Showing papers in "Geophysical Journal International in 2000"

Fréchet kernels for finite-frequency traveltimes—I. Theory

Abstract: Summary We use body wave ray theory in conjunction with the Born approximation tocompute 3-D Frechet kernels for finite-frequency seismic traveltimes, measured by cross-correlation of a broad-band waveform with a spherical earth synthetic seismogram. Destructive interference among adjacent frequencies in the broad-band pulse renders a cross-correlation traveltime measurement sensitive only to the wave speed in a hollow banana-shaped region surrounding the unperturbed geometrical ray. The Frechet kernel expressing this sensitivity is expressed as a double sum over all forward-propagating body waves from the source and backward-propagating body waves from the receiver to every single scatterer in the vicinity of this central ray. The kernel for a differential traveltime, measured by cross-correlation of two phases at the same receiver, is simply the difference of the respective single-phase kernels. In the paraxial approximation, an absolute or differential traveltime kernel can be computed extremely economically by implementing a single kinematic and dynamic ray trace along each source-to-receiver ray.

Joint inversion of receiver function and surface wave dispersion observations

Abstract: We implement a method to invert jointly teleseismic P-wave receiver functions and surface wave group and phase velocities for a mutually consistent estimate of earth structure. Receiver functions are primarily sensitive to shear wave velocity contrasts and vertical traveltimes, and surface wave dispersion measurements are sensitive to vertical shear wave velocity averages. Their combination may bridge resolution gaps associated with each individual data set. We formulate a linearized shear velocity inversion that is solved using a damped least-squares scheme that incorporates a priori smoothness constraints for velocities in adjacent layers. The data sets are equalized for the number of data points and physical units in the inversion process. The combination of information produces a relatively simple model with a minimal number of sharp velocity contrasts. We illustrate the approach using noise-free and realistic noise simulations and conclude with an inversion of observations from the Saudi Arabian Shield. Inversion results for station SODA, located in the Arabian Shield, include a crust with a sharp gradient near the surface (shear velocity changing from 1.8 to 3.5 km s−1 in 3 km) underlain by a 5-km-thick layer with a shear velocity of 3.5 km s−1 and a 27-km-thick layer with a shear velocity of 3.8 km s−1, and an upper mantle with an average shear velocity of 4.7 km s−1. The crust–mantle transition has a significant gradient, with velocity values varying from 3.8 to 4.7 km s−1 between 35 and 40 km depth. Our results are compatible with independent inversions for crustal structure using refraction data.

The three‐dimensional shear velocity structure of the mantle from the inversion of body, surface and higher‐mode waveforms

Abstract: SUMMARY We present a 3-D model of shear heterogeneity (Vsh) in the whole mantle, derived from the inversion of hand-picked body, surface and higher-mode waveforms. The forward and inverse problems are formulated using the non-linear asymptotic coupling theory, the zeroth-order asymptotic expansion of a Born seismogram computed by normal mode summation and including coupling across mode branches. We invert iteratively for mantle heterogeneity and for centroid moment tensors until convergence. Our model, SAW24B16, is parametrized laterally in spherical harmonics up to degree 24 and radially in 16 cubic b-splines with knots spaced to reflect the data sampling with depth. The power spectrum of the model is dominated by heterogeneity in the boundary layers at low degrees: degrees 5 and 6 near the surface and degree 2 near the core–mantle boundary. The rest of the lower mantle is dominated by degree 3. We find significant heterogeneity up to spherical harmonic degree 24 in the transition zone and the uppermost part of the lower mantle. Our model displays three slow domains extending continuously between uppermost and lowermost mantle, one originating under Africa and two in the Pacific. The results of our modelling also suggest an interaction near the surface between the anomalies in the Pacific and the network of mid-ocean ridges in the East Pacific, and between the African anomaly and the low-velocity zone in the Red Sea, the East African Rift, the Mid-Indian Ridge and the Mid-Atlantic Ridge. These anomalies appear to ascend into the upper mantle without altering their shape near the 670 km discontinuity. Fast anomalies accumulate near the 670 km discontinuity under the Southern Kurile, the Japan trench and the Izu arc, with little or no penetration into the lower mantle, in agreement with results from a variety of regional studies. Cross-sections through subduction zones such as the Marianas, Tonga–Kermadec, Java, the palaeosubduction zone beneath North America and the Peru–Chile trench show continuous fast structures penetrating into the lower mantle, with the depth of penetration varying from region to region. The distribution of both fast and slow anomalies near 670 km thus suggests that the discontinuity does not act as a strong barrier to upgoing and downgoing flow between the upper and the lower mantle.

Three-dimensional magnetotelluric inversion using non-linear conjugate gradients

Abstract: We have formulated a 3-D inverse solution for the magnetotelluric (MT) problem using the non-linear conjugate gradient method. Finite difference methods are used to compute predicted data efficiently and objective functional gradients. Only six forward modelling applications per frequency are typically required to produce the model update at each iteration. This efficiency is achieved by incorporating a simple line search procedure that calls for a sufficient reduction in the objective functional, instead of an exact determination of its minimum along a given descent direction. Additional efficiencies in the scheme are sought by incorporating preconditioning to accelerate solution convergence. Even with these efficiencies, the solution’s realism and complexity are still limited by the speed and memory of serial processors. To overcome this barrier, the scheme has been implemented on a parallel computing platform where tens to thousands of processors operate on the problem simultaneously. The inversion scheme is tested by inverting data produced with a forward modelling code algorithmically different from that employed in the inversion algorithm. This check provides independent verification of the scheme since the two forward modelling algorithms are prone to different types of numerical error.

