Relative Motion Model Research Articles

Nonlinear dynamical model of relative motion for the orbiting debrisproblem

A nonlinear dynamical model of relative motion is derived for application to the orbital breakup problem. This model is designed for analysis of debris density beginning at the time of breakup and continuing until after the cloud rings the Earth. A linear relative motion model is derived, which generalizes the Clohessy-Wiltshire equations to include all values of eccentricity and the secular term Ji. Then, selected higher-order terms are added, yielding generalized equations that are useful at large displacements from the reference ephemeris. A significant improvement over linear relative motion techniques is demonstrated for the expanding debris cloud. The inverse of the relative motion transformation is then shown to be an approximate solution to Lambert's problem for multiple orbits in a perturbed force field. This model enables an analysis of debris density differentially at a point in space as a function of initial breakup spread velocity statistics. Analysis is provided showing that particle density can vary by four orders of magnitude within the instantaneous cloud. Density extrema always occur at the pinched points of the cloud and, in a perturbed force field, also occur at discrete locations within the envelope of the expanding cloud.

The cycloid relative-motion model and the kinematics of transform faulting

Adequate models of instantaneous plate tectonics currently exist; however, a model to describe the continuous relative motion of lithospheric plates during a finite time interval has been necessary. The small-circle relative-motion model suggests that a particle on a given plate follows a circular path around a pole of relative motion, as viewed from another plate during finite relative displacement. It can be shown that the small-circle model is not generally valid in describing the finite relative motion of plates, so this motion must trace a curve that is more complex than a circle. A new approach has been developed that permits improved modeling of finite relative plate motion. The first-order cycloid relative-motion model (CYC1) is based upon the idea that each plate is in motion around a plate-specific pole (elsewhere termed an “absolute” or “no-net-torque” pole). The observed relative motion between two plates is the result of the two plate-specific motions. Combining the two rotations, a point on one plate moves along a cycloid figure of rotation around two axes as viewed from another plate. A cycloid (a two-axis curve) is the simplest spherical curve that is more complex than a circle (a one-axis curve). The mathematical expression of cycloid relative motion involves a series of coordinate transformations. The small-circle model is a subset of the cycloid model. CYC1 indicates that significant variations in the direction and velocity of relative motion can occur even when the governing axial positions and angular velocities are constant. Hence, a variety of boundary interactions are possible during finite relative displacements that would not have been predicted by a small-circle model of finite relative plate motion. The cycloid model indicates that transform faults are not simply lines of pure slip along which crust is conserved. Systematic changes in the amount of convergence or divergence along the length of a given transform fault are predicted. This gradient is probably reflected in local boundary deformation, and is predicted to be a factor controlling the length of a given fault segment. Transform faults are generally in motion relative to the corresponding relative pole and plate-specific poles. The relative velocity along a given transform fault and the spreading rate across the adjacent ridge segments vary as the radius from the fault to its relative pole changes. The curvature of a given transform fault is also predicted to change with finite displacement, as the fault moves with respect to its relative pole. Motion of a given transform fault with respect to its relative pole and to the plates that it bounds suggests that the traces of the resulting fracture zones should be complex curves that are not symmetrical across the ridge axis. Improved modeling of finite relative plate motion should enhance understanding of the structural, stratigraphic, magmatic, and metamorphic evolution of plate margins.

Diffusion theory of CIDEP spectra of spin correlated radical pairs

The antiphase structure (APS) of CIDEP spectra of spin correlated radical pairs in viscous liquids is investigated theoretically in a free diffusion model for relative motion of radicals. A very simple and accurate for formula for relative APS amplitude is derived. This formula predicts a very small APS amplitude for the radical pair 2 (CH 3) 2ĊOH at T≈ −45°C. The amplitude is two orders of magnitude smaller than the experimental one, suggesting that the free-diffusion-model description of the relative motion of radicals is not correct.

Anisotropy of the ultrasonic attenuation in soft tissues: Measurements i n v i t r o

This study was designed to measure the ultrasonic attenuation within phantoms and tissue samples over a broad bandwidth and at many angles of incidence with respect to intrinsic orientations in order to elucidate both the frequency and angular dependence of the attenuation coefficient. Significant angular dependence, or anisotropy, of the attenuation was observed in canine myocardium (maximum to minimum ratio: 2.2 to 1) and a tissue mimicking phantom of oriented graphite fibers in gelatin (max to min: 2 to 1). In control studies, insignificant anisotropy was observed in the attenuation in canine liver samples and phantoms with graphite powder suspended in gelatin. Comparisons of the magnitude of variations of the oriented-fiber phantom to that predicted by a viscous relative motion model are presented.

