Mean Topography Research Articles

Empirical path corrections for regional-phase amplitudes

AbstractUsing data from 385 events recorded at Lanzhou in central China, I compare two empirical methods for predicting and correcting for path effects on regional-phase amplitude ratios. The first method interpolates source- and distance-corrected seismic data to create geographical, path-correction surfaces. The second, or wave-guide, method employs correlations with path-averaged physical data such as topography to correct the seismic data. Path corrections can vary over an order of magnitude, and their use will sharpen differences in regional-phase ratios arising from different types of natural and man-made sources of seismic energy and, thus, will be important for monitoring a Comprehensive Test Ban Treaty.For Pg/Lg phase ratios in the band 0.5 to 1 Hz, interpolated path corrections reduced variance best using kriging (62%) and nearly as well using a radius 250 km, moving-window-mean smoother (56%). Wave-guide methods based on mean and rms topography reduced variance by 43%. Variance reduction is given relative to the standard correction for distance alone. Wave-guide methods were further tested by attempting to find correlations with topographic data that had been rotated geographically. For conservatively chosen sets of wave-guide parameters, the true orientations yielded the best variance reduction, adding confidence to the use of this method. Wave-guide methods complement interpolation methods because they extrapolate behavior beyond active seismic areas. However, I find broad regions that are fit poorly by wave-guide predictions, especially where the path effect changes rapidly, such as along the eastern edge of the Tibetan plateau where Pg/Lg ratios are underpredicted. The two methods can be combined using Bayesian kriging, forcing predictions to fit the data in seismically active areas and allowing more powerful extrapolation beyond.

Subgrid-Scale Parameterizations of Eddy-Topographic Force, Eddy Viscosity, and Stochastic Backscatter for Flow over Topography

Abstract General expressions for the eddy-topographic force, eddy viscosity, and stochastic backscatter, as well as a residual Jacobian term, are derived for barotopic flow over mean (single realization) topography. These subgrid-scale parameterizations are established on the basis of a quasi-diagonal direct interaction closure model, incorporating equations for the mean vorticity, vorticity covariance, and response functions. In general, the subgrid-scale parameterizations have a time–history integral representation, which reflects memory effects associated with turbulent eddies. In the Markov limit, the truncated equations for the ensemble mean and fluctuating parts of the vorticity have the same form as the full resolution equations but with the original “bare” viscosity and bare mean and fluctuating forcings renormalized by eddy drain viscosities, eddy-topographic force, and stochastic backscatter terms. The parameterizations are evaluated at canonical equilibrium states for comparison with G. Hollowa...

Exhumation processes

Abstract Deep-seated metamorphic rocks are commonly found in the interior of many divergent and convergent orogens. Plate tectonics can account for high-pressure metamorphism by subduction and crustal thickening, but the return of these metamorphosed crustal rocks back to the surface is a more complicated problem. In particular, we seek to know how various processes, such as normal faulting, ductile thinning, and erosion, contribute to the exhumation of metamorphic rocks, and what evidence can be used to distinguish between these different exhumation processes. In this paper, we provide a selective overview of the issues associated with the exhumation problem. We start with a discussion of the terms exhumation, denudation and erosion , and follow with a summary of relevant tectonic parameters. Then, we review the characteristics of exhumation in different tectonic settings. For instance, continental rifts, such as the severely extended Basin-and-Range province, appear to exhume only middle and upper crustal rocks, whereas continental collision zones expose rocks from 125 km and greater. Mantle rocks are locally exhumed in oceanic rifts and transform zones, probably due to the relatively thin crust associated with oceanic lithosphere. Another topic is the use of P-T-t data to distinguish between different exhumation processes. We conclude that this approach is generally not very diagnostic since erosion and normal faulting show the same range of exhumation rates, reaching maximum rates of >5–10 km Ma -1 for both processes. In contrast, ductile thinning appears to operate at significantly slower rates. The pattern of cooling ages can be used to distinguish between different exhumation processes. Normal faulting generally shows an asymmetric distribution of cooling ages, with an abrupt discontinuity at the causative fault, whereas erosional exhumation is typically characterized by a smoothly varying cooling-age pattern with few to no structural breaks. Last, we consider the challenging problem of ultrahigh-pressure crustal rocks, which indicate metamorphism at depths greater than 100–125 km. Understanding the exhumation of these rocks requires that we first know where and how they were formed. One explanation is that metamorphism occurred within a thickened crustal root, but it does seem unlikely that the crust, including an eclogitized mafic lower crust, could get much thicker than c. 110 km while maintaining a reasonable Moho depth (<70 km, assuming that the seismically defined Moho would be observed to lie above the eclogitized lower crust). Diamond-bearing crustal rocks cannot be explained by this scheme. The alternative is to accrete the upper 10–40 km of lithospheric mantle into the orogenic root. This scenario will provide sufficient pressures for both coesite- and diamond-bearing eclogite-facies metamorphism, while maintaining a reasonable Moho depth (<70 km) and reasonable mean topography (≤3 km). We speculate that the detachment and foundering of the mantle root may contribute to the exhumation of any crustal rocks contained within the mantle root.