A re‐assessment of focal depth distributions in southern Iran, the Tien Shan and northern India: do earthquakes really occur in the continental mantle?

Abstract: SUMMARY We investigate the depth distribution of earthquakes within the continental lithosphere of southern Iran, the Tien Shan and northern India by using synthetic seismograms to analyse P and SH body waveforms. In the Zagros mountains of southern Iran, earthquakes are apparently restricted to the upper crust (depths of <20 km), whereas in the Tien Shan and northern India they occur throughout the thickness of the continental crust, to depths of ∼40–45 km. We find no convincing evidence for earthquakes in the continental mantle of these regions, in spite of previous suggestions to the contrary, and question whether seismicity in the continental mantle is important in any part of the world. In some regions, such as Iran, the Aegean, Tibet and California, seismicity is virtually restricted to the upper continental crust, whereas in others, including parts of East Africa, the Tien Shan and northern India, the lower crust is also seismically active, although usually less so than the upper crust. Such variations cannot reliably be demonstrated from published catalogue or bulletin locations, even from ones in which depth resolution is generally improved. In contrast to the oceanic mantle lithosphere, in which earthquakes certainly occur, the continental mantle lithosphere is, we suggest, virtually aseismic and may not be significantly stronger than the lower continental crust. These variations in continental seismogenic thickness are broadly correlated with variations in effective elastic thickness, suggesting that the strength of the continental lithosphere resides in the crust, and require some modification to prevalent views of lithosphere rheology.

Modelling teleseismic waves in dipping anisotropic structures

Abstract: SUMMARY The existence of seismic discontinuities within the continental upper mantle has long been recognized, with more recent studies often indicating an association with elastic anisotropy. Their near-vertical sampling renders teleseismic P and S waves suitable for characterization of mantle discontinuities, but computationally e⁄cient methods of calculating synthetic seismograms are required for structures that exhibit lateral variability. We consider lithospheric models consisting of planar, homogeneous anisotropic layers with arbitrary dip.We adopt the traveltime equation of Diebold for dipping, plane-layered media as the basis for a high-frequency asymptotic method that does not require ray tracing. Traveltimes of plane waves in anisotropic media are calculated from simple analytic formulae involving the depths of layers beneath a station and the vertical components of phase slowness within the layers. We compute amplitudes using the re£ection and transmission matrices for planar interfaces separating homogeneous anisotropic media. Modelling indicates that upper-mantle seismic responses depend in a complex fashion on both layer dip and anisotropy, particularly in the case of converted phases. Azimuthal anisotropy generally displays a distinctive 180 0 backazimuthal periodicity in Ps conversion amplitude, as opposed to the 360 0 symmetry produced by dip. In contrast, anisotropy with a steeply plunging axis may under certain conditionsbe di⁄cultto distinguish from interface dip, asboth exhibit a 360 0 symmetry. We demonstrate the application of the method on Ps and Sp conversion data from the Yellowknife Array, which show evidence for both dipping and anisotropic layering, attributed to layers of anisotropic fabric in the upper mantle associated with ancient subducted slabs.

Probabilistic forecasting of earthquakes

Abstract: We present long‐term and short‐term forecasts for magnitude 5.8 and larger earthquakes. We discuss a method for optimizing both procedures and testing their forecasting effectiveness using the likelihood function. Our forecasts are expressed as the rate density (that is, the probability per unit area and time) anywhere on the Earth. Our forecasts are for scientific testing only; they are not to be construed as earthquake predictions or warnings, and they carry no official endorsement. For our long‐term forecast we assume that the rate density is proportional to a smoothed version of past seismicity (using the Harvard CMT catalogue). This is in some ways antithetical to the seismic gap model, which assumes that recent earthquakes deter future ones. The estimated rate density depends linearly on the magnitude of past earthquakes and approximately on a negative power of the epicentral distance out to a few hundred kilometres. We assume no explicit time dependence, although the estimated rate density will vary slightly from day to day as earthquakes enter the catalogue. The forecast applies to the ensemble of earthquakes during the test period. It is not meant to predict any single earthquake, and no single earthquake or lack of one is adequate to evaluate such a hypothesis. We assume that 1 per cent of all earthquakes are surprises, assumed uniformly likely to occur in those areas with no earthquakes since 1977. We have made specific forecasts for the calendar year 1999 for the Northwest Pacific and Southwest Pacific regions, and we plan to expand the forecast to the whole Earth. We test the forecast against the earthquake catalogue using a likelihood test and present the results. Our short‐term forecast, updated daily, makes explicit use of statistical models describing earthquake clustering. Like the long‐term forecast, the short‐term version is expressed as a rate density in location, magnitude and time. However, the short‐term forecasts will change significantly from day to day in response to recent earthquakes. The forecast applies to main shocks, aftershocks, aftershocks of aftershocks, and main shocks preceded by foreshocks. However, there is no need to label each event, and the method is completely automatic. According to the model, nearly 10 per cent of moderately sized earthquakes will be followed by larger ones within a few weeks.

