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.     

Shear-wave velocity structure for a spherically averaged earth

Summary. The shear-wave velocity distribution in a spherically averaged Earth is estimated statistically from previously published short-period S travel-time measurements (Uhrhammer). An algorithm is defined for integral inversion techniques which allows estimation of the variance of the velocity distribution from the uncertainties in the S slowness model. Comparisons are made between the resulting S -velocity solution and other solutions in common use. There are significant differences (at the 95 per cent confidence level) between the 5-velocity model determined here and the Jeffreys-Bullen model over the depth ranges of 150–550 km and 2100–2350 km. The 95 per cent confidence level in the present velocity distribution ranges from ± 0.025 km/s at 625 km to ±0.32km/s at 2766 km and averages about ±0.063 or ±1 percent.
Correlations between azimuthally dependent source and station adjustments (which were previously determined (Uhrhammer)) indicate widespread lateral inhomogeneities (up to 3.4 per cent) to depths of approximately 700 km. Up to three-quarters of the source adjustments are due to lateral velocity variations in the source regions. Station adjustments for differential 5 minus P times are significantly correlated with elevation and crustal age, but not with station instrumental magnification.     

Three-dimensional lithospheric modelling at NORSAR: linearity of the method and amplitude variations from the anomalies

Summary. A modification of the Aid et al . technique for three-dimensional lithospheric modelling is used to find smoothly varying models for the P -wave velocity structure beneath NORSAR. The method includes ray tracing and calculation of geometrical spreading in the anomalies. The results of linear inversion of the travel-time data compare well with those of previous investigators. The assumption of linearity, which removes the need to ray trace through the anomalies, is tested with iterative solutions for both synthetic and real data. A model with an rms velocity perturbation of 3 per cent, extending to 120 km depth, is found to be reasonably linear. In fact the procedure leads to two models which satisfy the same amount of the real data but which differ by far more than the standard errors. However, these differences are not significant once the imperfect resolution is accounted for by using the total estimation error of the stochastic inverse.
The depth of major anomalies appears to be greater than the array diameter and is therefore not well constrained. Comparing the geometrical spreading produced by these models with the amplitude variations observed at the array indicates that structure deeper than 120 km but shallower than 200 km makes an important contribution to the observations. None of the models used can produce variations as large as those in the amplitude data. For deep, essentially two-dimensional, anomalies the fit to these data is much better for sources to the NE of the array than for sources in other quadrants.     

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.     

P-wave velocity anisotropy in crystalline rocks

Summary. Compressional wave velocities and anisotropy coefficients determined at high hydrostatic pressures are compiled from the data published for the main types of crystalline rocks. The crack-free elastic anisotropy of igneous crustal rocks is generally very low, between 1 and 3 per cent on average. The anisotropy of metamorphic rocks is higher (up to 22 per cent), but very variable. The average anisotropy coefficients in schists and amphibolites are about 10 per cent, in gneisses between 3 and 7 per cent, and in granulites less than 3 per cent. The average anisotropy of olivine ultramafites is between 7 and 12 per cent, whereas in pyroxenites and eclogites it is usually less than 4 per cent. A comparison of ranges of average velocities and average anisotropies for the individual rock groups suggests that, whereas in the crust the lateral velocity variations are mainly due to compositional changes, in the olivine of the uppermost mantle the velocity variations due to anisotropic structures could be of the same magnitude as the variations due to inhomogeneities.     

Surface wave array tomography in SE Tibet from ambient seismic noise and two-station analysis – II. Crustal and upper-mantle structure

We determine the 3-D shear wave speed variations in the crust and upper mantle in the southeastern borderland of the Tibetan Plateau, SW China, with data from 25 temporary broad-band stations and one permanent station. Interstation Rayleigh wave (phase velocity) dispersion curves were obtained at periods from 10 to 50 s from empirical Green's function (EGF) derived from (ambient noise) interferometry and from 20 to 150 s from traditional two-station (TS) analysis. Here, we use these measurements to construct phase velocity maps (from 10 to 150 s, using the average interstation dispersion from the EGF and TS methods between 20 and 50 s) and estimate from them (with the Neighbourhood Algorithm) the 3-D wave speed variations and their uncertainty. The crust structure, parametrized in three layers, can be well resolved with a horizontal resolution about of 100 km or less. Because of the possible effect of mechanically weak layers on regional deformation, of particular interest is the existence and geometry of low (shear) velocity layers (LVLs). In some regions prominent LVLs occur in the middle crust, in others they may appear in the lower crust. In some cases the lateral transition of shear wave speed coincides with major fault zones. The spatial variation in strength and depth of crustal LVLs suggests that the 3-D geometry of weak layers is complex and that unhindered crustal flow over large regions may not occur. Consideration of such complexity may be the key to a better understanding of relative block motion and patterns of seismicity.     

