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Velocity structure and evolution of the moon

Seismic data from the Apollo Passive Seismic Network stations are analyzed to determine the velocity structure and to infer the composition and physical properties of the lunar interior. Data from artificial impacts (SIBV booster and LM-ascent stage) cover a distance range of 9 to 1750 km. Travel times and amplitudes, as well as theoretical seismograms, are used to derive a velocity model for the outer 150 km of the moon. The P-wave velocity model confirms an earlier report of a lunar crust in the eastern part of Oceanus Procellarum. The crust is about 60 km thick and may consist of two layers in the mare regions. Possible values for the P-wave velocity in the uppermost mantle are between 7.6 and 9.0 km/sec. The 9 km/sec velocity represents either a localized heterogeneous unit, or a thin layer less than about 40 km in thickness. The elastic properties of the deep interior, as inferred from the seismograms of natural events (meteoroid impacts and moonquakes) occurring at great distances, indicate that there is an increase in attenuation and a possible decrease of velocity at depths below about 1000 km.

Toksoz, M. N.↗

Shear wave velocities in the earth's mantle.

Direct measurement of the travel time gradient for S waves together with travel time data are used to derive a shear velocity model for the earth's mantle. In order to satisfy the data it is necessary to discard the usual assumption of lateral homogeneity below shallow depths. A shear velocity differential is proposed for a region between western North America and areas of the Pacific Ocean. Distinctive features of the velocity model for the upper mantle beneath western North America are a low-velocity zone centered at 100 km depth and zones of high velocity gradient beginning at 400, 650, and 900 km.

Robinson, R.↗

Preliminary estimates of Gulf Stream characteristics from TOPEX data and a precise gravimetric geoid

TOPEX sea surface height data has been used, with a gravimetric geoid, to calculate sea surface topography across the Gulf Stream. This topography was initially computed for nine tracks on cycles 21 to 29. Due to inaccurate geoid undulations on one track, results for eight tracks are reported. The sea surface topography estimates were used to calculate parameters that describe Gulf Stream characteristics from two models of the Gulf Stream. One model was based on a Gaussian representation of the velocity while the other was a hyperbolic representation of velocity or the sea surface topography. The parameters of the Gaussian velocity model fit were a width parameter, a maximum velocity value, and the location of the maximum velocity. The parameters of the hyperbolic sea surface topography model were the width, the height jump, position, and sea surface topography at the center of the stream. Both models were used for the eight tracks and nine cycles studied. Comparisons were made between the width parameters, the maximum velocities, and the height jumps. Some of the parameter estimates were found to be highly (0.9) correlated when the hyperbolic sea surface topography fit was carried out, but such correlations were reduced for either the Gaussian velocity fits or the hyperbolic velocity model fit. A comparison of the parameters derived from 1-year TOPEX data showed good agreement with values derived by Kelly (1991) using 2.5 years of Geosat data near 38 deg N, 66 deg W longitude. Accuracy of the geoid undulations used in the calculations was of order of +/- 16 cm with the accuracy of a geoid undulation difference equal to +/- 15 cm over a 100-km line in areas with good terrestrial data coverage. This paper demonstrates that our knowledge or geoid undulations and undulation differences, in a portion of the Gulf Stream region, is sufficiently accurate to determine characteristics of the jet when used with TOPEX altimeter data. The method used here has not been shown to be more accurate than methods that average altimeter data to form a reference surface used in analysis to obtain the Gulf Stream characteristics. However, the results show the geoid approach may be used in areas where lack of current meandering reduces the accuracy of the average surface procedure.

Rapp, Richard H.↗

A Velocity Distribution Model for Steady State Heat Transfer

Consider a box that is filled with an ideal gas and that is aligned along Cartesian coordinates (x, y, z) having until length in the 'y' direction and unspecified length in the 'x' and 'z' directions. Heat is applied uniformly over the 'hot' end of the box (y = 1) and is removed uniformly over the 'cold' end (y = O) at a constant rate such that the ends of the box are maintained at temperatures T(sub 0) at y = O and T(sub 1) at y = 1. Let U, V, and W denote the respective velocity components of a molecule inside the box selected at some random time and at some location (x, y, z). If T(sub 0) = T(sub 1), then U, Y, and W are mutually independent and Gaussian, each with mean zero and variance RT(sub 0), where R is the gas constant. When T(sub 0) does not equal T(sub 1) the velocity components are not independent and are not Gaussian. Our objective is to characterize the joint distribution of the velocity components U, Y, and W as a function of y, and, in particular, to characterize the distribution of V given y. It is hoped that this research will lead to an increased physical understanding of the nature of turbulence.