Non‐linear global P‐wave tomography by iterated linearized inversion

Abstract: Summary Recent advances in global imaging have lead to tomographic mantle models with regional scale details To improve these models further, we have extended the usual linearized approach to traveltime tomography to non-linear tomography Here ‘non-linear’ means that seismic ray bending due to inferred velocity heterogeneity is taken into account in an iterative method in which inversion steps are alternated with 3-D ray tracing to update ray paths and traveltimes As a starting point for our non-linear inversion we have used the mantle model of Bijwaard et al(1998) and ray tracing is performed following Bijwaard & Spakman (1999a) We have not attempted a full exploration of the non-linear nature of the traveltime inverse problem This would at the very least require tests with different starting models and the relocation of all events in each of these models The main results are as follows We observe no overall dramatic change in anomaly patterns, but subtle changes on the global mantle scale lead to a small increase in variance reduction and model amplitudes These small changes together with very similar resolution estimates for the linear and non-linear inversions do not allow us to investigate formally possible model improvements However, expected non-linear effects such as the focusing of structures and a baseline shift towards lower velocities indicate an improved solution, which is also more consistent with expected physics than a fully linearized inversion Apart from that, some very strong changes occur in distinct upper mantle regions such as below Japan, Tibet, South America, Europe and Tonga–Fiji, where 3-D ray bending effects are substantially larger than in the deeper mantle since model amplitudes fall off rapidly with depth In the lower mantle, how-ever, increased focusing effects can be observed that may prove important for detailed interpretations

Upper mantle stratification by P and S receiver functions

Abstract: Summary Seismic stratification of the upper mantle is investigated by applying two complementary techniques to the records of the Graefenberg array in southern Germany. The anisotropic P receiver function technique (Kosarev et al. 1984; Vinnik & Montagner 1996) is modified by using summary seismic events instead of individual events and different weighting functions instead of the same function for the harmonic angular analysis of the SV and T components of the Pds phases. The summary events provide better separation of the second azimuthal harmonic than the individual events. The parameters of the second harmonics of SV and T thus evaluated should be similar if they reflect the effects of azimuthal anisotropy. This can be used as a criterion to identify the anisotropy. To detect the Sdp phases and their azimuthal variations caused by azimuthal anisotropy we have developed a stacking technique, which can be termed the S receiver function technique It includes axis rotation to separate interfering P and S arrivals, determination of the principal (M) component of the S-wave motion, deconvolution of the P components of many recordings by their respective M components and stacking of the deconvolved P components with weights depending on the level of noise and the angle between the M direction and the backazimuth of the event. Both techniques yield consistent results for the Graefenberg array. As indicated by the P receiver functions, the upper layer of the mantle between the Moho and 80 km depth is anisotropic with dVs/Vs around 0.03 and the fast direction close to 20° clockwise from north. The fast direction of anisotropy below this layer is around 110°, The boundary between the upper and the lower anisotropic layers is manifested by the detectable Pds and Sdp converted phases. Shear wave splitting in SKS is strongly dominated by azimuthal anisotropy in the lower layer (asthenosphere).

Fréchet kernels for finite‐frequency traveltimes—II. Examples

Abstract: Summary 3-D Born–Frechet traveltime kernel theory is recast in the context of scalar-wave propagation in a smooth acoustic medium, for simplicity. The predictions of the theory are in excellent agreement with ‘ground truth’ traveltime shifts, measured by cross-correlation of heterogeneous-medium and homogeneous-medium synthetic seismograms, computed using a parallelized pseudospectral code. Scattering, wave-front healing and other finite-frequency diffraction effects can give rise to cross-correlation traveltime shifts that are in significant disagreement with geometrical ray theory, whenever the cross-path width of wave-speed heterogeneity is of the same order as the width of the banana–doughnut Frechet kernel surrounding the ray. A concentrated off-path slow or fast anomaly can give rise to a larger traveltime shift than one directly on the ray path, by virtue of the hollow-banana character of the kernel. The often intricate 3-D geometry of the sensitivity kernels of P, PP, PcP, PcP2, PcP3, ? and P+pP waves is explored, in a series of colourful cross-sections. The geometries of an absolute PP kernel and a differential PP−P kernel are particularly complicated, because of the minimax nature of the surface-reflected PP wave. The kernel for an overlapping P+pP wave from a shallow-focus source has a banana–doughnut character, like that of an isolated P-wave kernel, even when the teleseismic pulse shape is significantly distorted by the depth phase interference. A numerically economical representation of the 3-D traveltime sensitivity, based upon the paraxial approximation, is in excellent agreement with the ‘exact’ ray-theoretical Frechet kernel.

