture dynamics with complex fault geometry, that is a non-planar fault and a fault rupturing a free surface with topography, are presented. A very interesting phenomenon was observed that topography can weaken the tendency for supershear transition to occur when rupture breaks out at a free surface. Undoubtedly, this new method provides an effective, at least an alternative, tool to simulate the rupture dynamics of a complex non-planar fault, and can be applied to model the rupture dynamics of a real earthquake with complex geometry.

Description: Perfectly matched layer (PML) is an efficient absorbing technique for numerical wave simulations. Since it appeared, various improvements have been made. The complex frequency-shifted PML (CFS-PML) improves the absorbing performance for near-grazing incident waves and evanescent waves. The auxiliary differential equation (ADE) formulation of the PML provides a convenient unsplit-field PML implementation that can be directly used with high order time marching schemes. The multi-axial PML (MPML) stabilizes the PML on anisotropic media. However, these improvements were generally developed for Cartesian grids. In this paper, we extend the ADE CFS-PML to general curvilinear (non-orthogonal) grids for elastic wave modelling. Unlike the common implementations to absorb the waves in the computational space, we apply the damping along the perpendicular direction of the PML layer in the local Cartesian coordinates. Further, we relate the perpendicular and parallel components of the gradient operator in the local Cartesian coordinates to the derivatives in the curvilinear coordinates, to avoid mapping the wavefield to the local Cartesian coordinates. It is thus easy to be incorporated with numerical schemes on curvilinear grids. We derive the PML equations for the interior region and for the free surface separately because the free surface boundary condition modifies the elastic wave equations. We show that the elastic wave modelling on curvilinear grids exhibits anisotropic effects in the computational space, which may lead to unstable simulations. To stabilize the simulation, we adapt the MPML strategy to also absorb the wavefield along the two parallel directions of the PML. We illustrate the stability of this ADE CFS-MPML for finite-difference elastic wave simulations on curvilinear grids by two numerical experiments.

Description: Post-collisional (25–8 Ma) ultrapotassic mafic magmatic rocks occur to the north of the India–Asia collision zone within the Lhasa terrane of the southern Tibetan Plateau, forming a near 1000 km long semi-continuous igneous belt. They include both extrusive and intrusive facies, although lava flows dominate. To understand their petrogenesis, the mineral chemistry of olivine phenocrysts and xenocrysts and whole-rock major and trace element and Sr–Nd–Pb isotope data are presented for the most primitive mafic magmatic rocks (MgO 〉 6 wt %) from west to east. The studied samples are characterized by high MgO (6·28–15·75 wt %), K 2 O (4·76–8·89 wt %), SiO 2 (46·44–59·74 wt %), Ba (1368–14076 ppm), Th (69–336 ppm) and Ni (106–527 ppm) contents. Chondrite-normalized rare earth element (REE) patterns show enrichment in light rare earth elements (LREE), flat heavy REE (HREE) patterns and negative Eu anomalies. These REE patterns have a very distinctive inverted ‘spoon shape’, which appears to be a common characteristic of collision-related ultrapotassic magmas. Primitive mantle-normalized incompatible trace element patterns exhibit strong enrichments in large ion lithophile elements (LILE) relative to high field strength elements (HFSE) and strong negative Ta–Nb–Ti anomalies, which are typical of subduction-related magmas. The ultrapotassic magmatic rocks studied have extremely radiogenic initial Sr isotopic compositions (0·712379–0·737616) and low ( 143 Nd/ 144 Nd) i (0·511662–0·511984). Combined with their Pb isotope compositions [( 206 Pb/ 204 Pb) i = 18·30–18·92; ( 207 Pb/ 204 Pb) i = 15·65–15·87; ( 208 Pb/ 204 Pb) i = 39·02–39·76] these data are consistent with the involvement of a subducted continental crustal component in their petrogenesis. The Sr–Nd–Pb isotope compositions exhibit linear trends between depleted mid-ocean ridge basalt (MORB)-source mantle (DMM) and Indian continental crust. The extreme enrichment of the upper mantle below south Tibet is considered to result from the addition of components derived from subducted Indian continental crust to the overlying mantle wedge during northward underthrusting of Indian continental lithosphere beneath the Lhasa terrane since India–Asia collision at ~55 Ma. The post-collisional K-rich mafic magmas in south Tibet were generated by partial melting of pyroxenite in a mantle source region that was created by reaction of hydrous fluids and siliceous melts from subducted granulite–eclogite-facies Indian continental crustal rocks with the surrounding peridotitic mantle. A continuous process from slab roll-back, through break-off, to detachment of the slab may have induced partial melting of the pyroxenites. Cessation of the post-collisional ultrapotassic magmatism at ~8 Ma may be linked to the onset of flat slab subduction beneath southern Tibet and the elimination of the wedge of Tibetan subcontinental lithospheric mantle and underlying asthenosphere; geophysical data indicate that at the present day eclogite-facies Indian continental crust directly underthrusts the crust of the Lhasa terrane with no intervening mantle wedge. The proportion of the Indian continental crustal component in the mantle source of the ultrapotassic mafic magmas decreases eastward, as do the ages and volumes of the magmatic rocks. There are no outcrops of post-collisional K-rich mafic magmatic rocks (MgO 〉 6 wt %) to the east of 87°E in the Lhasa terrane, which may indicate a change in subduction geometry at this longitude.