Hall, Eric B.↗

Mass loading and velocity diffusion models for heavy pickup ions at comet Grigg-Skjellerup

We compare model predictions of cometary water group ion densities and the solar wind slow down with measurements made by the Giotto Johnstone plasma analyzer implanted ion sensor at the encounter with comet Grigg-Skjellerup (G-S) on July 10, 1992. The observed slope of the ion density profile on approach to the comet is unexpectedly steep. Possible explanations for this are discussed. We present also a preliminary investigation of the quasilinear velocity-space diffusion of the implanted heavy ion population at G-S using a transport equation including souce, convection, adiabatic compression, and velocity diffusion terms. Resulting distributions are anisotropic, in agreement with observations. We consider theoretically the waves that may be generated by the diffusion process for the observed solar wind conditions. At initial ion injections, waves are generated at omega approximately Omega(sub i) the ion gyrofrequency, and lower frequencies are predicted for diffusion toward a bispherical shell.

Huddleston, D. E.↗

Constraints on lunar structure

A brief review is given of the constraints placed on lunar structure and composition by seismic data and density models. Bounds on the crustal velocity structure in Mare Cognitum are derived using travel-time data from artificial impacts, and a velocity model is determined on the basis of synthetic seismograms. It is shown that the velocities of P- and S-waves in the mantle can be fixed by a least-squares analysis of arrival times from meteor impacts and moonquakes, and that lunar density can be determined from the seismic structure, mean density, and moment of inertia. Olivine-pyroxene mixtures and certain olivine-rich compositions are found to be consistent with the seismic-velocity and density limits. Maximum radii are calculated for pure Fe and pure FeS cores, and it is concluded that the possibility of an ancient lunar magnetic dynamo may have to be reevaluated in the light of these figures.

Dainty, A. M.↗

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Tsaoussi, Lucia S.↗

The role of the margins in ice stream dynamics

At first glance, it would appear that the bed of the active ice stream plays a much more important role in the overall force balance than do the margins, especially because the ratio of the half-width to depth for a typical ice stream is large (15:1 to 50:1). On the other hand, recent observations indicate that at least part of the ice stream is underlain by a layer of very weak till (shear strength about 2 kPa), and this weak basal layer would then imply that some or all of the resistive drag is transferred to the margins. In order to address this question, a detailed velocity profile near Upstream B Camp, which extends from the center of the ice stream, across the chaotic shear margin, and onto the Unicorn, which is part of the slow-moving ice sheet was measured. Comparison of this observed velocity profile with finite-element models of flow shows several interesting features. First, the shear stress at the margin is on the order of 130 kPa, while the mean value along the bed is about 15 kPa. Integration of these stresses along the boundaries indicates that the margins provide 40 to 50 percent, and the bed, 60 to 40 percent of the total resistive drag needed to balance the gravitational driving stress in this region. (The range of values represents calculations for different values of surface slope.) Second, the mean basal stress predicted by the models shows that the entire bed cannot be blanketed by the weak till observed beneath upstream B - instead there must be a distribution of weak till and 'sticky spots' (e.g., 85 percent till and 15 percent sticky spots of resistive stress equal to 100 kPa). If more of the bed were composed of weak till, then the modeled velocity would not match that observed. Third, the ice must exhibit an increasing enhancement factor as the margins are approached (E equals 10 in the chaotic zone), in keeping with laboratory measurements on ice under prolonged shear strain. Also, there is either a narrow zone of somewhat stiffer ice (E equals 5) outward of the shear margin, or the bed is frozen there. And last, the high shear stress and strain rate found at the margin are likely to cause significant viscous heating (q) in the marginal ice. The increase in temperature is proportional to qX/u, where X is the width of the shear zone and u is the transverse velocity component bringing cold ice in from the ice sheet outside the shear zone. Near upstream B, this heating is likely to cause an increase in temperature of 4 to 10 K. Plans are to measure this temperature increase in a series of bore holes near the margin during the 1992-93 field season, as well as to provide a more detailed description of the velocity field there.