Correcting regional seismic discriminants for path effects in western China

Abstract The effect of path on regional seismic wave propagation can be significant. In an effort to improve discriminant performance, we explore the effect of path upon Pg/Lg ratios. Our primary objective is to find path corrections that reduce scatter within earthquake and explosion ratio populations, while at the same time increasing the separation between the two populations. We emphasize the 1.5- to 3-Hz and 2- to 4-Hz bands, as Pg and Lg in these bands can often be observed at smaller magnitudes and greater distances than higher-frequency bands, which have previously been shown to be reliable discriminants. For data, we use 271 earthquakes from northwest China, 25 nuclear explosions from the Kazakh test site (KTS), and one nuclear explosion from the Lop Nor test site recorded at station WMQ. We also use 185 earthquakes from the same region and seven nuclear explosion from the Lop Nor test site recorded at station AAK. Event-station distances range from 200 to 1400 km, earthquake magnitudes range between mb 2.5 and 6.2, and explosion magnitudes range between mb 4.5 and 6.5. In addition to ratio-distance trends, we examine Pg/Lg ratio-parameter trends related to topography, basin thickness, and crustal thickness. The parameters we consider are mean, roughness, gradient mean, and gradient roughness of the topography, basin thickness, and crustal thickness along each event-station path. We also consider the same parameters after weighting by path length. Through linear regressions, we found path corrections that reduce scatter within event populations, and we also found path corrections that increase the separation between earthquakes and KTS explosions recorded at WMQ. We obtained the best improvement in discrimination performance at WMQ by removing the trends of topography roughness, mean topography, and the gradient of basin thickness after weighting the parameters by path length. For AAK, we found that removing the trends of mean topography and the basement roughness improved discrimination performance over the uncorrected case. However, unlike WMQ, weighting these parameters by path length degraded discriminant performance. Because we see no predictable or repeatable trends for “adjacent” central Asian stations and overlapping regions of interest, we recommend an even more empirical approach to correcting for the effect of path. Where earthquakes are abundant, such as the Tian Shan, contouring a grid of ratio residuals (for each band of interest) may be a simpler method of finding appropriate path corrections.

Detection of Early Glaucomatous Structural Damage With Confocal Scanning Laser Tomography

The authors determine which optic disc topographic parameters obtained by the Heidelberg Retina Tomograph (HRT, Heidelberg Engineering, Heidelberg, Germany) are most useful in detecting individuals with early glaucomatous visual field loss. Ninety-nine eyes of 49 healthy individuals and 50 age-matched individuals with early glaucomatous visual field loss were included. Three images were obtained and the mean topography image was created and used in the analyses. The HRT discriminant analysis function (software version 2.01) was applied and compared to the Fisher linear discriminant function developed in this population. Analysis was repeated after stratifying by disc area (< 2 mm2 or 2-3 mm2). There were statistically significant differences between the healthy and glaucomatous groups for all optic disc topographic parameters (p < 0.05) measured. These differences remained after the analysis was repeated controlling for disc size, except for height variation contour. Applying the HRT discriminant function to this study population resulted in sensitivity and specificity of 62% and 94%, respectively. The sensitivity was 83% while specificity remained high (91%) for larger disc sizes. Using this data, additional discriminant functions that differentiated similarly between the two groups were found. The best formula used cup-shape measure (third moment), rim area, height variation contour, and retinal nerve fiber layer thickness and had a sensitivity and specificity of 78% and 88%, respectively. Several different discriminant analysis formulas are capable of detecting early glaucomatous visual field loss in a comparable manner. The characteristics of the study population are likely to influence the discriminating power of these various formulas.