Description: 〈span〉〈div〉SUMMARY〈/div〉Accurate identification of the locations and orientations of small-scale faults plays an important role in seismic interpretation. We have developed a 3D migration scheme that can image small-scale faults using diffractions in time. This provides a resolution beyond the classical Rayleigh limit of half a wavelength in detecting faults. The scheme images weak diffractions by building a modified dip-angle gather, which is obtained by replacing the two dip angles dimensions of the conventional 2D dip-angle gather with tangents of the dip angles. We build the modified 2D dip-angle gathers by calculating the tangents of dip angles following 3D prestack time migration (PSTM). In the resulting modified 2D dip-angle gathers, the Fresnel zone related to the specular reflection exhibits an ellipse. Comparing with the conventional 2D dip-angle gather, diffraction event related a fault exhibits a straight cylinder shape with phase-reversal across a line related the orientation of the fault. As a result, we can not only mute the Fresnel zones related to reflections, correct phase for edge diffractions and obtain the image of faults, but also detect the orientations of 3D faults using the modified dip-angle gathers. Like the conventional dip-angle gathers, the modified dip-angle gathers can also be used to image diffractions resulting from other sources. 3D Field data tests demonstrate the validity of the proposed diffraction imaging scheme.〈/span〉

Description: The Fanshan intrusion in the North China Craton (NCC) is concentrically zoned with syenite in the core (Unit 1), surrounded by ultramafic rocks (clinopyroxenite and biotite clinopyroxenite; Unit 2), and an outer rim of garnet-rich clinopyroxenite and orthoclase clinopyroxenite and syenite (Unit 3). The intrusive rocks are composed of variable amounts of Ca-rich augite, biotite, orthoclase, melanite, garnet, magnetite and apatite, with minor primary calcite. Monomineralic apatite rocks, nelsonite and glimmerite exclusively occur in Unit 2. Geochemically, the Fanshan rocks are highly enriched in light rare earth elements (LREE) and large ion lithophile elements (LILE), moderately depleted in high field strength elements (HFSE), and have a limited range of Sr–Nd–O isotopic compositions. The similar mineralogy, mineral compositions, and trace element characteristics of the three units suggest that all the rocks are co-magmatic. The parental magma is ultrapotassic and is akin to kamafugite. Very low-degree partial melting of metasomatized lithospheric mantle best explains the geochemistry and petrogenesis of the parental magmas of the Fanshan intrusion. We propose that the mantle source may have been metasomatized by a hydrous carbonate-bearing melt, which has imprinted the enriched Sr–Nd isotopic signature and incompatible element enrichment with conspicuous negative Nb–Ta–Zr–Hf–Ti anomalies and LREE enrichments. The mantle source enrichment may be correlated with oceanic sediment recycling during southward subduction of the Paleo-Asian oceanic plate during the Carboniferous and Permian. We propose that crystal settling and mechanical sorting combined with repeated primitive magma replenishment and mixing with previously fractionated magma is the predominant process responsible for the formation of the apatite ores.

Description: First-arrival traveltime is commonly used in problems that involve static correction, pre-stack migration, earthquake location, seismic tomography, etc. The classical eikonal equation discretized with regular rectilinear grids is effective for calculating the first-arrival traveltimes in a rectangular domain, but is less efficient for an Earth model that has an irregular surface. Here, we present a topography-dependent eikonal equation in 2-D that makes use of the wave equation in a curvilinear coordinate system, and is equivalent to a direct derivation of the classical eikonal equation together with a transformation from Cartesian to curvilinear coordinates. The topography-dependent eikonal equation is reduced to the classical version when the surface is flat. The topography-dependent equation (in the curvilinear coordinate system) displays the mathematical form of an anisotropic eikonal equation (even though the medium is isotropic in the Cartesian coordinate system). Then, we use a Lax–Friedrichs sweeping scheme, which has been developed as an iterative method for Hamilton–Jacobi equations, to approximate the viscosity solutions (first-arrival traveltimes) of the topography-dependent eikonal equation formulated in the curvilinear coordinate system. Several numerical experiments performed with different models illustrate that the method is stable and accurate in calculating seismic traveltimes with an irregular (non-flat) surface.