Locating some types of random errors in Digital Terrain Models

The increasing use of Geographical Information System applications has generated a strong interest in the assessment of data quality. As an example of quantitative raster data, we analysed errors in Digital Terrain Models (DTM). Errors might be classified as systematic (strongly dependent on the production methodology) and random. The present work attempts to locate some types of randomly distributed, weakly spatially correlated errors by applying a new methodology based on Principal Components Analysis. The Principal Components approach presented is very different from the typical scheme used in image processing. A prototype implementation has been conducted using MATLAB, and the overall procedure has been numerically tested using a Monte Carlo approach. A DTM of Stockholm, with integer-valued heights varying from 0 to 59 m has been used as a testbed.The model was contaminated by adding randomly located errors, distributed uniformly within 4 m and 4m. The procedure has been applied using both spike shaped (isolated errors) and pyramid-like errors. The preliminary results show that for the former, roughly half of the errors have been located with a Type I error probability of 4.6 per cent on average, checking up to 1 per cent of the dataset. The associated Type II error of the larger errors (of exactly 4m or 4 m) drops from an initial value of 1.21 per cent down to 0.63 per cent. By checking another 1 per cent of the dataset, such error drops to 0.34 per cent implying that about 71 per cent of the 4m errors have been located; Type I error was below 11.27 per cent. The results for pyramid-like errors are slightly worse, with a Type I error of 25.80 per cent on average for the first 1 per cent effort, and a Type II error drop from an initial value of 0.81 per cent down to 0.65 per cent. The procedure can be applied both for error detection during the DTM generation and by end users. It might also be used for other types of quantitative raster data.     

Anomalous Love-wave phase velocities in the Pacific: sequential pure-path and spherical harmonic inversion

Summary. We have determined the lateral distribution of Love-wave phase velocities in the Pacific for the periods 40, 67, 91 and 125 s. Application of the pure-path and spherical harmonic representation methods indicates that the velocities are primarily a function of the age of the seafloor. A comparison of the results from these two techniques indicates inherent modelling constraints in both methods. The pure-path method is limited by its a priori nature while the spherical harmonic approach is unsuitable in describing sharp lateral velocity gradients. To circumvent these limitations, we propose the sequential application of the pure-path and spherical harmonic methods. The sequential inversion separates the velocity distribution into two separate components; velocity as a function of the age of the oceanic plate and variations superimposed on this relationship. Application of this method demonstrates the presence of velocity anomalies which cannot be modelled by an age–velocity relationship. These anomalies are tentatively correlated with regions of anomalous seafloor depths and/or the presence of active hot-spots. In the central south Pacific, an area with numerous active hot-spots coincides roughly with a region of anomalously slow Love wave velocities. A method for determining the errors associated with the slowness distributions calculated by the spherical harmonic method is presented and provides a means for determining the resolvability of these features.     

Determination of rasterizing error a case study with the soil map of The Netherlands

Abstract

The digital soil map of The Netherlands (scale 1: 50 000) in vector form was rasterized using three sizes of raster cell and two different rasterizing methods. The rasterizing errors were estimated for several map sheets of different complexity using the double-conversion method, the Switzer method and the Goodchild method. The relationship between the complexity of the maps, indicated by the boundary index, and the rasterizing error is presented as a regression equation. The double-conversion method provided a better estimation of the rasterizing error than the other two methods. Differences of less than 1 per cent were found between the rasterizing methods used.     

