Showing papers in "Geophysical Journal International in 2007"

Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements

Abstract: SUMMARY Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency‐time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.

On Postglacial Sea Level

Abstract: Summary An exact method is presented for calculating the changes in sea level that occur when ice and water masses are rearranged on the surface of elastic and viscoelastic non-rotating Earth models. The method is used to calculate the instantaneous elastic and delayed vi scoelastic sea level changes following the partial melting of late Quaternary ice sheets. We find that there can be large errors in the usual assumption that changes in sea level are uniform over the ocean basins. If a quantity of ice equivalent to a uniform 100-m rise in sea level melts from the Laurentide and Fennoscandian ice sheets, then in the South Pacific the instantaneous rise in sea level can be as large as 120m. In the North Atlantic the instantaneous rise is always less than 100 m. There is a zone in the North Atlantic with almost no sea level change and near Greenland and Norway the sea level falls, rather than rises, by over 100 m. One thousand years after the melting a forebulge migrating towards the ice loads causes water to flow from the South Pacific into the North Pacific suggesting that raised beaches should occur in the South Pacific. The gravitational attraction of an ice mass upon a nearby ocean tends to hold sea level high in the vicinity of the ice. This extra load near the ice may have a significant influence on postglacial isostatic adjustment.

Statistical Significance of the Fold Test in Palaeomagnetism

Abstract: Summary The significance of the change in direction dispersion on applying the fold test in palaeomagnetism is used as the criterion for deciding whether or not the fold test has statistical significance. A set of tables is compiled which can be used for quick application of the test.

Ambient noise Rayleigh wave tomography across Europe

Abstract: SUMMARY We extend ambient noise surface wave tomography both in bandwidth (10‐50 s period) and in geographical extent (across much of Europe) compared with previous applications. 12 months of ambient noise data from 2004 are analysed. The data are recorded at about 125 broadband Seismic stations from the Global Seismic Network and the Orfeus Virtual European Broad-band seismic Network. Cross-correlations are computed in daily segments, stacked over 1 yr, and Rayleigh wave group dispersion curves from 8 to 50 s period are measured using a phase-matched filter, frequency time analysis technique. We estimate measurement uncertainties using the seasonal variation of the dispersion curves revealed in 3 month stacks. On average, uncertainties in group delays increase with period from ∼ 3t o∼7 s from periods of 10 to 50 s, respectively. Group speed maps at periods from 10 to 50 s are estimated. The resulting path coverage is denser and displays a more uniform azimuthal distribution than from earthquake-emitted surface waves. The fit of the group speed maps to the ambient noise data is significantly improved below 30 s compared to the fit achieved with earthquake data. Average resolution is estimated to be about 100 km at 10 s period, but degrades with increasing period and toward the periphery of the study region. The resulting ambient noise group speed maps demonstrate significant agreement with known geological and tectonic features. In particular, the signatures of sedimentary basins and crustal thickness are revealed clearly in the maps. These results are evidence that surface wave tomography based on crosscorrelations of long time-series of ambient noise data can be achieved over a broad period band on nearly a continental scale and yield higher resolution and more reliable group speed maps than based on traditional earthquake-based measurements.

Kinematics of the Western Africa-Eurasia plate boundary from focal mechanisms and GPS data