Evaluation of Tropospheric Water Vapor Simulations from the Atmospheric Model Intercomparison Project

Simulations of humidity from 28 general circulation models for the period 1979–88 from the Atmospheric Model Intercomparison Project are compared with observations from radiosondes over North America and the globe and with satellite microwave observations over the Pacific basin. The simulations of decadal mean values of precipitable water (W) integrated over each of these regions tend to be less moist than the real atmosphere in all three cases; the median model values are approximately 5% less than the observed values. The spread among the simulations is larger over regions of high terrain, which suggests that differences in methods of resolving topographic features are important. The mean elevation of the North American continent is substantially higher in the models than is observed, which may contribute to the overall dry bias of the models over that area. The authors do not find a clear association between the mean topography of a model and its mean W simulation, however, which suggests that the bias over land is not purely a matter of orography. The seasonal cycle of W is reasonably well simulated by the models, although over North America they have a tendency to become moister more quickly in the spring than is observed. The interannual component of the variability of W is not well captured by the models over North America. Globally, the simulated W values show a signal correlated with the Southern Oscillation index but the observations do not. This discrepancy may be related to deficiencies in the radiosonde network, which does not sample the tropical ocean regions well. Overall, the interannual variability of W, as well as its climatology and mean seasonal cycle, are better described by the median of the 28 simulations than by individual members of the ensemble. Tests to learn whether simulated precipitable water, evaporation, and precipitation values may be related to aspects of model formulation yield few clear signals, although the authors find, for example, a tendency for the few models that predict boundary layer depth to have large values of evaporation and precipitation. Controlled experiments, in which aspects of model architecture are systematically varied within individual models, may be necessary to elucidate whether and how model characteristics influence simulations.

The climate of antarctica in the UGAMP GCM: Sensitivity to topography

Most spectral general circulation models (GCMs) use an envelope topography to set on land surface elevations. The UK Universities Global Atmospheric Modelling Programme General Circulation Model (UGAMP GCM) uses such a formulation for Antarctica, based on the US Navy 10 are minute charts of the region. In the marginal regions of the continent, an envelope topography consistently overestimates the elevation leading to lower-than-observed surface temperatures. Furthermore, errors in excess of 1000 m exist in the US Navy data, and the UGAMP GCM treats the major ice shelves as sea ice, introducing a 12% reduction in the snow-covered area of the continent. Here, we use a new high-resolution, high-accuracy digital elevation model to improve the representation of Antarctica in the UGAMP GCM. The effect of changing the land-sea mask and the topography on the surface temperature, precipitation and wind held is investigated for both summer and winter runs. Changing the land�sea mask had a dramatic effect on temperature, producing a reduction of 13.3°C for the sector west of the Ross Ice Shelf. Using the new mean topography also introduces substantial differences in temperature, wind speed and precipitation for summer and winter.

Assimilation of Geosat altimeter data into an eddy‐resolving primitive equation model of the North Atlantic Ocean

We present a new method for assimilating observations of sea surface height (SSH) into a high‐resolution primitive equation model. The method is based on the concept of reinitialization. First, the surface velocity increments necessary to adjust the model forecast to the observed geostrophic surface currents are projected onto deep velocity increments by a linear regression method. Second, changes in the density field required to balance the changes in the velocity field geostrophically are obtained from an inversion of the thermal wind equation. A unique partition of the density increments into corresponding temperature and salinity changes is realized by conserving the local θ‐S relation of the model forecast. In contrast to pure statistical methods that infer temperature and salinity changes from correlations with SSH anomalies, our approach explicitly conserves water mass properties on isopycnals. For the assimilation experiment we use optimally interpolated maps of Geosat SSH anomalies (the mean topography is taken from the model), which are assimilated into the World Ocean Circulation Experiment (WOCE) Community Modeling Effort (CME) model of the North Atlantic Ocean at 5‐day intervals covering the year 1987. It is shown that the assimilation significantly improves the model's representation of eddy activity, with the hydrographic structure of individual eddies agreeing well with independent hydrographic observations. The importance of a careful treatment of water mass properties in the assimilation process is discussed and further illustrated by comparing different assimilation schemes.