Analytical models for relative motion under constant thrust

A general formulation for relative motion is presented allowing for arbitrary perturbing or thrust forces on each of the two satellites. Exact as well as approximate perturbation solutions for the relative motion under constant radial or circumferential forces acting on the subsatellite are established. The validity and usefulness of these solutions is assessed for a few realistic applications related to EURECA rendezvous manoeuvering with the Shuttle. The results are of general Interest for the fast calculation of relative subsatellite motion under thrust forces.

The 23 May 1989 MacQuarie Ridge Earthquake: A very broad band analysis

We use data from the GEOSCOPE global seismograph network to determine source parameters for the 23 May 1989 Macquarie Ridge earthquake. By moment tensor inversion of long‐period surface waves we obtain a seismic moment of 1.8–2.4 × 1021 N m, which makes this the largest seismic event to have occurred worldwide since the 1977 Sumba earthquake. The focal mechanism shows pure right‐lateral strike‐slip motion on a plane parallel with Macquarie Ridge and the Pacific‐Australian plate boundary. The mechanism is consistent with the strike‐slip motion predicted for this area from relative plate motion models. We invert broad band teleseismic P and SH waveforms to determine source complexity, using the results from the long‐period analysis as a priori soft constraints. The broad band waveforms show that the release of seismic energy was concentrated in the first 30 s of seismic rupture, but fault slip continued for more than 60 s. Lack of directivity in the long‐period and broad band waveforms indicates that the rupture propagated bilaterally or vertically from the nucleation point.

Two-particle description of turbulence, Markov property, and intermittency

It is shown that the hypothesis of independent increments for velocity, which is widely used by many authors [e.g., A. M. Obukhov, Adv. Geophys. 6, 113 (1959)] in the Lagrangian description of turbulence, is inconsistent with the Navier–Stokes equations in a fundamental way. A more general Lagrangian description of turbulent velocity such as the Markov process with dependent increments, which recognizes the condition of incompressibility and the important phenomenon of intermittency, is proposed. A model of intermittent relative motion of fluid particles in turbulent flow is presented. The high-order Lagrangian moments and the probability distribution are obtained. The distribution for the intermittent vorticity is also proposed.

Speed limit for oceanic transform faults

Oceanic transform faults with slip rates greater than ∼145 km/m.y. do not currently exist along the East Pacific Rise where sea-floor spreading rates range from 145 to 160 km/m.y. Instead, offsets of the the very fast spreading East Pacific Rise are accommodated by microplates, propogating rifts, or overlapping spreading centers. This suggests that there might be a speed limit above which transform faults do not exist. A physical reason for a speed limit is not known, but it might be related to unstable stress fields near the rifts tips, causing them to episodically propagate and prevent a transform fault from being formed. The spreading rates quoted are from our new (0-0.73 Ma) relative-motion model for the Pacific and Nazca plates.

Episodic North America and Pacific Plate motions

The North America plate motion for the period 20–0 m.y. is modeled by two absolute angular velocity vectors, with a change occurring at about 9 m.y. The model incorporates new geologic constraints based on (1) the recognition of a discontinuity in North America plate motion at 9 m.y., (2) a reexamination of the Iceland and Yellowstone hotspot traces, (3) improved delineation of the present North America – Pacific relative motion, and (4) a revised history of Pacific absolute motion. The two‐stage model is consistent with several features of the late Cenozoic geologic history of North America, including geological observations relating to tectonism along a large portion of both the eastern and western boundaries of North America. This plate model, combined with a previously established Pacific plate model, makes specific predictions concerning the 15–0 m.y. history of the North America‐Pacific plate boundary which compare favorably with the known history. These models together resolve most of the discrepancies previously encountered between absolute and relative motion models of the two plates. The implications of the North America plate model are the greatest for those events related to the 9 m.y. change in its motion. Among the geologic consequences of this change are rifting in the western United States, intense compressional deformation along the northern Caribbean plate boundary, a hiatus in Aleutian arc volcanic activity, and a change in the orientation of the Lesser Antilles arc. This picture reinforces the notion that the major plates behave rigidly and transmit stresses over great distances. The predictive power of the model may help in interpreting the history of the North America plate boundary in those areas where clear observations are lacking. An extra force needs to be applied to a plate to cause a change in plate motion. By treating the plate as a rigid spherical shell overlying a uniformly viscous fluid, we derive a simple class of forces sufficient to cause a given change in plate motion. Such force balance considerations indicate that an additional force applied in the northwest Pacific region, toward the northeast, would result in the observed change in North America plate motion. This force is surprisingly similar to that which apparently caused a large change in Pacific plate motion about 5 m.y. later. We propose that a common mantle process is responsible for both changes and is related to the ability of the northwest Pacific subducted lithosphere to enter into the lower mantle.