Abstract: SUMMARY The Western Mediterranean displays a complex pattern of crustal deformation distributed along tectonically active belts developed in the framework of slow oblique plate convergence. We used earthquake and Global Positioning System (GPS) data to study the present-day kinematics and tectonics of the Africa-Eurasia plate boundary in this region. Crustal seismicity and focal mechanisms, analysed in terms of seismic moment release and seismic deformation, outline the geometry of major seismic belts and characterize their tectonics and kinematics. Continuous GPS data have been analysed to determine Euler vectors for the Nubian and Eurasian plates and to provide the global frame for a new Mediterranean GPS velocity field, obtained by merging continuous and campaign observations collected in the 1991‐2005 time span. GPS velocities and displacements predicted by the Nubia-Eurasia rotation pole provide estimates of the deformation accommodated across the tectonically active belts. The rather simple deformation occurring in the Atlantic region, characterized by extension about perpendicular to the Middle Atlantic and Terceira ridges and right-lateral motion along the Gloria transform fault, turns into a complex pattern of deformation, occurring along broader seismic belts, where continental lithosphere is involved. Our analysis reveals a more complex fragmentation of the plate boundary than previously proposed. The roughly E-W trending mainly compressive segments (i.e. southwestern Iberia, northern Algeria and southern Tyrrhenian), where plate convergence is largely accomodated across rather localized deformation zones, and partially transferred northward to the adjacent domains (i.e. the Algero-Balearic and Tyrrhenian basins), are interrupted by regions of more distributed deformation (i.e. the Rif-Alboran-Betics, Tunisia-Libya and eastern Sicily) or limited seismicity (i.e. the Strait of Sicily), which are characterized by less homogeneous tectonics regimes (mainly transcurrent to extensional). In correspondence of the observed breaks, tectonic structures with different orientation interfere, and we find belts with only limited deformation (i.e. the High and Middle Atlas, the Tunisian Atlas and the offshore Tunisia-Libya belt) that extends from the plate boundary into the Nubian plate, along pre-existing tectonic lineaments. Our analysis suggest that the Sicilian-Pelagian domain is moving independently from Nubia, according to the presence of a right-lateral and extensional decoupling zone corresponding to the Tunisia-Libya and Strait of Sicily deformation zone. Despite the space variability of active tectonic regimes, plate convergence still governs most of the seismotectonic and kinematic setting up to the central Aeolian region. In general, local complexities derive from pre-existing structural features, inherited from the tectonic evolution of the Mediterranean region. On the contrary, along Calabria and the Apennines the contribution of the subducted Ionian oceanic lithosphere and the occurrence of microplates (i.e. Adria) appear to substantially modify both tectonics and kinematics. Finally, GPS data across the Gibraltar Arc and the Tyrrhenian-Calabria domain support the hypothesis that slab rollback in these regions is mostly slowed down or stopped.

New Computations of the Tide‐generating Potential

Abstract: Summary A time-harmonic expansion of the gravitational tide potential is computed using an ephemeris of high precision for the Moon and the Sun and the latest I.A.U. astronomical constants. The results, which are computed for three different epochs and by novel methods, are compared with Doodson's classic expansion. The chief differences are due to secular trends in large terms and to revised constants which reduce all the solar terms. A new expansion is also given for the radiational tide potential.

Glacial-Isostatic Adjustment—I. The Forward Problem

Abstract: Summary The isostatic adjustment of a radially stratified visco-elastic spheroid is treated using space-time Green functions for the associated surface mass load boundary value problem. These impulse response functions are convolved with a Heaviside function to give the time dependent deformation of the planet which would be produced by a unit point mass brought up from infinity at t= 0 and allowed to remain on the surface. The resulting ’ Heaviside Green functions ’ can be employed to simulate all of the important signatures of glacial isostatic adjustment. Given a space-time dependent surface mass load consisting of ice sheet ablation histories and a model of the simultaneous filling of the ocean basins, these source terms are simply convolved with the Heaviside Green function appropriate to a specific response signature. A realistic model of the spatial distribution of the main late Pleistocene ice loads and of their temporal disintegration is constructed. The response of two visco-elastic earth models is computed and compared to a global set of relaxation data (relative sea-level curves). On the basis of this initial comparison of theory and observation the possibility that the lower mantle has a viscosity which is significantly in excess of the viscosity of the upper mantle is excluded. In addition, clear evidence of the presence of the lithosphere has been found in relaxation data from sites which were near the edge of the Laurentide ice sheet. Such data should therefore prove useful as a basis for analysis of lateral variations in lithosphere thickness. Further extensions of the calculation are suggested.

A Procedure for Modelling Shallow Dislocation Sources

Abstract: Summary. Expressions for displacements on the surface of a layered half-space due to an arbitrary oriented shear dislocation are given in terms of generalized ray expansions. Useful approximations of these expressions for shallow events as recorded at teleseismic distances for realistic earth models are presented. The results of this procedure are used to generate synthetic P, SV and SH waveforms for various assumptions of stress-drop.

