Global mapping of upper mantle reflectors from long-period SS precursors

Long-period precursors to SS resulting from underside reflections off upper mantle discontinuities ( SdS where d is the discontinuity depth) can be used to map the global distribution and depth of these reflectors. We analyse 5,884 long-period seismograms from the Global Digital Seismograph Network (1976-1987, shallow sources, transverse component) in order to identify SdS arrivals. Corrections for velocity dispersion, topography and crustal thickness at the SS bounce point, and lateral variation in mantle velocity are critical for obtaining accurate estimates of discontinuity depths. The 410 and 660 km discontinuities are observed at average depths of 413 and 653 km, and exhibit large-scale coherent patterns of topography with depth variations up to 40 km. These patterns are roughly correlated with recent tomographic models, with fast anomalies in the transition zone associated with highs in the 410 km discontinuity and lows in the 660 km discontinuity, a result consistent with laboratory measurements of Clapeyron slopes for the appropriate phase changes. The best resolved feature in these maps is a trough in the 660 km discontinuity in the northwest Pacific, which appears to be associated with the subduction zones in this region. Amplitude variations in SdS arrivals are not correlated with discontinuity depths and probably result from focusing and defocusing effects along the ray paths. The SdS arrivals suggest the presence of regional reflectors in the upper mantle above 400 km. However, only the strongest of these features are above probable noise levels due to sampling inadequacies.     

Crustal structure from an OBS survey of the Nootka fault zone off western Canada

Summary. The Nootka fault zone is the boundary between the small Explorer and Juan de Fuca plates which are situated between the America and Pacific plates off western Canada. To investigate the crustal structure in the region, three explosive/large airgun refraction lines were shot into three ocean bottom seismometers (OBSs) with three-component geophone assemblies. In this phase of the study, P -wave velocity—depth models are interpreted by comparison of the travel time and amplitude characteristics of the observed data with theoretical seismograms computed using a WKBJ algorithm. The interpretation gives relatively consistent results for the upper crust. However, the structure of the lower crust is significantly different among the various profiles. Upper mantle velocities range from 7.5 to 8.3 kms⁻¹ and the sub-bottom crustal thickness vanes from 6.4 to 11 km. Nevertheless, these seismic models are consistent in general terms with oceanic crustal models represented by ophiolite complexes. Some aspects of the differences among profiles can be explained by consideration of a recent tectonic model for the development of the fault zone. This requires, within a 1 Myr time interval, variations in the process of crustal formation at the ridge, crustal 'maturing', or both. The abnormally thick crust near a spreading centre may result in part from the complex interaction of the Juan de Fuca and Explorer plates with the larger and older America and Pacific plates. Upper mantle velocity variations are consistent with the concept of velocity anisotropy. The different record sections show that seismic energy is attenuated for ray paths traversing the Nootka fault zone.     

Upper-mantle structure of the Baltic Shield below the Swedish National Seismological Network (SNSN) resolved by teleseismic tomography

Upper-mantle structure under the Baltic Shield is studied using non-linear high resolution teleseismic P -phase tomography. Observed relative arrival-time residuals from 52 teleseismic earthquakes recorded by the Swedish National Seismological Network (SNSN) are inverted to delineate the structure of the upper mantle. The network consists of 47 (currently working) three-component broad-band stations located in an area about 450 km wide and 1450 km long. In order to reduce complications due to possible significant three-dimensionality of Earth structure, events chosen for this study lay close to in-line with the long-axis of the array  (±30°)  . Results indicate P -wave velocity perturbations of ±3 per cent down to at least 470 km below the network. The size of the array allows inversion for structures even at greater depths, and lateral variations of velocity at depths of up to 680 km appear to be resolved. Below the central part of the array (60°–64° N), where ray coverage is best, the data reveals a large region of relatively low velocity at depths of over about 300 km. At depths less than about 250–300 km, the models include a number of features, including an apparent slab-like structure dipping gently towards the north.     