A test of alternative Caribbean Plate relative motion models

Two contrasting models have been proposed to describe the present‐day motions between the Caribbean Plate and neighboring plates. One model, based on both North America‐Caribbean and Cocos‐Caribbean data, assumes that North America‐Caribbean motion is reflected by the spreading rate (approximately 2 cm/yr) inferred from magnetic anomalies at the Cayman Spreading Center and the azimuths of nearby transforms (Jordan, 1975). This geometry was used by Minster and Jordan (1978) in deriving global plate motion model RM2. The other model, based only on North America‐Caribbean data, uses rates and azimuths inferred from the geometry of the Lesser Antilles Wadati‐Benioff zone (Sykes et al., 1982). The Cayman Spreading Center data were discounted assuming that they underestimate the full North America‐Caribbean motion owing to the complex tectonics of the Greater Antilles. The latter model assumes plate convergence at the Lesser Antilles at a rate about twice as fast as, and an azimuth differing by 25° from, the Jordan model. The two models also differ in their predictions of South America‐Caribbean motion; the Jordan model predicts oblique convergence whereas Sykes et al. predict oblique divergence. We use the NUVEL‐1 global relative motion data set, which incorporates recent data not used in earlier studies, to discriminate between the alternative models. We find that the Jordan geometry provides a better fit to the direction of North America‐Caribbean motion. Moreover, we find that models based on this geometry better fit the direction of Cocos‐Caribbean motion observed in earthquake slip vectors along the Middle America Trench. Since the prediction of this direction depends strongly on the rate of North America‐Caribbean motion, we conclude that the Jordan model better describes Caribbean Plate motions. The discrepancy between the two models results from the different methods of estimating plate motions. Sykes et al. (1982) report that they determined a Caribbean‐North America convergence rate of approximately 4 cm/yr from the length of the Lesser Antilles Wadati‐Benioff zone; we employ a similar procedure and obtain a rate closer to 2 cm/yr. We also find that the method they report using to determine the convergence direction is unable to distinguish between the alternative azimuths. We thus conclude that estimates of the rate and direction of plate motion from Wadati‐Benioff zone configurations are insufficiently robust and that such estimates are better derived using rates from magnetic anomalies and azimuths from transform faults and slip vectors. We further conclude that successful estimates of relative motion require internal consistency between the Euler vectors of all relevant plates, as demonstrated by the powerful Cocos‐Caribbean constraint not incorporated in the Sykes et al. model.

Plates and their motions

The last reviews which covered research in plate motions were those of Herron and Pitman [1975] on marine magnetic anomalies and Dewey [1975] on plate tectonics, both reporting on research for the period 1971–1974. In the last 12 years there has been considerable refinement of relative motion models, as well as further development of global models. Also, major effort has gone into defining reference frames for the study of plate motions, and discriminating between them. More recently, the role of errors in individual plate rotations and the associated uncertainties in reconstructions have received attention. In this report I concentrate on work published in the last 4 years, 1983–1986, citing a minimum of publications from previous years; however, some papers in press for early 1987 have been included. This report first reviews work on relative plate motions for the present and past, and reconstructions, and then models for these motions, global ones for driving forces and local ones determining subduction history and back‐arc spreading. The problem of reference frames, both hotspot and paleomagnetic, is discussed next. I end with a review of work on the errors in plate motions.

Cycloid kinematics of relative plate motion

The trajectory of a point on one plate as observed from another plate is generally a complex curve and not a small circle around a single axis of relative motion, as is commonly assumed. The shape of the relative-motion path is given the general name “spherical cycloid” because of its morphological similarity to cycloid planetary trajectories described by early astronomers. The cycloid relative-motion model predicts that the following phenomena occur during finite displacements: (1) the relative velocity and the curvature of the trajectory of a point on one plate relative to another plate varies systematically; (2) plates wobble relative to one another, and (3) the angle of convergence and/or divergence varies systematically along the length of any given transform fault. The small-circle relative-motion model, whereby transform faults have been considered “lines of pure slip” along which crust is “conserved,” is not generally valid for finite relative displacements.