Shallow subduction zone earthquakes and their tsunamigenic potential

Abstract: SUMMARY We have examined the source spectra of all shallow subduction zone earthquakes from 1992 to 1996 with moment magnitude 7.0 or greater, as well as some other interesting events, in the period range 1‐20 s, by computing moment rate functions of teleseismic P waves. After comparing the source spectral characteristics of ‘tsunami earthquakes’ (earthquakes that are followed by tsunamis greater than would be expected from their moment magnitude) with regular events, we identified a subclass of this group: ‘slow tsunami earthquakes’. This subclass consists of the 1992 Nicaragua, the 1994 Java and the February 1996 Peru earthquakes. We found that these events have an anomalously low energy release in the 1‐20 s frequency band with respect to their moment magnitude, although their spectral drop-oV is comparable to those of the other earthquakes. From an investigation of the centroid and body wave locations, it appears that most earthquakes in this study conformed to a simple model in which the earthquake nucleates in a zone of compacted and dehydrated sediments and ruptures up-dip until the stable sliding friction regime of unconsolidated sediments stops the propagation. Sedimentstarved trenches, e.g. near Jalisco, can produce very shallow slip, because the fault material supports unstable sliding. The slow tsunami earthquakes also ruptured up-dip; however, their centroid is located unusually close to the trench axis. The subduction zones in which these events occurred all have a small accretionary prism and a thin layer of subducting sediment. Ocean surveys show that in these regions the ocean floor close to the trench is highly faulted. We suggest that the horst-and-graben structure of a rough subducting oceanic plate will cause contact zones with the overriding plate, making shallow earthquake nucleation and up-dip propagation to the ocean floor possible. The rupture partly propagates in sediments, making the earthquake source process slow. Two factors have to be considered in the high tsunami-generating potential of these events. First, the slip propagates to shallow depths in low-rigidity material, causing great deformation and displacement of a large volume of water. Second, the measured seismic moment may not represent the true earthquake displacement, because the elastic constants of the source region are not taken into account in the standard CMT determination.

Observations of flexure and the rheology of oceanic lithosphere

Abstract: The principal evidence for the long-term (i.e. > 1 Myr) mechanical behaviour of the oceanic lithosphere has come from studies of how it deforms in response to large loads such as volcanoes and sediments. A model widely used to explain the deformation is an elastic plate in which flexural rigidity depends on the thermal age of the lithosphere at the time of loading. An elastic model, however, is time-invariant and does not take into account temporal changes that may occur in the flexural rigidity as a consequence of loading. There is evidence, for example, that the flexural rigidity of the oceanic lithosphere also depends on load age, being large at short times and small at long times. Thus, competing effects may exist between thermal cooling which strengthens the lithosphere and some form of load-induced stress relaxation which weakens it. In order to investigate the relative roles of these processes, we have developed a multilayered viscoelastic model which is based on the results of experimental rock mechanics that creep in the lithosphere is a thermally activated process, and on a thermal structure that is given by the plate-cooling model. By comparing the predictions of the model with a new compilation of flexural rigidity estimates, we have found that, if the upper mantle viscosity is 1020 Pa s, the activation energy that best describes the long-term mechanical behaviour of the oceanic lithosphere is 120 KJ mol−1. This parameter pair explains the dependence of flexural rigidity on both plate and load age. It also helps account for the subsidence and uplift history of oceanic islands and the stratigraphic patterns that develop in the flexural moats that flank them. At atolls, a multilayered viscoelastic model explains the rapid subsidence that follows shield building and does not require that the age of the lithosphere that supports a volcano is thermally ‘re-set’ to a younger value. Our studies suggest that, while the oceanic lithosphere has viscoelastic properties, the viscosity of its upper layers is so much higher than that of its lower layers that in effect it behaves as a thin elastic plate on long timescales. There will therefore be a certain permanence to the observations of oceanic flexure such that they may be used, with some confidence, to evaluate the tectonic setting of individual features of the seafloor and, in some cases, their age.

Variations in the geomagnetic dipole moment over the last 12 000 years

Abstract: SUMMARY An analysis has been made of archaeointensity data for the past 12 000 years. There are 3243 results from diVerent areas of the world covering the past 12 000 years. Of these, 2203 are from the European region and 1040 are from the rest of the world. The archaeointensity data set analysed in the present study is almost three times larger than that used by McElhinny & Senanayake (1982). Although there is no major diVerence between our global data and the earlier data, the data for the non-European region have been improved and we now have a data set for Asia.

Review of the low‐temperature magnetic properties of magnetite from a rock magnetic perspective

Abstract: The low-temperature magnetic properties of magnetite are reviewed, and implications for rock magnetism considered. The behaviour of fundamental properties of magnetite at low temperatures near the Verwey transition (Tv ) are documented, and attention is given to various Verwey transition theories. The low-temperature behaviour of the magnetic energies that control domain structure is reviewed in detail. For the first time in rock magnetic literature, the low-temperature anomaly in spontaneous magnetization (Ms ) is documented and the differences between the saturation magnetization and Ms near the Verwey transition are discussed. It is argued that the low-temperature behaviour of the magnetocrystalline anisotropy, and in particular the anomaly at Tv , is most likely to affect multidomain remanence during low-temperature cycling. For multidomain crystals it is calculated that the large increase in magnetocrystalline anisotropy intensity and reduction in symmetry on cooling through Tv is likely to reduce the stability of closure domains.