Upper mantle heterogeneities beneath Central Europe

Summary. An inversion of ISC travel-time data from selected earthquakes in the distance range 30°-90° to 53 stations in Central Europe has been used to model velocity down to 600 km depth. The model explains 0.1–0.2s of the residuals, as for other array studies, leaving 0.5 s unexplained as noise. The uppermost 100 km of the mantle and crust contains inhomogeneities that correlate remarkably well with the geology. This may be due to deep-seated thermal anomalies or, in some areas, to delays introduced by passage of the rays through sedimentary cover. The deeper anomalies are smaller and unrelated to those in the lithosphere, which suggests that the asthenosphere is decoupled from the rigid lithosphere. The structure at 600 km depth is again quite inhomogeneous and might be due to undulations of the 650 km discontinuity. The models show some suggestion of a high velocity slab trending from east to west beneath the Alps.     

A lower mantle S-wave triplication and the shear velocity structure of D"

Summary. A lower mantle S-wave triplication detected with short- and long-period WWSSN and CSN recordings indicates a substantial shear velocity discontinuity near 280 km above the core–mantle boundary. The triplication can be observed in rotated SH seismograms from intermediate and deep focus events throughout the distance range from 70° to 95°. Three distinct source region–receiver array combinations that have been investigated in detail demonstrate consistent travel time and relative amplitude behaviour of the triplication, with slight systematic shifts in the triplication indicating up to 40 km variations in the depth of the discontinuity. Modelling of the observations with synthetic seismograms produced with the Cagniard de Hoop and reflectivity methods constrains the shear velocity increase to be 235 ± 0.25 per cent, comparable to upper mantle discontinuities. Short-period observations indicate that the velocity increase may be a sharp first-order discontinuity, or may extend over a transition zone no more than 50 km thick. The shear velocity gradient below the discontinuity, within the D" layer, is not well-constrained by the SH data, but slightly positive or near zero velocity gradients are consistent with the long-period amplitude ratios of ScSH/SH .     

Seismic structure of the upper mantle beneath the United States by three-dimensional inversion of body wave arrival times

Summary. Teleseismic P and S arrival times to North American stations are obtained from the ISC bulletins for the 10-yr period 1964–73, and relative travel-time delays are calculated with respect to standard tables. Station anomalies as well as variations of the delays with azimuth and epicentral distance from station are analysed, and the location of the velocity anomalies responsible for them is discussed. Inversion of the P delays to infer upper mantle velocity structure down to a depth of 700 km is obtained using three-dimensional blocks, as proposed by Aki, Christofferson & Husebye. Three layers can be resolved in this depth range. It is found that the heterogeneities responsible for the travel-time delays are primarily located in the first 250 km of the upper mantle, and that they correlate with surface features. Significant heterogeneities subsist to depths of at least 700 km and their broad scale pattern also correlates with the surface features: in the third layer (500 to 700 km depth) there is an increase of velocity from the West to the East of the United States, while the second layer (250 to 450 km depth) exhibits a reversed pattern. A tentative interpretation of these deeper anomalies is made, as being due mainly to topography of the major upper mantle discontinuities, near 400 and 650 km depth.     

Lateral variations of S velocity in the upper mantle from higher Rayleigh modes

Summary. The generalized inverse theory has been applied to interpret several sets of higher mode data, previously obtained for the United States and the Pacific Ocean. The depth-resolving power of these data allows us to find the distribution of S velocity down to about 600 km. The main lateral variations of S velocity are found in the uppermost 250 km, the south-western United States showing the lowest velocities and the central-north-eastern United States the highest velocities. Between 250 and 500 km an opposite situation seems to occur, western velocities being the greatest ones, but these lateral variations are 3 to 5 times less than above and they cannot be surely established under the variance estimated for the data. Finally no lateral variations are resolved between 500 and 700 km. Some remarks may be made about the corresponding absolute models: (1) the agreement is good with published models, built with the fundamental mode alone; (2) the slight lowvelocity zone which is not required when inverting the fundamental mode alone in the central and north-eastern United States, is required when highermode data are added; (3) a rather strong increase of the S -velocity gradient is found near 360 km depth, both for the average data across the United States and the Pacific Ocean.     