Stable Iterative Methods for the Inversion of Geophysical Data

Abstract: Summary Interpretation of earth electrical measurements can often be assisted by inversion, which is a non-linear model-fitting problem in these cases. Iterative methods are normally used, and the solution is defined by ' best fit ' in the sense of generalized least-squares. The inverse problems we describe are ill-posed. That is, small changes in the data can lead to large changes in both the solution and in the iterative process that finds the solution. Through an analysis of the problem, based on local linearization, we define a class of methods that stabilize the iteration, and provide a robust solution. These methods are seen as generalizations of the well-known Singular Value Truncation and Marquardt Methods of iterative inversion. Here, and in a companion paper, we give examples illustrating the successful application of the method to ill-posed problems relating to the resistivity of the Earth. In this paper we present an analysis of the solution to a number of geophysical inverse problems. We also provide a reference for the companion paper (Joint Inversion of Geophysical Data, Vozoff & Jupp 1975), where the results are applied to some specific examples. Solutions to geophysical inverse problems are generally non-unique (Backus & Gilbert 1967, 1968, 1970), and it is usual to reduce the non-uniqueness by restricting the complexity of the Earth models. The mathematical problem that arises is commonly ill-posed (unstable) in the sense that small changes in the data lead to large changes in the solution. The solution methods must take careful account of this inherent problem. In the companion paper, and the example given in Section 3 we have data in the form of apparent resistivity measurements for both magnetotelluric (MT), and Direct Current (DC) survey methods. The restricted class of earth models consists of horizontally layered, isotropic media, with constant resistivity in each layer. The simplified inverse problem is, in this case, to find the layer resistivities and thicknesses that best fit the observed data. The analysis of the problem is not, however, restricted to layered models, but applies to any geophysical inverse problem in which the partial derivatives of the (predicted) data with respect to the (unknown) model parameters can be calculated.

A procedure for tidal analysis with a Bayesian information criterion

Abstract: SUMMARY A computer algorithm for tidal analysis is developed, based on a Bayesian method proposed by Ishiguro ef af (1983) The basic assumption of the method is smoothness of the drift This assumption is represented in the form of prior probability in the Bayesian model Once the prior distribution is determined, the parameters used in the analysis model are obtained by maximizing the posterior distribution of the parameters For the given data, ABIC (Akaike's Bayesian Information Criterion, Akaike 1980) is used to select the optimum values of the hyperparameters of the prior distribution and combination of parameters The program, BAYTAP-G, can be adapted to tidal data which includes such irregularities as drift, occasional steps and disturbances caused by meteorological influences The applicability of this program is examined using simulated data and real strain data

Fault locking, block rotation and crustal deformation in the Pacific Northwest

Abstract: SUMMARY We interpret Global Positioning System (GPS) measurements in the northwestern United States and adjacent parts of western Canada to describe relative motions of crustal blocks, locking on faults and permanent deformation associated with convergence between the Juan de Fuca and North American plates. To estimate angular velocities of the oceanic Juan de Fuca and Explorer plates and several continental crustal blocks, we invert the GPS velocities together with seafloor spreading rates, earthquake slip vector azimuths and fault slip azimuths and rates. We also determine the degree to which faults are either creeping aseismically or, alternatively, locked on the block-bounding faults. The Cascadia subduction thrust is locked mainly offshore, except in central Oregon, where locking extends inland. Most of Oregon and southwest Washington rotate clockwise relative to North America at rates of 0.4–1.0 ° Myr–1. No shear or extension along the Cascades volcanic arc has occurred at the mm/yr level during the past decade, suggesting that the shear deformation extending northward from the Walker Lane and eastern California shear zone south of Oregon is largely accommodated by block rotation in Oregon. The general agreement of vertical axis rotation rates derived from GPS velocities with those estimated from palaeomagnetic declination anomalies suggests that the rotations have been relatively steady for 10–15 Ma. Additional permanent dextral shear is indicated within the Oregon Coast Range near the coast. Block rotations in the Pacific Northwest do not result in net westward flux of crustal material—the crust is simply spinning and not escaping. On Vancouver Island, where the convergence obliquity is less than in Oregon and Washington, the contractional strain at the coast is more aligned with Juan de Fuca—North America motion. GPS velocities are fit significantly better when Vancouver Island and the southern Coast Mountains move relative to North America in a block-like fashion. The relative motions of the Oregon, western Washington and Vancouver Island crustal blocks indicate that the rate of permanent shortening, the type that causes upper plate earthquakes, across the Puget Sound region is 4.4 ± 0.3 mm yr–1. This shortening is likely distributed over several faults but GPS data alone cannot determine the partitioning of slip on them. The transition from predominantly shear deformation within the continent south of the Mendocino Triple Junction to predominantly block rotations north of it is similar to changes in tectonic style at other transitions from shear to subduction. This similarity suggests that crustal block rotations are enhanced in the vicinity of subduction zones possibly due to lower resisting stress.