Echelmeyer, Keith↗

A method for landing gear modeling and simulation with experimental validation

This document presents an approach for modeling and simulating landing gear systems. Specifically, a nonlinear model of an A-6 Intruder Main Gear is developed, simulated, and validated against static and dynamic test data. This model includes nonlinear effects such as a polytropic gas model, velocity squared damping, a geometry governed model for the discharge coefficients, stick-slip friction effects and a nonlinear tire spring and damping model. An Adams-Moulton predictor corrector was used to integrate the equations of motion until a discontinuity caused by a stick-slip friction model was reached, at which point, a Runga-Kutta routine integrated past the discontinuity and returned the problem solution back to the predictor corrector. Run times of this software are around 2 mins. per 1 sec. of simulation under dynamic circumstances. To validate the model, engineers at the Aircraft Landing Dynamics facilities at NASA Langley Research Center installed one A-6 main gear on a drop carriage and used a hydraulic shaker table to provide simulated runway inputs to the gear. Model parameters were tuned to produce excellent agreement for many cases.

Daniels, James N.↗

Waveform effects of a metastable olivine tongue in subducting slabs

Velocity models of subducting slabs with a kinetically-depressed olivine to beta- and gamma-spinel transition are constructed, and the effect that such structures would have on teleseismic P waveforms are examined using a full-wave finite-difference method. These 2D calculations yielded waveforms at a range of distances in the downdip direction. The slab models included a wedge-shaped, low-velocity metastable olivine tongue (MOTO) to a depth of 670 km, as well as a plausible thermal anomaly; one model further included a 10-km-thick fast layer on the surface of the slab. The principal effect of MOTO is to produce grazing reflections at wide angles off the phase boundary, generating a secondary arrival 0 to 4 seconds after the initial arrival depending on the take-off angle. The amplitude and timing of this feature vary with the lateral location of the seismic source within the slab cross-section.

Vidale, John E.↗

The p-wave upper mantle structure beneath an active spreading centre - The Gulf of California

Over 1400 seismograms of earthquakes in Mexico are analyzed and data sets for the travel time, apparent phase velocity, and relative amplitude information are utilized to produce a tightly constrained, detailed model for depths to 900 km beneath an active oceanic ridge region, the Gulf of California. The data are combined by first inverting the travel times, perturbing that model to fit the p-delta data, and then performing trial and error synthetic seismogram modelling to fit the short-period waveforms. The final model satisfies all three data sets. The ridge model is similar to existing upper mantle models for shield, tectonic-continental, and arc-trench regimes below 400 km, but differs significantly in the upper 350 km. Ridge model velocities are very low in this depth range; the model 'catches up' with the others with a very large velocity gradient from 225 to 390 km.

Walck, M. C.↗

Improved large perturbation propulsion models for control system design (1988-1989) and large perturbation models of high velocity propulsion systems (1989-1990) and reduced order propulsion models for control system design (1990-1991)

Methods for modeling high speed propulsion systems will be discussed. Included in this category are internal flow propulsion systems without rotating machinery, such as inlets, ramjets, and scramjets. Among the modeling topics discussed are modeling of linear isentropic flow, heat exchange, gasdynamics, lumped parameter systems, and infinite dimensional systems. Furthermore, a generalized overview of modeling high speed propulsion systems is presented in this collection of papers.

Hartley, Tom T.↗

Velocity dispersion of M87 using a population model

The velocity dispersion of M 87 (NGC 4486) is determined using (1) a single star of class K0 III and (2) two different population models to represent the spectral region of the G-band. Although the models fit the overall spectrum better than the single-star, there is only a small difference in the derived velocity dispersion. This work revises the earlier velocity dispersion result of Brandt and Roosen (1969) down to 350 km/sec, in agreement with Faber and Jackson (1976) and Sargent et al. (1978).