Ranked-Segment Distribution Curve for Interpretation of Optic Nerve Topography

The objective of this article was to evaluate whether a new method for analysis of optic nerve topography, the ranked-segment distribution (RSD) curve, can differentiate between normal and glaucoma eyes. Topographic optic nerve parameters of 39 normal subjects aged 50-79 years were measured using a confocal scanning laser ophthalmoscope (Heidelberg Retina Tomograph). Disc parameters were determined from the mean topography of three images of each eye obtained with a 15 degrees field of view. Rim area and retinal nerve fiber layer cross-section area were measured in 36 segments (each of 10 degrees) around the disc margin. For each parameter, the 36 segments were ranked in descending order and graphically depicted as the RSD curve. In normal eyes, the fifth percentile values for each of the ranked segments were calculated and graphed to compare with glaucoma eyes within the same age group. Evaluation of RSD curves was done automatically with a computer program using predefined criteria. Three primary open-angle glaucoma cases are presented to demonstrate the RSD curve method. In these three glaucoma eyes, RSD curves demonstrated defects more consistently than stereoscopic disc photography, nerve fiber layer photography, and computerized visual field testing. In two cases, RSD curves differentiated between diffuse and localized defect as well as demonstrated the locations of the defects. The RSD curve technique may assist in the interpretation of topographic optic nerve parameters and in the detection of glaucomatous optic neuropathy.

Accuracy assessment of the large‐scale dynamic ocean topography from TOPEX/POSEIDON altimetry

The quality of TOPEX/POSEIDON determinations of the global scale dynamic ocean topography have been assessed by determining mean topography solutions for successive 10‐day repeat cycles and by examining the temporal changes in the sea surface topography to identify known features. The assessment is based on the analysis of TOPEX altimeter data for cycles 1 through 36. Important errors in the tide model used to correct the altimeter data have been identified. The errors were reduced significantly by use of a new tide model derived with the TOPEX/POSEIDON measurements. Maps of the global 1‐year mean topography, produced using four of the most accurate models of the marine geoid, show that the largest error in the dynamic ocean topography is now the uncertainty in the geoid. Temporal variations in the spatially smoothed maps of the annual sea surface topography show expected features, such as the known annual hemispherical sea surface rise and fall and the seasonal variability due to monsoon influence in the Indian Ocean. Changes in the sequence of 10‐day topography maps show the development and propagation of an equatorial Kelvin wave in the Pacific beginning in December 1992 with a propagation velocity of approximately 3 m/s. The observations are consistent with observed changes in the equatorial trade winds, and with tide gauge and other in situ observations of the strengthening of the 1992 El Niño. Comparison of TOPEX‐determined sea surface height at points near oceanic tide gauges shows agreement at the 4 cm RMS level over the tropical Pacific. The results show that the TOPEX altimeter data set can be used to map the ocean surface with a temporal resolution of 10 days and an accuracy which is consistent with traditional in situ methods for the determination of sea level variations.

Significance probability mapping: the final touch in t-statistic mapping.

Significance Probability Mapping (SPM), based on Student's t-statistic, is widely used for comparing mean brain topography maps of two groups. The map resulting from this process represents the distribution of t-values over the entire scalp. However, t-values by themselves cannot reveal whether or not group differences are significant. Significance levels associated with a few t-values are therefore commonly indicated on map legends to give the reader an idea of the significance levels of t-values. Nevertheless, a precise significance level topography cannot be achieved with these few significance values. We introduce a new kind of map which directly displays significance level topography in order to relieve the reader from converting multiple t-values to their corresponding significance probabilities, and to obtain a good quantification and a better localization of regions with significant differences between groups. As an illustration of this type of map, we present a comparison of EEG activity in Alzheimer's patients and age-matched control subjects for both wakefulness and REM sleep.