A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences

Abstract: SUMMARY It is common practice to refer to three independent stages of creep under static loading conditions in the laboratory: namely transient, steady-state, and accelerating. Here we suggest a simple damage mechanics model for the apparently trimodal behaviour of the strain and event rate dependence, by invoking two local mechanisms of positive and negative feedback applied to constitutive rules for time-dependent subcritical crack growth. In both phases, the individual constitutive rule for measured strain e takes the form e(t)=e 0 [1+t/mt]m, where t is the ratio of initial crack length to rupture velocity. For a local hardening mechanism (negative feedback), we find that transient creep dominates, with 0

Slip rate on the Dead Sea transform fault in northern Araba valley (Jordan)

Abstract: The Araba valley lies between the southern tip of the Dead Sea and the Gulf of Aqaba. This depression, blanketed with alluvial and lacustrine deposits, is cut along its entire length by the Dead Sea fault. In many places the fault is well defined by scarps, and evidence for left-lateral strike-slip faulting is abundant. The slip rate on the fault can be constrained from dated geomorphic features displaced by the fault. A large fan at the mouth of Wadi Dahal has been displaced by about 500 m since the bulk of the fanglomerates were deposited 77–140 kyr ago, as dated from cosmogenic isotope analysis (^(10)Be in chert) of pebbles collected on the fan surface and from the age of transgressive lacustrine sediments capping the fan. Holocene alluvial surfaces are also clearly offset. By correlation with similar surfaces along the Dead Sea lake margin, we propose a chronology for their emplacement. Taken together, our observations suggest an average slip rate over the Late Pleistocene of between 2 and 6 mm yr^(−1), with a preferred value of 4 mm yr^(−1). This slip rate is shown to be consistent with other constraints on the kinematics of the Arabian plate, assuming a rotation rate of about 0.396° Myr^(−1) around a pole at 31.1°N, 26.7°E relative to Africa.

Three‐dimensional Fréchet differential kernels for seismicdelay times

Abstract: Summary Seismic traveltimes are the most widely exploited data in seismology. Their Frechet or sensitivity kernels are important tools in tomographic inversions based on the Born or single-scattering approximation. The current study is motivated by a paradox posed by two seemingly irreconcilable observations in the numerical calculations for the sensitivity kernels of the traveltime perturbations. Calculations of kernels for 2-D media by the normal-mode approach indicate that traveltimes are most sensitive to the structure on and around the geometrical ray paths corresponding to the seismic arrivals, whereas calculations for 3-D media by geometrical ray theory predict exactly zero sensitivities on the ray paths. In the current work, we employ these two completely different wave-propagation approaches, the more efficient geometrical ray theory and the more accurate normal-mode theory, to investigate the 3-D sensitivities of the delay times to shear-wave speed variations. Expressions for the delay-time Frechet kernels are presented for both methods, and extensive numerical experiments are conducted for various types of seismic phases as well as for different reference earth models. The results show that the contradictory observations are but two examples of a wide range of behaviours in the delay-time sensitivity. For most of the seismic phases in realistic reference models with multiple discontinuities, wave-speed gradients and low-velocity zones, the wavefields are highly complicated and ray theory, which describes the response by the contributions of a few geometrical rays between the source and receiver, produces qualitatively different delay-time kernels from those obtained by the normal-mode theory, which includes essentially all contributions.

Seismicity of the Sea of Marmara (Turkey) since 1500

Abstract: SUMMARY We use the earthquake history of the last 500 years to help evaluate the tectonic and hazard contexts of the1999 earthquakes at Izmit and Dzce in westernTurkey.The 20th century has been unusually active, but over the 500 year period the seismic moment release can account for the known right-lateral shear velocity across the Marmara region observed by GPS. Two areas of known late Quaternary faulting stand out as unusually quiet over this period: the northwest shore of the Sea of Marmara and the southern branch of the North Anatolian fault system between Bursa and Mudurnu.

Reply to comment by W. Fjeldskaar ‘What about the asthenosphere viscosity? Sea‐level change, glacial rebound and mantle viscosity for northern Europe’

Abstract: viscosity profiles that best match the observational database. include a low-viscosity channel in the upper mantle (Fjeldskaar Neither point to a well-developed low-viscosity channel in the 2000). In our paper we clearly noted that we examined only a upper mantle, and the second model compares well with the part of the possible earth-model space and that we restricted results from the sea-level analysis only. ourselves to a three-mantle-layer model comprising a lithoThe second reason for not pursuing the more detailed sphere, an upper mantle extending from the base of the solutions for the Scandinavian region is that a major limitation lithosphere down to the 670 km seismic discontinuity, and a in the modelling is the inadequate knowledge of the temporal lower mantle. A broad range of parameters defining these three and spatial distribution of the ice cover over the region, and, layers was explored and no a priori values were attached to based on tests with different ice models, we concluded that this any one layer. This is important in that considerable trade-off was more important than differences in predictions between between parameters can result. We were careful to note that the threeand five-layer mantle models: unless some modification analysis yielded only first-order results and that the resulting of the ice sheet was permitted in the inversion, this would earth-model parameters are effective values that, while they result in a very considerable dependence of earth-model results appear to give an adequate description of the rebound evidence on the adopted ice model (for example, compare Figs 16(a) (the relative sea-level change and shoreline migration), may and (b) and Fig. 33(b) in LSJ). We concluded that further not be a true reflection of the actual physical layering within the improvements in the knowledge of the spatial and temporal Earth. We also noted that further work is required to examine distribution of the ice are required before it becomes worthwhile whether a higher degree of mantle layering is appropriate to explore the earth structure in greater detail. Subsequent (e.g. p. 135). inversions in LSJ therefore placed greater emphasis on the ice The reason we did not conduct a more exhaustive search of model than on the detailed earth structure, although care was the model space was two-fold. The first was that our earlier taken at all times to ensure that an adequate separation of the experience with the British rebound modelling (Lambeck et al. earthand ice-model parameters occurred. 1996) led to the conclusion that five-layer mantle models, Three inversions of independent sea-level data for ice-sheet including the low-viscosity asthenosphere option, yielded only parameters and (three-layered) mantle parameters led to a marginal improvement in the overall comparison of preconsistent conclusions about likely ice thicknesses during Latedictions of sea-level change with observations. Fig. 1 illustrates glacial times. These data sets are the Lateand postglacial the two sets of effective earth-model parameters that were geological evidence for sea-level change across the region found to be optimal for the threeand five-layer models. The (LSJ), the tide-gauge data for the region (Lambeck et al. five-layer model is physically more intuitive but, in the British 1998b), and the timing and elevation data of various Baltic lake Isles case, it does not lead to a significant improvement in the stages (Lambeck 1999). In all cases, thick, quasi-parabolic ice ability to predict Lateand postglacial sea levels and shoreline models, in which ice thickness increases rapidly with distance locations compared to the three-layer model. In this particular from the ice margin, yield predictions that are inconsistent case the observational database has only limited resolving with the sea-level and shoreline observations for the southern power for isolating the higher-resolution structure in the mantle, and southeastern Scandinavia and Baltic regions (see also and for ‘all predictive purposes of sea-level change and shoreTushingham & Peltier 1991 and Lambeck et al. 1990). With line evolution, three-layer or five-layer models are essentially the exception of some of the Norwegian coastal zones, the