Angione, R. J.↗

A Possible Explanation for the Z-R Parameter Inconsistency when Comparing Stratiform and Convective Rainfall

The well-known Z-R power law Z A R(sup b) uses two parameters, A and b, in order to relate rainfall rate R to measured weather radar reflectivity Z. A common method used by researchers is to compute Z and R from disdrometer data and then extract the A-b parameter pair from a log-linear line fit to a scatter plot of Z-R pairs. Even though it may seem far more truthful to extract the parameter pair from a fit of radar Z(sub R) versus gauge rainfall rate R(sub G), the extreme difference in spatial and temporal sampling volumes between radar and rain gauge creates a slew of problems that can generally only be solved by using rain gauge arrays and long sampling averages. Disdrometer derived A-b parameters are easily obtained and can provide information for the study of stratiform versus convective rainfall. However, an inconsistency appears when comparing averaged A-b pairs from various researchers. Values of b range from 1.26 to 1.51 for both stratiform and convective events. Paradoxically the values of A fall into three groups: 150 to 200 for convective; 200 to 400 for stratiform; and 400 to 500 again for convective. This apparent inconsistency can be explained by computing the A-b pair using the gamma DSD coupled with a modified drop terminal velocity model, v(D) alpha D(sup beta) - w, where w is a somewhat artificial constant vertical velocity of the air above the disdrometer. This model predicts three regions of A, corresponding to w less than 0, w = 0, and w greater than 0, which approximately matches observed data.

gamma DSD↗

Measurements and a model for convective velocities in the turbulent boundary layer

A physical model is presented which describes convective velocities within a flat plate turbulent boundary layer. A production zone concept is used as a basis for the physical model. The production zone concept employs the idea that packets of turbulent fluid are generated near the viscous sublayer. These packets are found to be discernible from the mean motion and may move either outward from the production zone or inward depending on their circulation relative to the fluid surrounding the packet. The packets are predicted to travel with a convective velocity different from the local mean velocity throughout most of the boundary layer. The model also predicts that the convective velocities will be functions of wave number outside the production zone.

Cliff, W. C.↗

Geosat Data Assimilation with Application to the Eastern North Atlantic

An attempt is made to determine the three-dimensional ocean circulation from satellite altimeter measurements by assimilating Geosat sea surface height data into an eddy-resolving QuasiGeostrophic (QG) model of the eastern North Atlantic Ocean. Results are tested against independent information from hydrographic field observations and moored current meter data collected during the Geosat ERM. The comparison supports the concept of inferring aspects of the three-dimensional flow field from sea surface height observations by combining altimetric measurements with the dynamics of ocean circulation models. A Holland-type QG model with open boundaries is set up on a 2000 km X 2000 km domain of the eastern North Atlantic between 25 deg. and 45 deg. N, 32 deg. and 8 deg. W. By using a simple nudging technique, about two years of Geosat altimeter data are assimilated into the model every five days as space-time objective analyses on the model grid. The error information resulting from the analysis is used during the assimilation procedure to account for data uncertainties. Results show an intense eddy field, which in the surface layer interacts with a meandering Azores Front. Compared to Geosat, the model leads to smoothed fields that follow the observations. Model simulations are significantly correlated with hydrographic data from March 1988 and June 1989, both close to the surface and in the subsurface. Good agreement is also found between the model velocity fields and moored current meter data in the top two model layers. The agreement is visually weak in the bottom layer, although a coherence analysis reveals an agreement between the model simulation and current meter data over the full water column at periods exceeding 80 days.

Stammer, Detlef↗

An investigation of helicopter dynamic coupling using an analytical model

Many attempts have been made in recent years to predict the off-axis response of a helicopter to control inputs, and most have had little success. Since physical insight is limited by the complexity of numerical simulation models, this paper examines the off-axis response problem using an analytical model, with the goal of understanding the mechanics of the coupling. A new induced velocity model is extended to include the effects of wake distortion from pitch rate. It is shown that the inclusion of these results in a significant change in the lateral flap response to a steady pitch rate. The proposed inflow model is coupled with the full rotor/body dynamics, and comparisons are made between the model and flight test data for a UH-60 in hover. Results show that inclusion of induced velocity variations due to shaft rate improves correlation in the pitch response to lateral cycle inputs.

Keller, Jeffrey D.↗