Joint Inversion of Geophysical Data

Abstract: Summary. By jointly inverting several different kinds of geophysical measurements at a site we avoid some of the ambiguity inherent in the individual methods. We show how this can be done for the combination of DC resistivity and magnetotelluric measurements on a layered medium by considering a simple 3-layer model. The combination resolves the resistivity of the thin resistive second layer, even though neither of the two methods can do so alone. The method is then applied to field data from a shallow sedimentary basin. A blind zone occurs beneath a thick near-surface conductive shale. By a study of the eigenvalue structure of the model it can be seen that resolution in this zone would be slightly enhanced by higher frequency magnetotelluric data, but additional DC data at larger spacing would yield no improvement.

Role of Phase Transitions in a Dynamic Mantle

Abstract: Summary The interaction of solid-solid phase transitions with convection in the Earth's mantle involves, for univariant systems: (1) effects of latent heat and advection of ambient temperature on the position of the phase boundary and on its associated body force, and (2) the coupling of latent heat with the ordinary thermal expansivity of the material. For divariant systems, an effective thermal expansion coefficient and a modified adiabatic temperature gradient may be defined for the phase transition zone. Linear stability theory for a fluid layer with a univariant phase change is reviewed and applied to the endothermic spinel-oxide transformation. The theory of the stability of a fluid layer with a divariant phase transformation is developed and critical Rayleigh numbers are given for a model of the olivine-spinel transition. Of special interest is the case where the Earth's temperature gradient exceeds the adiabatic temperature gradient outside the phase transition zone but is smaller than the increased adiabatic temperature gradient in the two-phase olivine-spinel region. The thermal structure of the descending lithosphere is calculated, including the effects of frictional heating on the slip zone and of the olivine-spinel and spinel-oxide transitions; temperature contrasts of 700 °K can exist between the slab and adjacent mantle at 800 km depth. The net body force on the descending slab due to thermal contraction and the major mineralogical phase changes is downward. The olivine-spinel transition may be responsible for the tensional focal mechanisms of intermediate depth earthquakes while the spinel-oxide transformation may be related to the compressional focal mechanisms of deep earthquakes.

Speculations on the Thermal and Tectonic History of the Earth

Abstract: Summary The connection between the Earth’s thermal history and convection in the mantle is exploited to elucidate the early evolution of the Earth. It appears probable that convection extending over almost all of the mantle has dominated vertical heat transport throughout the whole of the Earth’s history. Only in boundary layers at the surface and at a depth of 650-700 km is conduction likely to be important. The resulting evolution appears to be consistent with geological observations on early Precambrian rocks. Various arguments are put forward in favour of two horizontal scales of convective flow in the mantle at depths less than 650 km. The large scale flow is related to the motion of major plates, and must be ordered over distances of more than 5000 km. Its evolution and energetics are discussed and there are no obvious problems in maintaining the proposed convective motions. Small scale flow with an extent of the order of 500 km appears necessary both to explain the heat flow through older parts of the Earth‘s surface and to reconcile the geophysical observations with the results of numerical experiments. Though the existence of the small scale flow is at present speculative, various tests of its presence are proposed.

Multi-interferogram method for measuring interseismic deformation: Denali Fault, Alaska

Abstract: SUMMARY Studies of interseismic strain accumulation are crucial to our understanding of continental deformation, the earthquake cycle and seismic hazard. By mapping small amounts of ground deformation over large spatial areas, InSAR has the potential to produce continental-scale maps of strain accumulation on active faults. However, most InSAR studies to date have focused on areas where the coherence is relatively good (e.g. California, Tibet and Turkey) and most analysis techniques (stacking, small baseline subset algorithm, permanent scatterers, etc.) only include information from pixels which are coherent throughout the time-span of the study. In some areas, such as Alaska, where the deformation rate is small and coherence very variable, it is necessary to include information from pixels which are coherent in some but not all interferograms. We use a three-stage iterative algorithm based on distributed scatterer interferometry. We validate our method using synthetic data created using realistic parameters from a test site on the Denali Fault, Alaska, and present a preliminary result of 10.5 ± 5.0 mm yr −1 for the slip rate on the Denali Fault based on a single track of radar data from ERS1/2.