A precisely dated Proterozoic palaeomagnetic pole from the North China craton, and its relevance to palaeocontinental reconstruction

Abstract: A palaeomagnetic pole position, derived from a precisely dated primary remanence, with minimal uncertainties due to secular variation and structural correction, has been obtained for China’s largest dyke swarm, which trends for about 1000 km in a NNW direction across the North China craton. Positive palaeomagnetic contact tests on two dykes signify that the remanent magnetization is primary and formed during initial cooling of the intrusions. The age of one of these dykes, based on U–Pb dating of primary zircon, is 1769.1 ± 2.5 Ma. The mean palaeomagnetic direction for 19 dykes, after structural correction, is D = 36°, I = − 5°, k = 63, α95 = 4°, yielding a palaeomagnetic pole at Plat=36°N, Plong=247°E, dp = 2°, dm = 4° and a palaeolatitude of 2.6°S. Comparison of this pole position with others of similar age from the Canadian Shield allows a continental reconstruction that is compatible with a more or less unchanged configuration of Laurentia, Siberia and the North China craton since about 1800 Ma

Characterization of the magnetotelluric tensor in terms of its invariants

Abstract: Summary The magnetotelluric impedance tensor is defined in terms of seven independent parameters that are invariant under a rotation of the horizontal axes on the surface of the Earth, plus an angle that defines the orientation of the axes of reference. The invariants are algebraically related to but nevertheless different from those recently proposed by Szarka & Menvielle (1997). They have been chosen in such a way as to have clear representations on a Mohr circle diagram and also to reveal geoelectric properties of the Earth near the site where the impedance data are measured. The first two invariants define the properties of a 1-D earth when the next four invariants are negligibly small. If the next two are also non-negligible, the earth is 2-D with a strike direction that can be recovered. The last three invariants indicate different degrees of three-dimensionality and the discussion of them with reference to small-scale galvanic distortion in an otherwise 1- or 2-D structure largely retraces the insightful pioneering work of Bahr (1988). The properties of the invariants are illustrated with numerical calculations for a synthetic model consisting of a small conductive anomaly in the form of a cube at the surface of an otherwise 2-D earth that is divided by a vertical fault into regions with a strong resistivity contrast. Results are presented for synthetic data that contain only numerical noise, and for data to which 2 per cent random Gaussian noise has been added. The theoretical properties of the invariants are verified by the pure numerical data, and are confirmed statistically by the noisy data.

Numerical simulations of the propagation path and the arrest of fluid‐filled fractures in the Earth

Abstract: SUMMARY We use a boundary element method to study the growth and quasi-static propagation of £uid-¢lled fractures in regions with inhomogeneous and deviatoric stresses. The wholesale migration of fractures due to their opening at one end and closing at the other can be simulated when using a ¢nite £uid mass contained in a fracture and considering £uid compression or expansion with changing fracture volume; these fractures are driven by stress gradients and by the density diierences between the £uid and the surrounding rock. Contrary to commonly held beliefs, the fracture growth and the propagation directions are not controlled only by the direction of the principal stresses, but also by tectonic stress gradients, apparent buoyancy forces and the length of the fractures themselves. The models help to explain the formation of sills, the lateral migration of magmas under volcanoes and the absence of volcanoes under the shallow parts of the Nazca plate.

Seismic wave propagation in cracked porous media

Abstract: Summary The movement of interstitial fluids within a cracked solid can have a significant effect on the properties of seismic waves of long wavelength propagating through the solid. We consider three distinct mechanisms of wave-induced fluid flow: flow through connections between cracks in an otherwise non-porous material, fluid movement within partially saturated cracks, and diffusion from the cracks into a porous matrix material. In each case the cracks may be aligned or randomly oriented, leading, respectively, to anisotropic or isotropic wave speeds and attenuation factors. In general, seismic velocities exhibit behaviour that is intermediate between that of empty cracks and that of isolated liquid-filled cracks if fluid flow is significant. In the range of frequencies for which considerable fluid flow occurs there is high attenuation and dispersion of seismic waves. Fluid flow may be on either a wavelength scale or a local scale depending on the model and whether the cracks are aligned or randomly oriented, resulting in completely different effects on seismic wave propagation. A numerical analysis shows that all models can have an effect over the exploration seismic frequency range.