The three-dimensional shear wave structure in the mantle by overtone waveform inversion - I. Radial seismogram inversion

Summary. The three-dimensional (3-D) shear wave structure of the mantle, down to the depth of about 900 km, is obtained by inverting waveforms of radial component seismograms. Radial component seismograms contain large amplitude overtone signals which circle the Earth as wave packets and are sometimes called X1, X2, X3, … We use data which contain R1, X1 and X2 and filtered between 2 and 10mHz. It is shown that, unless each seismogram is weighted, all seismograms are not fitted uniformly. Only data from large earthquakes are fitted and the final velocity anomalies are biased by the small number of large earthquake data. Resolution is good at shallow depths, becomes worse in the intermediate depth range between about 400 and 500 km and then becomes better at greater depth ranges (600–900km). Even though we use only spheroidal mode data, velocity anomalies in the shallow structure show excellent correlation with the age of the surface rocks of the Earth. In the deeper regions, between about 600 and 900km, South America shows a fast velocity anomaly which may indicate the slab penetration beyond 700 km there. Another region which shows a fast velocity anomaly is the Mariana trench, but other subduction regions do not show such features.     

Travel-time anomalies in the mantle under the North Atlantic

Summary. Lateral heterogeneity exists in the Earth's mantle, and may result in seismic velocity anomalies up to several per cent. If convection cells and plumes extend down to the core, then these features may be associated with local inhomogeneities observed in the lower mantle.
Published data for direct and core-reflected P -wave residuals are used to delineate velocity anomalies in the middle—lower mantle under the North Atlantic. Differential ( PcP — P ) residuals indicate travel-time anomalies near the core—mantle transition, and may be due to core topography or lateral variations in velocity. It is assumed that the anomalies occur near the midpoints of the ray paths. The main source of error in the data set may arise from phases which have been identified incorrectly. Hence trend-surfaces are fitted to the residual data to show only the large-scale trends in anomaly values, with wavelengths of the order of 1000 km.
The Azores and Colorado hot spots occur in a region covered by the data. A possible interpretation of the trend maps is that an anomalous zone extends from a relatively fast region at the core boundary at 35° N, 50° W up to these hot spots, at about 30 degrees from the vertical. This may agree with the suggestion of Anderson that plumes are chemical rather than thermal in origin. If inclⁱned plumes do exist, the deviation from the ideal vertical plume or convection cell boundary may imply that lateral shear or other distortion effects exist in the mantle.     

Seismic Modelling of Lateral Heterogeneity At the Base of the Mantle

Summary. Results from several recent studies suggest that there are lateral heterogeneities of up to a few per cent in the lowermost 150–200 km of the mantle (Bullen's D " region). Inferred anomaly sizes span the range from less than 50 km to greater than 1000 km.
In this study differences in the velocity structure among regions at the base of the mantle were inferred from an analysis of amplitude ratios of PKPAB and PKPDF for given earthquake-station pairs at distances greater than 155° (Sacks, Snoke & Beach). We distinguish two kinds of regions: A (anomalous) regions in which the mean, median and spread in AB/DF amplitude ratios are significantly higher (> 50 per cent) than for a reference radial earth model and N (normal) regions in which the distribution of the amplitude ratios is as expected.
The AB branch has near-grazing incidence to the core and therefore maximum sensitivity to velocity structure compared to the near-normal incident DF phases. Using an iterative, forward-modelling approach, we have determined general characteristics of the velocity structure for regions at the base of the mantle which can produce amplitude-ratio distributions similar to those for an A region. Agreement between model and data is obtained over the period range from 0.5 s to greater than 10 s using a laterally heterogeneous model for the D " region. the model consists of cells which are 200 km in lateral extent with velocity variations of up to ±1 per cent. This structure is modulated by a region-wide (1000km) perturbation which increases smoothly from zero at the edges of the region to a negative 1 per cent at the centre. Small cells (∼40 km) cannot produce anomalously large amplitude, long-period AB arrivals, and larger cells (∼1000km) cannot match the observed scatter. the ∼200 km scale anomalies could be small-scale convection cells confined to the D " region.     