Three‐dimensional critical wedges: Tectonics and topography in oblique collisional orogens

In orogens deforming in oblique compression, both the long wavelength (mean) topography of averaged slopes and the higher frequency topography (first harmonic) of valleys and ridges are related to the mechanics of deformation in three dimensions and cannot be adequately modeled in two dimensions. A method of analysis of the principal stresses, failure planes, and topography is presented for three‐dimensional critical wedges. In a critical Coulomb orogen which is at failure throughout, the components of the stress tensor are interrelated through the failure condition defined in terms of the principal stresses. Variation of any of the Cartesian components must be accommodated by adjustment of one or more of the other components so that the orogen remains at failure. This coupling of Cartesian components to maintain the wedge at failure permits exploration of the behavior of a three‐dimensional, critical orogen in which shear stresses arise outside of the plane of convergence. Internal adjustment of shear stresses to externally imposed stress conditions results in the formation of characteristic orogen shapes. For an oblique collision zone such as the Southern Alps of New Zealand, the resultant mountain belt is one of an obliquely deforming outboard fold‐thrust belt with subdued relief rising abruptly into a steep backslope to the main divide which falls steeply to the indentor, forming the inboard slope. The outboard topographic slope is reduced in relation to that of the two‐dimensional orogen. The rigid indentor has a fixed strike and therefore imposes a failure orientation adjacent to the indentor that differs from that of the ideal three‐dimensional critical wedge solution. This produces several different slip orientations and minor partitioning of strain near the indentor. First harmonic topography of valleys and ridges arises due to nonlinear, heterogeneous behavior of both erosional and mechanical processes and is characterized by uplift‐controlled ridges in the outboard and incision‐controlled valleys in the inboard.

New conditioned stimulus trace circuit for the rabbit's nictitating membrane response

Classical conditioning is most effective when conditioned stimulus (CS) onset precedes unconditioned stimulus (US) onset during training, and often produces a conditioned response (CR) with a mean topography that peaks when the US is expected, even if the CS terminates before US onset. It is commonly proposed that the CS activates some form of internal stimulus trace that subsequently becomes associated with the US and generates the CR. A new CS trace circuit (CSTC) suitable for this role is presented, and computer simulation results of its operation are compared with empirical results. The CSTC responds appropriately to changes in CS amplitude and duration and more favorably models the mean topography of the rabbit's nictitating membrane response than previous computational trace models.

Buoyancy-driven Abyssal Circulation in a Circumpolar Ocean

Abstract Simple models are developed to describe the abyssal circulation in a circumpolar ocean driven by localized annual sources of water representing convection events. Models are based on a geostrophic reduced-gravity formulation and are located on a zonally periodic beta plane. Nonlinear analytical solutions are first obtained for the evolution of an initially prescribed water mass distribution in the presence of a zonal mean flow and topography that is a function of the meridional coordinate only. For large time, our model suggests that diffusion results in a zonally uniform interface height with associated geostrophic currents if the initial water mass has nontrivial zonally averaged meridional structure. Possible influence of neglected effects on this large time behavior are discussed. Solutions are also presented for the evolution of an abyssal water mass introduced into an area where no equally dense water existed previously, and for a water mass added to a preexisting abyssal layer of equal den...

Influence of non-uniform temperature distribution on the steady motion of ice sheets

The plane steady flow of a grounded ice sheet is analysed under the assumption that the ice behaves as a nonlinearly viscous fluid with a strongly temperature-dependent rate factor. It is supposed that the accumulation/ablation distribution on the (unknown) free surface is prescribed, and that there is a given basal sliding condition connecting the tangential velocity, tangential traction and normal pressure. The basal boundary is defined as the smooth contour which describes the mean topography viewed on the ice-sheet lengthscale, and is assumed to have small slope. The perturbation analysis which reduces the isothermal or constant rate factor equations to an ordinary differential equation for the leading-order profile is now extended with similar success to the non-isothermal problem when the temperature distribution is prescribed. That is, the thermomechanically coupled energy balance is not solved, but families of temperature distributions qualitatively compatible with observed patterns are adopted to exhibit the effects of significant creep-rate variation with temperature.