S-wave travel times for a spherically averaged earth

Summary. Shear-wave travel times in a spherically averaged earth are estimated using 'differential' S minus P ( S – P ) travel-time measurements and detailed statistical procedures. Fourteen earthquakes and 48 stations are specially selected, yielding 302 S - P times for 6° < Δ < 111°. Analysis of variance techniques are used to estimate simultaneously azimuthally varying source and station adjustments while constructing an S – P travel-time model. A method of weighting the equations of condition based on the distribution of stations and epicentres is developed to reduce the effects of systematic errors due to non-random sampling of the Earth. The resulting S - P travel times are added to the 1939 Jeffreys–Bullen and the 1968 Herrin P travel times as a function of distance to obtain shear-wave travel-time models. Confidence intervals for the models are estimated from the variance of the observed S – P travel times.
The standard error for a single observed S – P travel time (6° < Δ < 111°) is 2.1 s and the residual distribution is not significantly different from a normal distribution at the 95 per cent confidence level. For 30° < Δ < 80° the mean S travel time is 1.3 s later than the corresponding mean for Jeffreys–Bullen tables, which is significant at the 95 per cent confidence level.     

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.     

Modelling of solar quiet magnetic field variations near a conductivity anomaly

Summary. A simplified model of the solar quiet-time ionospheric current system is used to calculate the induced currents in a model earth. The conductivity is assumed to be constant below a depth of about 400 km and zero above that depth. The current induced in the north—south conductivity anomaly under the Rocky Mountains is then estimated from the time-varying potential difference between points at 30 and 45° latitude at the surface of the conducting sphere. The purpose of these calculations is to investigate whether variations in the latitude of the northern hemisphere current system vortex will substantially alter the relationship between the observed magnetic field components at the Earth's surface and the local magnetic field gradient caused by the conductivity anomaly. We find that a 10° shift in the latitude of the ionospheric current focus causes a change of 6 per cent or less in the transfer function from the field components to the gradient in the total field. Thus such latitude shifts cannot explain much of the magnetic field gradient variation at periods near 24 hr that has been observed near Boulder, Colorado.     

Baptiste Lake,Alberta — A late Holocene history of changes in a lake and its catchment in the southern Boreal forest

Lead-210 assay and dating are subject to several sources of error, including natural variation, the statistical nature of measuring radioactivity, and estimation of the supported fraction. These measurable errors are considered in calculating confidence intervals for ²¹⁰Pb dates. Several sources of error, including the effect of blunders or misapplication of the mathematical model, are not included in the quantitative analysis. First-order error analysis and Monte Carlo simulation (of cores from Florida PIRLA lakes) are used as independent estimates of dating uncertainty. CRS-model dates average less than 1% older than Monte Carlo median dates, but the difference increases non-linearly with age to a maximum of 11% at 160 years. First-order errors increase exponentially with calculated CRS-model dates, with the largest 95% confidence interval in the bottommost datable section being 155±90 years, and the smallest being 128±8 years. Monte Carlo intervals also increase exponentially with age, but the largest 95% occurrence interval is 152±44 years. Confidence intervals calculated by first-order methods and ranges of Monte Carlo dates agree fairly well until the ²¹⁰Pb date is about 130 years old. Older dates are unreliable because of this divergence. Ninety-five per cent confidence intervals range from about 1–2 years at 10 years of age, 10–20 at 100 years, and 8–90 at 150 years old.This is the third of a series of papers to be published by this journal which is a contribution of the Paleoecological Investigation of Recent Lake Acidification (PIRLA) project. Drs. D.F. Charles and D.R. Whitehead are guest editors for this series.     