Teleseismic delay-time tomography of the upper mantle beneath southeastern India: imprint of Indo–Antarctica rifting

A 3-D P -velocity map of the crust and upper mantle beneath the southeastern part of India has been reconstructed through the inversion of teleseismic traveltimes. Salient geological features in the study region include the Archean Dharwar Craton and Eastern Ghat metamorphic belt (EGMB), and the Proterozoic Cuddapah and Godavari basins. The Krishna–Godavari basin, on the eastern coastal margin, evolved in response to the Indo–Antarctica breakup. A 24-station temporary network provided 1161 traveltimes, which were used to model 3-D P -velocity variation. The velocity model accounts of 80 per cent of the observed data variance. The velocity picture to a depth of 120 km shows two patterns: a high velocity beneath the interior domain (Dharwar craton and Cuddapah basin), and a lower velocity beneath the eastern margin region (EGMB and coastal basin). Across the array velocity variations of 7–10 per cent in the crust (0–40 km) and 3–5 per cent in the uppermost mantle (40–120 km) are observed. At deeper levels (120–210 km) the upper-mantle velocity differences are insignificant among different geological units. The presence of such a low velocity along the eastern margin suggests significantly thin lithosphere (<100 km) beneath it compared to a thick lithosphere (>200 km) beneath the eastern Dharwar craton. Such lithospheric thinning could be a consequence of Indo–Antarctica break-up.     

Three-dimensional seismic structure of the upper mantle beneath the central part of the Eurasian continent

This work is a study of the upper-mantle seismic structure beneath the central part of the Eurasian continent, including the northern Mongolia, Altai and Sayan orogenic areas and the Baikal rift zone. Seismic velocity models are reconstructed using the inverse teleseismic scheme. This scheme uses information from earthquakes located within the study area recorded by the Worldwide Network. The seismic anomaly structure is obtained for different volumes in the study area that partially overlap one another. Special attention has been paid to the reliability of the results: several noise and resolution comparisons are made.
The main results are as follows. (1) A cell structure of anomalies is observed beneath the Altai–Sayan region: positive, cold anomalies correspond to regions of recent orogenesis, negative anomalies are located beneath the depression of the Great Lakes in Mongolia and Hubsugul Lake. (2) A large negative anomaly is observed beneath the Hangai dome in Mongolia. (3) Strong velocity variations are obtained in a zone around Baikal Lake. A large negative anomaly is traced beneath the southern margin of the Siberian craton down to a depth of 700 km. Contrasting positive anomalies (4–5 per cent) are observed at a depth of 100–300 km beneath the Baikal rift. Our geodynamical interpretation of the velocity structure obtained beneath central Asia involves the existence of two processes in the mantle: thermal convection with regular cells, and a narrow plume beneath the southern border of the Siberian plate.     

New insights into the P- and S-wave velocity structure of the D" discontinuity beneath the Cocos plate

Broad-band P - and S -waves from earthquakes in South America recorded at Californian network stations are analysed to image lateral variations of the D"-discontinuity beneath the Cocos plate. We apply two array processing methods to the data set: a simplified migration method to the P -wave data set and a double-array method to both the P - and S -wave data sets, allowing us to compare results from the two methods. The double-array method images a dipping reflector at a depth range from 2650 to 2700 km in the southern part of the study area. We observe a step-like topography of 100 km to a shallower reflector at about 2600 km depth to the north, as well as evidence for a second (deeper) reflector at a depth range from 2700 to 2750 km in the north. Results from the simplified migration agree well with those from the double-array method, similarly locating a large step in reflector depth in a similar location (about 2650 km depth in the south and about 2550 km in the north) as well as the additional deeper reflector at the depth of about 2750 km in the north. Waveform modelling of the reflected waves from both methods suggests a positive velocity contrast for S waves, but a negative velocity contrast for P waves for the upper reflector in agreement with predictions from mineral physical calculations for a post-perovskite phase transition. The data also show some evidence for the existence of another deeper reflector that could indicate a double intersection of the geotherm with the post-perovskite stability field, that is, the back-transformation of post-perovskite to perovskite close to the core–mantle boundary.     