Inference of mantle viscosity from GRACE and relative sea level data

Abstract: SUMMARY Gravity Recovery And Climate Experiment (GRACE) satellite observations of secular changes in gravity near Hudson Bay, and geological measurements of relative sea level (RSL) changes over the last 10 000 yr in the same region, are used in a Monte Carlo inversion to infer-mantle viscosity structure. The GRACE secular change in gravity shows a significant positive anomaly over a broad region (>3000 km) near Hudson Bay with a maximum of ∼2.5 μGal yr−1 slightly west of Hudson Bay. The pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ICE-5G deglaciation history, strongly suggesting a postglacial rebound origin for the gravity change. We find that the GRACE and RSL data are insensitive to mantle viscosity below 1800 km depth, a conclusion similar to that from previous studies that used only RSL data. For a mantle with homogeneous viscosity, the GRACE and RSL data require a viscosity between 1.4 × 1021 and 2.3 × 1021 Pa s. An inversion for two mantle viscosity layers separated at a depth of 670 km, shows an ensemble of viscosity structures compatible with the data. While the lowest misfit occurs for upper- and lower-mantle viscosities of 5.3 × 1020 and 2.3 × 1021 Pa s, respectively, a weaker upper mantle may be compensated by a stronger lower mantle, such that there exist other models that also provide a reasonable fit to the data. We find that the GRACE and RSL data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle.

Glacial-Isostatic Adjustment—II. The Inverse Problem

Abstract: Summary The principle of correspondence is invoked to determine Laplace transform domain solutions to the surface mass loading problem for radially stratified visco-elastic (Maxwell) spheroids. These Laplace transform domain solutions are expressed in terms of visco-elastic analogues of the conventional surface load Love numbers of elasticity. These visco-elastic Love numbers may be approximately transformed to the time domain using an extremal technique. Application of this technique shows that the Love number time histories may be well approximated by the linear superposition of a discrete set of purely exponential relaxations plus a constant term. Alternatively the discrete spectrum of relaxation times involved in the synthesis of each Love number time history may be found exactly by solving the associated homogeneous problem. Such solutions determine the set of eigen-decay times associated with the normal modes of viscous gravitational relaxation of the visco-elastic planetary model. The solution of the inhomogeneous problem may be expressed in the form of a normal mode expansion. This normal mode expansion is employed as the basis for the construction of a rigorous first-order perturbation theory for the inference of the viscosity of the deep interior of the planet. A variational principle is derived which determines to first order that shift in position of a free decay pole in the relaxation spectrum which is forced by the addition of a radially-distributed perturbation of viscosity to the starting model. This determines the differential kernels required for the solution of the inverse problem. The uniqueness of the state of isostatic equilibrium for the viscously incompressible Maxwell models employed in this analysis is demonstrated and this uniqueness allows us to calculate the shift in the residue which is associated with the shift in position of a free decay pole for the inhomogeneous problem. The inhomogeneous problem is thus closed to first order. A formula is derived for the differential kernels appropriate to the inhomogeneous problem. The time domain form of these kernels may be calculated analytically. The structure of the full inverse theory is sufficiently simple that it may be employed to rigorously test the compatibility of the simple Maxwell model with the observed relaxation of the Earth's shape which accompanied deglaciation at the end of the last ice age.

Full waveform tomography for lithospheric imaging: results from a blind test in a realistic crustal model

Abstract: SUMMARY A comprehensive validation of 2-D, frequency-domain, acoustic wave-equation tomography was undertaken in a ‘blind test’, using third-party, realistic, elastic wave-equation data. The synthetic 2-D, wide-angle seismic data were provided prior to a recent workshop on the methods of controlled source seismology; the true model was not revealed to the authors until after the presentation of our waveform tomography results. The original model was specified on a detailed grid with variable P-wave velocity, S-wave velocity, density and viscoelastic Q-factor structure, designed to simulate a section of continental crust 250 km long and 40 km deep. Synthetic vertical and horizontal component data were available for 51 shot locations (spaced every 5 km), recorded at 2779 receivers (spaced every 90 m), evenly spread along the surface of the model. The data contained energy from 0.2 to 15 Hz. Waveform tomography, a combination of traveltime tomography and 2-D waveform inversion of the early arrivals of the seismic waveforms, was used to recover crustal P-velocity structure from the vertical component data, using data from 51 sources, 1390 receivers and frequencies between 0.8 and 7.0 Hz. The waveform tomography result contained apparent structure at wavelength-scale resolution that was not evident on the traveltime tomography result. The predicted (acoustic) waveforms in the final result matched the original elastic data to a high degree of accuracy. During the workshop, the exact model was revealed; over much of the model the waveform tomography results provided a good correspondence with the true model, from large- to intermediate-(wavelength) scales, with a resolution limit on the order of 1 km. A significant, near-surface low-velocity zone, invisible to traveltime methods, was correctly recovered; the results also provided a high-resolution image of the complex structure of the entire crust, and the depth and nature of the crust–mantle transition. Some inaccuracies were observed near the edges of the images due to the limited ray coverage inherent to the footprint of the survey geometry. Several aspects of the waveform tomography strategy were critical to the success of the acoustic method with realistic, synthetic, viscoelastic data: (i) the accuracy of the starting model from traveltime tomography, (ii) implementation in the frequency domain, (iii) the use of complex-valued frequencies to effect time damping of the data residuals, (iv) the selection of a suitable subset of data and data frequencies, (v) progressive inversion of low- to high-frequency components of the data, (vi) initial, pre-inversion matching of the amplitudes between observed and modelled data, and (vii) sufficient preconditioning of both the data and the update images. Combined, these strategies were effectively equivalent to a multiscale approach that mitigated the non-linearity of the seismic inverse problem. During the inversion we carried out repeated forward modelling to ensure our modelled waveforms matched the observed data as closely as possible in both frequency and time domains. The synthetic data set used in this paper provides a benchmark for future testing of modelling, inversion, and imaging algorithms for wide-angle lithospheric imaging.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - V. Local time stepping and p-adaptivity