The Circulation in the Gulf of Mexico Derived from Estimated Dynamic Height Fields

Abstract Monthly mean dynamic height topographies for the upper 500 m of the Gulf of Mexico, seasonal mean topographies for the upper 1000 m and annual topographies for the deep flow are presented. The dynamic height values on a 1° × 1° grid were determined from observed temperature values and salinities derived from mean T-S relations. The seasonal intrusion of the Loop Current is observed and found to vary directly with the geostrophic transport through the Yucatan Straits. At the Straits, the transport in the upper 500 m is a maximum in June. The transports in the upper 500 m of an anticyclone in the western Gulf are a maximum in winter and summer, and a minimum in spring and fall. There is a permanent westerly flow on the Texas Shelf. After turning cyclonically, this flow joins the eastward transport of the northern limb of the anticyclone in the western Gulf of Mexico. Most of this eastward flow recirculates in the anticyclone; however, a portion flows cast across the central Gulf to become entrained...

Classification and chronology of monthly mean topography patterns at the 100mb-level in the Northern Hemisphere

An attempt was made to classify the monthly mean topography patterns of the 100mb-level in the Northern Hemisphere from January 1956 to December 1970. The winter types are classified into eight by the range and height of circumpolar low pressure and by the range and height of high pressure area in middle or lower latitudes. The summer types are classified into five by the absolute height of anticyclone in the Eastern Hemisphere and its latitudinal range. According to this classification criteria, the chronology was made and the normal annual change of the types was shown. Lastly, discussions about the relations between the types at the 100mb-level and at the 500mb-level, 50mb-level and 10mb-level are presented. It was made clear that some winter types at the 100mb-level have a close relation to the zonal or meridional circulation types of the 500mb-level. A positional relation of the centers of the circumpolar low pressure was found between the 50mb-level and 100mb-level. Among the relationships as far as analysed, the phenomena shown as the topography patterns at the 100mb-level occur earlier than those shown as the circulation type at the 10mb-level with some exception.

Mean Topography of Normal corneas*

A survey was made of corneal topography in ‘normal’ eyes, i.e. eyes meeting certain requirements such as near‐emmetropia, absence of disease and Injury, and no prolonged wear of contact lenses. Previous investigations Indicated that there was no need to monitor the fixation angle and accommodative state of subjects. No artificial method of widening the palpebral aperture was used. The results are presented as asphericities measured from the sphere that best fits the optic‐cap region of each individual cornea. Asymmetry of asphericities about the ophthalmometric axis in any meridian is usually the case in individual corneas and is also present in the pooled results. In particular, the nasal semi‐meridian in eyes of both males and females has greater positive asphericity than the temporal semimerldian. The results are expected to be of use for investigations of the fit of contact lenses and for studies of the dioptric image formed by the cornea.

CRITICAL TRAVEL DISTANCE OF WAVES IN SHALLOW WATER

A new criterion for shallow water wave analysis is evaluated from prototype data off the German coast on the reef and wadden sea areas south of the outer Elbe river. Correlations of mean wave heights H with mean wave peri- - H ods T, and wave height distribution factors C. /-, = -l/3 t-^ respectively show that the mean periods and both complete height and period distributions of waves in shallow water can be expressed as functions of mean height and topography. So the mean wave height H proves to be the characteristic parameter for the description of the complete shallow water wave climate. The upper envelop of the values H = f (meteorology, topography) is defined as the case of fully developed sea, which leads to the function of the highest mean wave heights Hmax.

Chronology of the pressure patterns at the 50mb-level in the Northern Hemisphere

Chronology is made by using monthly mean topography charts of the 50mb-level in the Northern Hemisphere during ten years from 1956 to 1965. The patterns are divided into two groups: winter and summer types. They are, subclassified into three types:W 1,W 2, andW 3 in winter, and two types,S andS′, in summer. The results indicate that they have a fairly regular annual march: June, July and August are a summer type, and the other nine months are a winter type. The chronology revealed a periodic secular change; that is, theW 2-,W 3- andS(III)-types prevail every other year. It is indicated that the periodicity is closely connected to phenomena such as the sudden warming in the polar stratosphere in winter and the 26-months' oscillation of tropical stratospheric zonal wind.