A geometrical approach to time evolving wave fronts

The parameter that defines the ray tracing equations in the direct geometrical approach is the product of the radius of curvature of the wave front by the velocity on the wave front ( RV ). To show this, we derive motion equations for the centre and the radius of curvature of an expanding wave front. The continuity of RV along rays implies Snell's Law. For constant velocities the equation for the radius of curvature reduces to the original Huygens' Principle. The variable RV can be computed during ray tracing and used to determine the local radius of curvature, which in turn can be used in geometrical spreading, amplitude corrections and structure interpretation.     

Three-dimensional geometrical ray theory and modelling of transmitted seismic energy of data from the Nevada Test Site

This paper presents a geometrically based algorithm for computing synthetic seismograms for energy transmitted through a 3-D velocity distribution. 3-D ray tracing is performed to compute the traveltimes and geometrical spreading (amplitude). The formulations of both kinematic and dynamic ray-tracing systems are presented. The two-point ray-tracing problem is solved by systematically updating the initial conditions and adjusting the ray direction until the ray intersects the specified endpoint. The amount of adjustment required depends on the derivatives of the position with respect to the given starting angles between consecutive rays. The algorithm uses derivatives to define the steepest-descent direction and to update the initial directions. The convergence rate depends on the complexity of the model.
Test seismograms compare favourably with those from a 2-D asymptotic ray theory algorithm and a 3-D Gaussian-beam algorithm. The algorithm is flexible in modelling arbitrary source and recorder geometries for various smoothly varying 3-D velocity distributions. The algorithm is further tested by simulating surface-to-tunnel vibroseis field data. Shear waves as well as compressional waves may be approximately included. Application of the algorithm to a data set from the Rainier Mesa of the Nevada Test Site produced a good fit to the transmitted (first arrival) traveltimes and amplitudes, with approximately 15 per cent variation in the local 3-D velocity.     

The crustal structure of the Reykjanes Ridge at 59° 30'N

Summary. In order to examine the development of the oceanic crust in the neighbourhood of a slowly spreading ridge, a seismic refraction experiment was carried out at 59° 30'N on the Reykjanes Ridge. Three 120 km long overlapped split profiles were shot parallel to the trend of the ridge, on the eastern flank, and recorded on up to five recording sonobuoys. The profiles were at distances of 0, 30 and 90km from the ridge axis, corresponding to approximate crustal ages of 0, 3 and 9 Myr. Data from the main profiles were supplemented by using a large chamber air gun during recovery of the buoys.
The analysis of the data combined standard travel-time interpretation, the 'tau' method of systematic travel-time inversion and detailed amplitude modelling using the Reflectivity Method to calculate synthetic seismograms. Detailed velocity-depth models were constructed for each of the profiles.
There is no indication of a significant magma chamber at the ridge crest, although a slight velocity inversion in layer 3 suggests a zone of elevated temperature. Away from the crest there was a slight positive velocity gradient in layer 3. Layer 2 was most effectively modelled by a region of varying velocity gradients, which thinned with age and the transition to layer 3 is marked by a sharp change in velocity gradient. The transition to mantle velocities is also best modelled by a high velocity gradient rather than an interface.
Although some lateral variation in properties is apparent along the profiles, the lateral velocity gradients were sufficiently weak to allow an effective analysis in terms of laterally uniform models.     