Abstract: SUMMARY This article describes the extension of the arbitrary high-order Discontinuous Galerkin (ADER-DG) method to treat locally varying polynomial degress of the basis functions, so-called p-adaptivity, as well as locally varying time steps that may be different from one element to another. The p-adaptive version of the scheme is useful in complex 3-D models with small-scale features which have to be meshed with reasonably small elements to capture the necessary geometrical details of interest. Using a constant high polynomial degree of the basis functions in the whole computational domain can lead to an unreasonably high CPU effort since good spatial resolution at the surface may be already obtained by the fine mesh. Therefore, it can be more adequate in some cases to use a lower order method in the small elements to reduce the CPU effort without loosing much accuracy. To further increase computational efficiency, we present a new local time stepping (LTS) algorithm. For usual explicit time stepping schemes the element with the smallest time step resulting from the stability criterion of the method will dictate its time step to all the other elements of the computational domain. In contrast, by using local time stepping, each element can use its optimal time step given by the local stability condition. Our proposed LTS algorithm for ADER-DG is very general and does not need any temporal synchronization between the elements. Due to the ADER approach, accurate time interpolation is automatically provided at the element interfaces such that the computational overhead is very small and such that the method maintains the uniform high order of accuracy in space and time as in the usual ADER-DG schemes with a globally constant time step. However, the LTS ADER-DG method is computationally much more efficient for problems with strongly varying element size or material parameters since it allows to reduce the total number of element updates considerably. This holds especially for unstructured tetrahedral meshes that contain strongly degenerate elements, so-called slivers. We show numerical convergence results and CPU times for LTS ADER-DG schemes up to sixth order in space and time on irregular tetrahedral meshes containing elements of very different size and also on tetrahedral meshes containing slivers. Further validation of the algorithm is provided by results obtained for the layer over half-space (LOH.1) benchmark problem proposed by the Pacific Earthquake Engineering Research Center. Finally, we present a realistic application on earthquake modelling and ground motion prediction for the alpine valley of Grenoble.

Fault zone monitoring with passive image interferometry

Abstract: SUMMARY The technique of passive image interferometry applies interferometric methods to correlation functions of seismic noise to monitor small temporal variations of the Earth interior. We computed the autocorrelation function of seismic noise recorded at a single seismometer located in the vicinity of the source region of the Mw = 6.6 Mid-Niigata earthquake. Analysing the temporal evolution of the autocorrelation function, which is interpreted as the source‐ receiver collocated elastic wave Green’s function, we detect a sudden decrease of relative seismic velocity in the Earth crust of −0.6 per cent that coincides with the occurrence of the earthquake. This drop of seismic velocity is likely to be caused by the change of stress in the source region of the earthquake.