The shear-wave velocity structure in the upper mantle beneath Eurasia

We develop an approach that allows us to invert for the mantle velocity structure within a finely parametrized region as a perturbation with respect to a low-resolution, global tomographic model. We implement this technique to investigate the upper-mantle structure beneath Eurasia and present a new model of shear wave velocity, parametrized laterally using spherical splines with ∼2.9° spacing in Eurasia and ∼11.5° spacing elsewhere. The model is obtained from a combined data set of surface wave phase velocities, long-period waveforms and body-wave traveltimes. We identify many features as narrow as few hundred kilometres in diameter, such as subducting slabs in eastern Eurasia and slow-velocity anomalies beneath tectonically active regions. In contrast to regional studies in which these features have been identified, our model encompasses the structure of the entire Eurasian continent. Furthermore, including mantle- and body-wave waveforms helped us constrain structures at depths larger than 250 km, which are poorly resolved in earlier models. We find that up to +9 per cent faster-than-average anomalies within the uppermost ∼200 km of the mantle beneath cratons and some orogenic regions are separated by a sharp gradient zone from deeper, +1 to +2 per cent anomalies. We speculate that this gradient zone may represent a boundary separating the lithosphere from the continental root, which might be compositionally distinct from the overlying lithosphere and remain stable either due to its compositional buoyancy or due to higher viscosity compared with the suboceanic mantle. Our regional model of anisotropy is not significantly different from the global one.     

Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant

The dynamical flattening of the Earth, as observed by geodetic techniques, is different by about 1 per cent from the value associated with the PREM density profile with hydrostatic equilibrium. In this paper, we compute a new dynamical flattening H induced by PREM mean density with hydrostatic equilibrium, to which we add lateral heterogeneities associated with (1) seismic velocity variations observed by tomography and (2) internal boundary topographies. First, we compute mantle circulation associated with the density anomalies derived from a tomography model. The flow-induced boundary deformations are then converted into additional mass anomalies which are added to the tomography model for computing the associated perturbation to the Earth's inertia tensor. Finally, we show that it is possible to obtain a dynamical flattening from the total inertia tensor (i.e. the sum of the PREM inertia tensor and of the perturbation) in agreement with that observed.     

Crustal and uppermost mantle structure in southern Africa revealed from ambient noise and teleseismic tomography

Rayleigh wave phase velocity maps in southern Africa are obtained at periods from 6 to 40 s using seismic ambient noise tomography applied to data from the Southern Africa Seismic Experiment (SASE) deployed between 1997 and 1999. These phase velocity maps are combined with those from 45 to 143 s period which were determined previously using a two-plane-wave method by Li & Burke. In the period range of overlap (25–40 s), the ambient noise and two-plane-wave methods yield similar phase velocity maps. Dispersion curves from 6 to 143 s period were used to estimate the 3-D shear wave structure of the crust and uppermost mantle on an 1°× 1° grid beneath southern Africa to a depth of about 100 km. Average shear wave velocity in the crust is found to vary from 3.6 km s^–1 at 0–10 km depths to 3.86 km s^–1 from 20 to 40 km, and velocity anomalies in these layers correlate with known tectonic features. Shear wave velocity in the lower crust is on average low in the Kaapvaal and Zimbabwe cratons and higher in the surrounding Proterozoic terranes, such as the Limpopo and the Namaqua-Natal belts, which suggests that the lower crust underlying the Archean cratons is probably less mafic than beneath the Proterozoic terranes. Crustal thickness estimates agree well with a previous receiver function study of Nair et al. . Archean crust is relatively thin and light and underlain by a fast uppermost mantle, whereas the Proterozoic crust is thick and dense with a slower underlying mantle. These observations are consistent with the southern African Archean cratons having been formed by the accretion of island arcs with the convective removal of the dense lower crust, if the foundering process became less vigorous in arc environments during the Proterozoic.     

Surface wave tomography of the western United States from ambient seismic noise: Rayleigh and Love wave phase velocity maps

We present the results of Rayleigh wave and Love wave phase velocity tomography in the western United States using ambient seismic noise observed at over 250 broad-band stations from the EarthScope/USArray Transportable Array and regional networks. All available three-component time-series for the 12-month span between 2005 November 1 and 2006 October 31 have been cross-correlated to yield estimated empirical Rayleigh and Love wave Green's functions. The Love wave signals were observed with higher average signal-to-noise ratio (SNR) than Rayleigh wave signals and hence cannot be fully explained by the scattering of Rayleigh waves. Phase velocity dispersion curves for both Rayleigh and Love waves between 5 and 40 speriod were measured for each interstation path by applying frequency–time analysis. The average uncertainty and systematic bias of the measurements are estimated using a method based on analysing thousands of nearly linearly aligned station-triplets. We find that empirical Green's functions can be estimated accurately from the negative time derivative of the symmetric component ambient noise cross-correlation without explicit knowledge of the source distribution. The average traveltime uncertainty is less than 1 s at periods shorter than 24 s. We present Rayleigh and Love wave phase speed maps at periods of 8, 12, 16,and 20 s. The maps show clear correlations with major geological structures and qualitative agreement with previous results based on Rayleigh wave group speeds.     