An alternative interpretation of the Cayman trough evolution from a reidentification of magnetic anomalies

Abstract: Magnetic data were collected during the Wilkes (1973) and Seacarib II (1987) cruises to the Cayman trough. A new interpretation of magnetic data is carried out. An isochron pattern is drawn up from our anomaly identifications. An early Eocene age (49 Ma, Ypresian) for Cayman trough opening is proposed instead of the late Oligocene or middle Eocene ages suggested by previous studies. Our plate tectonic reconstruction is simpler and fits the on-land geology (Jamaica and Cuba) and the tectonics. Our reconstruction shows a southward propagation of the spreading centre between magnetic anomalies 8 and 6 (26 and 20 Ma). The trough width increases by 30 km in this period. The southward propagation of the Cayman spreading centre from the Middle Oligocene to the Early Miocene induced the development of the restraining bend of the Swan Islands, the formation of a 1 km high scarp on the eastern trace of the Cayman trough transform fault (Walton fault) and the formation of a pull-apart basin (Hendrix pull-apart). Magnetic anomalies and magnetization maps give information about the deformation and the rocks. The proposed evolutionary model of the Cayman trough from the inception of seafloor spreading to the present configuration is presented in relation to the tectonic escape of the northern boundary of the Caribbean plate from the Maastrichtian to the Present.

Spectral–finite element approach to three‐dimensional viscoelastic relaxation in a spherical earth

Abstract: Summary We present a spectral–finite element approach to the forward modelling of the visco-elastic response of a spherical earth with a 3-D viscosity structure to a surface mass load. It represents an alternative to a variety of numerical methods for 2-D and 3-D postglacial rebound modelling used recently (the finite element method, the perturbation method, the semi-analytical approach and the spectral–finite difference method). For a fixed time, the problem is reformulated in a weak sense and parametrized by tensor surface spherical harmonics in the angular direction, whereas piecewise linear finite elements span the radial direction. The solution is obtained with the Galerkin method, which leads to solving a system of linear algebraic equations. The time dependence of the problem is treated directly in the time domain (not in the Laplace domain) as a time evolution problem. The time derivative in the constitutive equation for a Maxwell viscoelastic body is approximated by the explicit Euler time-differencing scheme, which leads to time splitting of the stress tensor. The spectral–finite element method and the associated numerical code have been tested for 2-D (azimuthally symmetric) eccentrically nested spheres models, and good agreement has been obtained.

How are vertical shear wave splitting measurements affected by variations in the orientation of azimuthal anisotropy with depth

Abstract: Splitting measurements of teleseismic shear waves, such as SKS, have been used to estimate the amount and direction of upper mantle anisotropy worldwide. These measurements are usually made by approximating the anisotropic regions as a single, homogeneous layer and searching for an apparent fast direction (φ~) and an apparent splitting time (Δt~) by minimizing the energy on the transverse component of the back-projected seismogram. In this paper, we examine the validity of this assumption. In particular, we use synthetic seismograms to explore how a vertically varying anisotropic medium affects shear wave splitting measurements. We find that weak heterogeneity causes observable effects, such as frequency dependence of the apparent splitting parameters. These variations can be used, in principle, to map out the vertical variations in anisotropy with depth through the use of Frechet kernels, which we derive using perturbation theory. In addition, we find that measurements made in typical frequency bands produce an apparent orientation direction that is consistently different from the average of the medium and weighted towards the orientation of the anisotropy in the upper portions of the model. This tendency of the measurements to mimic the anisotropy at the top part of the medium may explain why shear wave splitting measurements tend to be correlated with surface geology. When the heterogeneity becomes stronger, multiple scattering reduces the amplitude of the tangential-component seismogram and the associated splitting time, so that a null result may be obtained despite the fact that the waves have travelled through a strongly anisotropic medium. Regardless of the amount of vertical heterogeneity, we find that there is very little dependence on backazimuth for the measured fast-axis direction or splitting time if the top and bottom halves of the medium average to similar fast-axis directions. If, however, the average fast-axis direction in the top half of the model differs from that in the bottom half, splitting-time measurements will show a significant dependence on backazimuth, but fast-axis direction measurements will remain relatively constant.