Ambient noise Rayleigh wave tomography of New Zealand

Abstract: SUMMARY We present the first New Zealand-wide study of surface wave dispersion, using ambient noise observed at 42 broad-band stations in the national seismic network (GeoNet) and the Global Seismic Network (GSN). Year-long vertical-component time-series recorded between 2005 April 1 and 2006 March 31 have been correlated with one another to yield estimated fundamental mode Rayleigh wave Green's functions. We filter these Green's functions to compute Rayleigh wave group dispersion curves at periods of 5–50 s, using a phase-matched filter, frequency–time analysis technique. The uncertainties of the measurements are estimated based on the temporal variation of the dispersion curves revealed by 12 overlapping 3-month stacks. After selecting the highest quality dispersion curve measurements, we compute group velocity maps from 7 to 25 s period. These maps, and 1-D shear wave velocity models at four selected locations, exhibit clear correlations with major geological structures, including the Taranaki and Canterbury Basins, the Hikurangi accretionary prism, and previously reported basement terrane boundaries.

Breakup and early seafloor spreading between India and Antarctica

Abstract: SUMMARY We present a tectonic interpretation of the breakup and early seafloor spreading between India and Antarctica based on improved coverage of potential field and seismic data off the east Antarctic margin between the Gunnerus Ridge and the Bruce Rise. We have identified a series of ENE trending Mesozoic magnetic anomalies from chron M9o (∼130.2 Ma) to M2o (∼124.1 Ma) in the Enderby Basin, and M9o to M4o (∼126.7 Ma) in the Princess Elizabeth Trough and Davis Sea Basin, indicating that India–Antarctica and India–Australia breakups were roughly contemporaneous. We present evidence for an abandoned spreading centre south of the Elan Bank microcontinent; the estimated timing of its extinction corresponds to the early surface expression of the Kerguelen Plume at the Southern Kerguelen Plateau around 120 Ma. We observe an increase in spreading rate from west to east, between chron M9 and M4 (38–54 mm yr–1), along the Antarctic margin and suggest the tectono-magmatic segmentation of oceanic crust has been influenced by inherited crustal structure, the kinematics of Gondwanaland breakup and the proximity to the Kerguelen hotspot. A high-amplitude, E–W oriented magnetic lineation named the Mac Robertson Coast Anomaly (MCA), coinciding with a landwards step-down in basement observed in seismic reflection data, is tentatively interpreted as the boundary between continental/transitional zone and oceanic crust. The exposure of lower crustal rocks along the coast suggests that this margin formed in a metamorphic core complex extension mode with a high strength ratio between upper and lower crust, which typically occurs above anomalously hot mantle. Together with the existence of the MCA zone this observation suggests that a mantle temperature anomaly predated the early surface outpouring/steady state magmatic production of the Kerguelen LIP. An alternative model suggests that the northward ridge jump was limited to the Elan Bank region, whereas seafloor spreading continued in the West Enderby Basin and its Sri Lankan conjugate margin. In this case, the MCA magnetic anomaly could be interpreted as the southern arm of a ridge propagator that stopped around 120 Ma.

A Model of the Geodynamo

Abstract: Summary The problem of the generation of the geomagnetic field by convection in the Earth's core is considered. The complete hydromagnetic problem including the Lorentz force is solved in the case of a cylindrical configuration. Because of the dominant effect of rotation this configuration incorporates the essential features of the dynamo process in the Earth's core. The results show general agreement with the known properties of geomagnetism and the Earth's core. It is found that the toroidal field in the core is of the same order of magnitude as the poloidal field. This result is consistent with the basic assumption of theory that the Lorentz force is small compared to the Coriolis force.

Balancing the plate motion budget in the South Island, New Zealand using GPS, geological and seismological data

Abstract: SUMMARY The landmass of New Zealand exists as a consequence of transpressional collision between the Australian and Pacific plates, providing an excellent opportunity to quantify the kinematics of deformation at this type of tectonic boundary. We interpret GPS, geological and seismological data describing the active deformation in the South Island, New Zealand by using an elastic, rotating block approach that automatically balances the Pacific/Australia relative plate motion budget. The data in New Zealand are fit to within uncertainty when inverted simultaneously for angular velocities of rotating tectonic blocks and the degree of coupling on faults bounding the blocks. We find that most of the plate motion budget has been accounted for in previous geological studies, although we suggest that the Porter’s Pass/Amberley fault zone in North Canterbury, and a zone of faults in the foothills of the Southern Alps may have slip rates about twice that of the geological estimates. Up to 5 mm yr −1 of active deformation on faults distributed within the Southern Alps <100 km to the east of the Alpine Fault is possible. The role of tectonic block rotations in partitioning plate boundary deformation is less pronounced in the South Island compared to the North Island. Vertical axis rotation rates of tectonic blocks in the South Island are similar to that of the Pacific Plate, suggesting that edge forces dominate the block kinematics there. The southward migrating Chatham Rise exerts a major influence on the evolution of the New Zealand plate boundary; we discuss a model for the development of the Marlborough fault system and Hikurangi subduction zone in the context of this migration.