On the use of dimensioned measures of error to evaluate the performance of spatial interpolators

Spatial cross‐validation and average‐error statistics are examined with respect to their abilities to evaluate alternate spatial interpolation methods. A simple cross‐validation methodology is described, and the relative abilities of three, dimensioned error statistics—the root‐mean‐square error (RMSE), the mean absolute error (MAE), and the mean bias error (MBE)—to describe average interpolator performance are examined. To illustrate our points, climatologically averaged weather‐station temperatures were obtained from the Global Historical Climatology Network (GHCN), Version 2, and then alternately interpolated spatially (gridded) using two spatial‐interpolation procedures. Substantial differences in the performance of our two spatial interpolators are evident in maps of the cross‐validation error fields, in the average‐error statistics, as well as in estimated land‐surface‐average air temperatures that differ by more than 2°C. The RMSE and its square, the mean‐square error (MSE), are of particular interest, because they are the most widely reported average‐error measures, and they tend to be misleading. It (RMSE) is an inappropriate measure of average error because it is a function of three characteristics of a set of errors, rather than of one (the average error). Our findings indicate that MAE and MBE are natural measures of average error and that (unlike RMSE) they are unambiguous.     

Controls on Rayleigh wave amplitudes: attenuation and focusing

A large data set of amplitude measurements of minor and major arc Rayleigh waves in the period range 73–171 s is collected. By comparing these amplitudes with the amplitudes of synthetic waveforms calculated by mode summation, maps of lateral variations in the apparent attenuation structure of the Earth are constructed. An existing formalism for predicting the effects of focusing is employed to calculate amplitude perturbations for the same data set. These perturbations are used to construct 'pseudo‐attenuation' maps and these results are compared with the apparent attenuation maps calculated from the data. It is shown that variations in Rayleigh wave amplitude perturbations in the Earth are dominated by attenuation at long wavelengths (below about degree 8) and by elastic structure at shorter wavelengths. It is also shown that the linear approximation for focusing is successful at predicting Rayleigh wave amplitudes using existing phase velocity maps. These results indicate that future attempts to model the velocity structure of the Earth would be assisted by incorporating amplitude data and by jointly inverting for Q structure.     

An estimate of hypocentre location accuracy in a large network: possible implications for tectonic studies in Italy

Data recorded by the Italian Telemetered Seismic Network (ITSN) of the Istituto Nazionale di Geofisica (ING) have been widely used in recent years to image slab structures and to find evidence for active processes along the Italian Peninsula. However, the use of seismic data for geostructural purposes may be affected by the well-known trade-off between earthquake location and seismic-velocity parameters. Furthermore, the confidence ellipse predicted by standard procedures may be inadequate for the representation of the probable error of a computed localization. This paper evaluates the probable errors on the hypocentre determinations of the seismic events recorded by the ITSN, using a Monte Carlo method.
We compute synthetic arrival times using a 1-D velocity model appropriate as an average for the Italian area. The hypocentres used are all those recorded by the ITSN during the period January 1992 to March 1994 (1972 events). Station locations are those of the current ITSN configuration. The synthetic arrival times are perturbed with a Gaussian distribution of errors and input to ING's standard hypocentral location procedure, but using crustal velocities differing by 10 per cent from those used to generate them. Each simulation is repeated at least 30 times. Average absolute shifts of hypocentres are assessed in grid cells of linear dimension 33 km covering the whole Italian region.
For regions within the ITSN, shifts are typically 5–10 km in location and up to 20 km in depth. However, for offshore and coastal regions, they are much greater: 50 km or more in both location and depth (far exceeding the equivalent uncertainties quoted by ING bulletins). Possible consequences of this are highlighted by producing a cross-section of subcrustal hypocentres from the Adriatic to the Tyrrhenian Sea, where the large uncertainty in depth precludes any confident interpretation of dipping tectonic features.