Seismotectonics and analysis of earthquakes from the Hindukush region

Summary. Over 80 earthquakes, exclusively from the Hindukush focal region, which were recorded at the Gauribidanur seismic array (GBA) have been used in this study. These events have similar epicentral distances and a narrow azimuthal range from GBA but varying focal depths from 10 to 240 km. A fault plane dipping steeply (75°) in the north-west direction and striking N 66° E has been investigated on the basis of the spatial distribution of earthquakes in two vertical planes through 68° E and 32° N. Short period P -wave recordings up to 30 s were processed using the adaptive cross-correlation filtering technique. Slowness and azimuthal anomalies were obtained for first arrivals. These anomalies show positive as well as negative bias and are attributed to a steep velocity gradient in the upper mantle between the 400–700 km depth range where the seismic rays have their maximum penetration. Relative time residuals between the stations of GBA owe their origin very near to the surface beneath the array. A search of the signals across the array revealed that most of the events occurring at shallower depths had complex signatures as compared to the deeper events. The structure near the source region, complicated source functions and the scattering confined to the crust—upper mantle near source are mainly responsible for the complexity of the Hindukush earthquakes as the transmission zone of the ray tubes from turning point to the recording station is practically the same.     

Amplification of ground motion and waveform complexity in fault zones: examples from the San Andreas and Calaveras Faults

Summary. P -wave seismograms at ranges less than 10 km are synthesized by asymptotic ray theory and by summation of Gaussian beams for point sources located in a low-velocity wedge surrounding a fault. The computations are performed using models of the wedge inferred from the analysis of reflection and refraction experiments across the San Andreas and Hayward-Calaveras faults. Calculations in these models show that the 10–20Hz vertical displacements of earthquakes located at 3–10km depth are amplified by up to an order of magnitude in a 1–2km wide region centred on the fault trace compared to displacements predicted by laterally homogeneous models of the crust. This amplification is not cancelled by high attentuation in the fault zone and compensates for the reduction in amplitudes directly above the source predicted from the radiation pattern of a strike-slip earthquake. Depending on the source depth of the earthquake and the structure and velocity contrast of the wedge, multiple triplications in the travel-time curve of direct P - and S -waves will occur at stations in the fault zone. A wedge model successfully predicts the triplications observed in the P waveforms of aftershocks of the Coyote Lake earthquake recorded in the fault zone, showing that body waves from microearthquakes can be used to determine the three-dimensional velocity structure of the fault zone. The amplification, waveform complexity, and distortion of ray paths introduced by the low- velocity wedge suggest that its effects should be included in the interpretation of strong ground motions and travel times observed in the fault zone. For realistic models of the wedge, asymptotically approximate methods of calculating the body waveforms are strictly valid for frequencies greater than 20Hz. Numerical methods may be necessary to calculate accurately the wavefield at lower frequencies.     

Preliminary Results on the 3-dimensional Seismic Structure of the Lithosphere under the USGS Central California Seismic Array

About 1500 readings of teleseismic P -time residuals obtained from the US Geological Survey seismograph network in central California have been used to obtain a three-dimensional image of seismic velocity anomalies for this area by the method of Aki, Christoffersson & Husebye We found that the California network is less suitable than the LASA and NORSAR arrays for this kind of studies because of its greater proportion of peripheral blocks in which the resolution is very poor for the stochastic inverse solution and the random error effect is severe for the generalized inverse solution. Nevertheless, the resultant velocity anomalies show a remarkable correlation with the San Andreas fault zone to a depth of 75 km. The anomaly pattern changes drastically as the depth exceeds 75 km, suggesting that the asthenosphere has been reached.     

Ray amplitudes of seismic body waves in laterally inhomogeneous media

Summary . The most complicated part in the computation of ray amplitudes of seismic body waves in laterally inhomogeneous media with curved interfaces lies in the evaluation of the geometrical spreading. Geometrical spreading can be simply expressed in terms of the Jacobian J of the transformation from the Cartesian into ray coordinates. Several systems of ordinary differential equations to compute the function J are suggested. For general three-dimensional media, in which the velocity changes with all the three spatial coordinates, a system of three non-linear ordinary differential equations of the first order is derived. If the velocity does not depend on one coordinate, the system of equations reduces to only one non-linear differential equation. The initial conditions for these differential equations at point (or line) source and at points of intersection of the ray with curved interfaces are presented.