Description: 〈span〉〈div〉Summary〈/div〉The computational cost of quasi-〈span〉P〈/span〉 wave extrapolation depends on the complexity of the medium, and specifically the anisotropy. Our effective-model method splits the anisotropic dispersion relation into an isotropic background and a correction factor to handle this dependency. The correction term depends on the slope (measured using the gradient) of current wavefields and the anisotropy. As a result, the computational cost is independent of the nature of anisotropy, which makes the extrapolation efficient. A dynamic implementation of this approach decomposes the original pseudo-differential operator into a Laplacian, handled using the low-rank approximation of the spectral operator, plus an angular dependent correction factor applied in the space domain to correct for anisotropy. We analyse the role played by the correction factor and propose a new spherical decomposition of the dispersion relation. The proposed method provides accurate wavefields in phase and more balanced amplitudes than a previous spherical decomposition. Also, it is free of 〈span〉SV〈/span〉-wave artefacts. Applications to a simple homogeneous transverse isotropic medium with a vertical symmetry axis (VTI) and a modified Hess VTI model demonstrate the effectiveness of the approach. The Reverse Time Migration applied to a modified BP VTI model reveals that the anisotropic migration using the proposed modelling engine performs better than an isotropic migration.〈/span〉

Description: A combined study of zircon U–Pb ages, whole-rock chemistry, Sr–Nd isotopes and in situ Lu–Hf isotopic ratios in zircons was carried out on Permian monzogranites and mafic microgranular enclaves (MME) and coeval massive gabbros in the northern Alxa block, North China. The data obtained were used to constrain magma sources and petrogenetic processes involved in the generation of this igneous suite. Zircon U–Pb dating yields ages of 271 ± 1 Ma, 270 ± 1 Ma and 276–270 Ma for the monzogranites, MME and massive gabbros, respectively. Two populations of MME, gabbroic (SiO 2 〈49 wt %) and dioritic (SiO 2 〉53 wt %) enclaves, are identified. They represent mafic to intermediate magmas quenched in a partially crystallized granitic ( sensu lato ) host; evidence to support this conclusion includes their fine-grained textures, sinuous margins and diffuse contacts with the host monzogranites. Back-veins and xenocrysts of quartz and plagioclase, as well as various disequilibrium textures and mineral assemblages, indicate mingling or mixing processes. The two magma systems, mafic and felsic, have broadly similar isotopic characteristics with whole-rock initial 87 Sr/ 86 Sr(i) ratios ranging from 0·7075 to 0·7077 in the monzogranite host and from 0·7067 to 0·7069 in the MME, with N d ( t) values ranging from –10·2 to –12·4 in monzogranites and from –8·2 to –9·9 in the MME. Zircon Hf(t) values of the monzogranites, gabbroic enclaves and massive gabbros show a wide range and significant overlap from –1·2 to –15·2, –4 to –13·3 and –5·4 to –19·5, respectively; the maximum frequency value of the Hf model age is almost coincident with the whole-rock Nd model age. Mafic, gabbroic rocks similar in composition to some enclaves form layered synplutonic intrusions several metres in thickness and more than 100 m in lateral extent. A mixing test based on mass balance for whole-rock major element compositions reveals that mixing was an efficient process between two coeval magmas. The fraction of felsic magma involved in the hybrid rocks ranged from 0·19–0·29 in the dioritic enclaves to 0·84 in granodiorite and good linear fits (r 2 〉 0·9) are obtained using the average composition of gabbroic enclaves and the most felsic monzogranite as end-members. Although the monzogranites and enclaves may be derived from distinct magma sources, they share similar isotopic signatures, pointing to interaction processes in the source region. The combination of information from geochronology, petrology, whole-rock geochemistry and isotopic compositions leads us to conclude that the processes of hybridization and magma mixing were effective at both the level of emplacement in the shallow crust and at depth in the magma source region. Hybridization in a source region within the lithospheric mantle, involving mantle and crustal source rocks, produced magma bimodality with strong geochemical affinities between end-members and clear calc-alkaline arc signatures, compatible with a subduction setting. A plausible subduction erosion plus relamination model, which differs from classical models based on mafic magma underplating, is proposed. Accordingly, the Yamatu monzogranites are argued to have been generated from granitic melt segregated and ponded in buoyant silicic diapirs, which formed by melting of subducted mélanges in the lithospheric mantle and eventually relaminated to the lower crust. They represent the melts that metasomatized the mantle region during a pre-Permian subduction event. The massive gabbros were formed by decompression melting of the previously metasomatized mantle. The gabbroic enclaves and gabbro layers of the Yamatu pluton are interpreted as magmas formed by decompression melting of this modified hydrated mantle. The dioritic enclaves represent hybrid liquids generated from reaction between granitic melts, which were derived from subducted mélanges, and the hydrated mantle or melts derived from it.