The Application of Finite Element Analysis to Body Wave Propagation Problems

Abstract: Summary The finite element method is shown to be a powerful tool for the numerical modelling of seismic body wave propagation problems. Applications extend to both problems on a scale of interest to engineers and also to large-scale seismological problems. Solutions are sought in the time domain. Efficient programs have been written to accomplish this. The scope of numerical solutions has been greatly enhanced by the use of a previously reported scheme for exactly cancelling reflections at the boundaries of the model. The finite difference results of Boore and the analytical results of Trifunac for the amplification due to a mountain and an alluvial valley respectively are compared with new finite element results. The new results agree well, although there are some difficulties with resonance in the alluvial valley problem. Boore's SH results have been extended to vertical P and SV incidence. A deep earthquake zone has been modelled realistically in two dimensions and earthquakes simulated at depth. It is suggested that the variation in observed amplitude across the top of the zone, due to refraction away from the slab, may be used to provide an estimate of the thickness of the slab from long-period observations of local earthquakes.

Calculating horizontal stress orientations with full or partial knowledge of the tectonic stress tensor

Abstract: Calculating horizontal stress orientations with full or partial knowledge of the tectonic stress tensor

Geometry and brittle deformation of the subducting Nazca Plate, Central Chile and Argentina

Abstract: SUMMARY We use data from the Chile Argentina Geophysical Experiment (CHARGE) broad-band seismic deployment to refine past observations of the geometry and deformation within the subducting slab in the South American subduction zone between 30 ◦ S and 36 ◦ S. This region contains a zone of flat slab subduction where the subducting Nazca Plate flattens at a depth of ∼100 km and extends ∼300 km eastward before continuing its descent into the mantle. We use a grid-search multiple-event earthquake relocation technique to relocate 1098 events within the subducting slab and generate contours of the Wadati-Benioff zone. These contours reflect slab geometries from previous studies of intermediate-depth seismicity in this region with some small but important deviations. Our hypocentres indicate that the shallowest portion of the flat slab is a

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes — III. Viscoelastic attenuation

Abstract: SUMMARY We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity–stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy–Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy–Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER–DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

Tidal Computations for Morecambe Bay

Abstract: Summary A numerical finite-difference technique for computing tides in areas of shoaling water has been established and used to calculate the M2 tide in Morecambe Bay An essential feature of the method is the representation of drying banks, which appear as the water level falls on the ebb, and which are re-submerged on the flood as the level rises again Since the non-linear advective acceleration should be important in shallow water, schemes for incorporating these terms are examined and the influence of advection on the tide assessed In a series of tests, the open sea tides applied to the outer boundary of the numerical bay model were taken first from existing tidal charts, then from calculations with a larger-scale encompassing model, and finally from observations of current In each case, the computed tidal elevations within the Bay turned out to be in satisfactory agreement with those obtained from observations However, it is significant that, in the first case, inaccuracy of the input tidal distribution deduced from charts gives rise to erroneous currents near the boundary

Spherically symmetric attenuation within the Earth from normal mode data

Abstract: SUMMARY Observations of the attenuation of free oscillations after large earthquakes are used to determine the spherically symmetric dissipative structure within the Earth. We model intrinsic attenuation of seismic energy between 0.3 and 10mHz with a frequency-independent Q model. The resolving power of our data indicates that simple models of Q can explain our observations and that we do not have enough information to constrain detailed absorption band models. The average shear Q is relatively well constrained for the mantle and is 250 f 2 per cent. The shear Q in the inner core is mostly constrained by new observations of PKIKP equivalent modes and is 110 f 25 per cent. This is lower than in some previous models, which have used possibly erroneous observations of core modes, though the new models still predict too little attenuation to match the observations of strong differential attenuation of the BC and DF branches of PKP at frequencies of about 1 Hz. Agreement between the mode and body-wave data sets should probably not be expected since it now seems likely that the PKIKP data sense an absorption band which is distinct from that sensed by the mode data. The distribution of bulk attenuation in the Earth remains ill-constrained though bulk attenuation is required somewhere to explain the attenuation of the radial modes. Successful models tend to put significant bulk Q in the upper mantle.