Magnetic properties of hydrothermally synthesized greigite (Fe3S4)- II. High- and low-temperature characteristics

Abstract: SUMMARY The magnetic behaviour of hydrothermally synthesized greigite was analysed in the temperature range from 4 K to 700°C. Below room temperature, hysteresis parameters were determined as a function of temperature, with emphasis on the temperature range below 50 K. Saturation magnetization and initial susceptibility were studied above room temperature, along with X-ray diVraction analysis of material heated to various temperatures. The magnetic behaviour of synthetic greigite on heating is determined by chemical alteration rather than by magnetic unblocking. Heating in air yields more discriminative behaviour than heating in argon. When heated in air, the amount of oxygen available for reaction with greigite determines the products and magnetic behaviour. In systems open to contact with air, haematite is the final reaction product. When the contact with air is restricted, magnetite is the final reaction product. When air is excluded, pyrrhotite and magnetite are the final reaction products; the amount of magnetite formed is determined by the purity of the starting greigite and the degree of its surficial oxidation. The saturation magnetization of synthetic greigite is virtually independent of temperature from room temperature down to 4 K. The saturation remanent magnetization increases slowly by 20‐30 per cent on cooling from room temperature to 4 K. A broad maximum is observed at ~10 K which may be diagnostic of greigite. The coercive and remanent coercive force both increase smoothly with decreasing temperature to 4 K. The coercive force increases from ~50 mT at room temperature to approximately 100‐120 mT at 4 K, and the remanent coercive force increases from approximately 50‐80 mT at room temperature to approximately 110‐180 mT at 4 K.

Microseismicity and faulting geometry in the Gulf of Corinth (Greece)

Abstract: SUMMARY During the summer of 1993, a network of seismological stations was installed over a period of 7 weeks around the eastern Gulf of Corinth where a sequence of strong earthquakes occurred during 1981. Seismicity lies between the Alepohori fault dipping north and the Kaparelli fault dipping south and is related to both of these antithetic faults. Focal mechanisms show normal faulting with the active fault plane dipping at about 45° for both faults. The aftershocks of the 1981 earthquake sequence recorded by King et al. (1985) were processed again and show similar results. In contrast, the observations collected near the western end of the Gulf of Corinth during an experiment conducted in 1991 (Rigo et al. 1996), and during the aftershock studies of the 1992 Galaxidi and the 1995 Aigion earthquakes (Hatzfeld et al. 1996; Bernard et al. 1997) show seismicity dipping at a very low angle (about 15°) northwards and normal faulting mechanisms with the active fault plane dipping northwards at about 30°. We suggest that the 8‐12 km deep seismicity in the west is probably related to the seismic‐aseismic transition and not to a possible almost horizontal active fault dipping north as previously proposed. The diVerence in the seismicity and focal mechanisms between east and west of the Gulf could be related to the diVerence in the recent extension rate between the western Gulf of Corinth and the eastern Gulf of Corinth, which rotated the faults dipping originally at 45° (as in the east of the Gulf ) to 30° (as in the west of the Gulf ).

Seismic behaviour of the Dead Sea fault along Araba valley, Jordan

Abstract: The Dead Sea fault zone is a major left-lateral strike-slip fault. South of the Dead Sea basin, the Wadi Araba fault extends over 160 km to the Gulf of Aqaba. The Dead Sea fault zone is known to have produced several relatively large historical earthquakes. However, the historical events are unequally distributed along the fault and only four events have been reported in the Araba valley over the last few thousands of years. Magnitudes estimated from the historical record are probably slightly smaller than that of the M_w ∼ 7.3 earthquake that struck the Gulf of Aqaba in 1995. The fault cuts straight across Pleistocene to Holocene alluvium and shows morphologic evidence for essentially pure strike-slip motion. Regional seismic monitoring reveals little microseismicity along the fault except around the Dead Sea and Gulf of Aqaba, where the fault splays into complex pull-apart basin fault systems. We have investigated the fault zone at several sites selected from SPOT images and the study of aerial photography. At the site of the now destroyed Tilah Castle, a well-preserved wall, dated to be about 1200 yr BP (^(14)C age on charcoal), is cut by the fault and offset by 2.2 m. Comparison with offset gullies at a nearby site 3 km to the north and at three other sites, respectively 25, 50 and 65 km to the south, reveals that this specific fault displacement is probably related to the last seismic event that ruptured that fault segment, possibly in AD 1458. Moreover, the offset gullies suggest a characteristic slip behaviour with recurring slip of about 1.5 m on average. Given the 4 ± 2 mm yr^(−1) slip rate derived for this fault segment, we infer that the fault should produce M_w ∼ 7 earthquakes along some segment in the Araba valley about every 200 years. The historical period, with only four well-documented large earthquakes in AD 1068, AD 1212, AD 1293 and AD 1458, thus appears to have been relatively quiescent, with a 20 per cent deficit of M_w ∼ 7 earthquakes. However, our data do not exclude the possibility of larger M_w ∼ 7.6 earthquakes or time clustering of earthquakes over longer timespans. An alternative seismic behaviour involves M_w ∼ 7.6 earthquakes about every 6000 years and M_w ∼ 7 earthquakes about every 250 years. The historical catalogue would then appear to be complete for M_w ∼ 7 earthquakes.

The seismic anomaly beneath Iceland extends down to the mantle transition zone and no deeper

Abstract: A 3-D teleseismic tomography image of the upper mantle beneath Iceland of unprecedented resolution reveals a subvertical low wave speed anomaly that is cylindrical in the upper 250 km but tabular below this. Such a morphological transition is expected towards the bottom of a buoyant upwelling. Our observations thus suggest that magmatism at the Iceland hotspot is fed by flow rising from the mantle transition zone. This result contributes to the ongoing debate about whether the upper and lower mantles convect separately or as one. The image also suggests that material flows outwards from Iceland along the Reykjanes Ridge in the upper 200 km, but is blocked in the upper 150 km beneath the Tjornes Fracture Zone. This provides direct observational support for the theory that fracture zones dam lateral flow along ridges.