The Nazca‐South America convergence rate and the recurrence of the Great 1960 Chilean Earthquake

The seismic slip rate along the Chile Trench estimated from the slip in the great 1960 earthquake and the recurrence history of major earthquakes has been interpreted as consistent with the subduction rate of the Nazca plate beneath South America. The convergence rate, estimated from global relative plate motion models, depends significantly on closure of the Nazca ‐ Antarctica ‐ South America circuit. NUVEL‐1, a new plate motion model which incorporates recently determined spreading rates on the Chile Rise, shows that the average convergence rate over the last three million years is slower than previously estimated. If this time‐averaged convergence rate provides an appropriate upper bound for the seismic slip rate, either the characteristic Chilean subduction earthquake is smaller than the 1960 event, the average recurrence interval is greater than observed in the last 400 years, or both. These observations bear out the nonuniformity of plate motions on various time scales, the variability in characteristic subduction zone earthquake size, and the limitations of recurrence time estimates.

Geodesy best student paper commended

Charles De Mets, a graduate student at Northwestern University, Evanston, Ill., is the first recipient of the AGU Geodesy Section's Best Student Paper Award, presented at the AGU Fall Meeting. The award was for his paper on the NUVEL‐1 relative plate motion model. This new model includes large amounts of geological data obtained in the last decade. NUVEL‐1 also incorporates modifications to the positions of some plate boundaries that are indicated in previous relative models. The comparison of this model with measurements of contemporary plate motion obtained from space techniques will be vital for the study of plate driving mechanisms, the rheology of the mantle, and the stability of geologic processes. The presentation and content of the paper were excellent. De Mets received his B.A. in Geology from Lawrence University, Appleton, Wis., in 1982 and his M.S. from Northwestern University in 1984. He expects to complete his Ph.D. work in 1987.

On lattice dynamical shell model parameters

Two points of practical detail are discussed concerning the formulation of a lattice dynamical shell model. The first point concerns the form of the diagonal element of the shell-shell submatrix which as it is expressed in the literature in terms of other shell model parameters is given erroneously. The second point concerns some explicit transformations among the short-range force constants which leave both eigenvalues and core eigenvectors of the dynamical matrix unchanged but alter the relative motion between core and shell. This relative motion models to some extent a real difference in motion between inner and outer electrons which developments in accuracy of both neutron and X-ray scattering experiments suggest may be fairly measurable in favourable materials.

An alternative model for early Tertiary absolute plate motions

Research Article| August 01, 1978 An alternative model for early Tertiary absolute plate motions Donna M. Jurdy Donna M. Jurdy 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08540 Search for other works by this author on: GSW Google Scholar Author and Article Information Donna M. Jurdy 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08540 Publisher: Geological Society of America First Online: 02 Jun 2017 Online ISSN: 1943-2682 Print ISSN: 0091-7613 Geological Society of America Geology (1978) 6 (8): 469–472. https://doi.org/10.1130/0091-7613(1978)6<469:AAMFET>2.0.CO;2 Article history First Online: 02 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Donna M. Jurdy; An alternative model for early Tertiary absolute plate motions. Geology 1978;; 6 (8): 469–472. doi: https://doi.org/10.1130/0091-7613(1978)6<469:AAMFET>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract The absolute plate motions for early Tertiary time are reconsidered. The no-net-torque determination of Solomon and others indicated absolute plate motions at 55 m.y. ago that were considerably different from the present motions. To test whether these motions are truly characteristic of early Tertiary time or merely a consequence of uncertainties, an alternative model for the relative motions is considered. A single major change is made in the relative motions scheme: Antarctica is treated as two plates. The role of Antarctica is particularly important in the relative motion scheme because it is the sole link between the large Pacific Ocean plates and the other, largely continental plates. Although this relative plate motion model for early Tertiary time does not yield absolute motions that are compatible with those of the present, there are considerable differences from Solomon and others' determination. Thus, past relative plate motions must be further constrained to give absolute motions that can confidently be compared to the present set and used in testing hypotheses about driving forces. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Linear volcanism in French Polynesia

The island chains of French Polynesia form subparallel line segments whose southeasterly extensions are perpendicular to the East Pacific Rise, the site of present sea-floor spreading in the eastern Pacific Ocean. Samples collected from island members of the Society and Austral Islands chains are used, together with previously reported age determinations for the Marquesas and Pitcairn-Gambier Islands, in a geochronological study of the southeastward migration of volcanism in each of those four lineaments. The suggestion from geomorphologic evidence that island ages increase to the northwest within each island chain, is confirmed by KAr whole-rock ages. The linear volcanism which built the islands of French Polynesia began in the Miocene and continues today. Rates of migration of volcanism are calculated from the nearly linear relationship between average island ages and distance from the southeast ends of the four island lineaments. The four rates are indistinguishable, within limits of detection, at 11 ± 1 cm/year. These rates are consistent with the model of rigid Pacific plate movement over four fixed sources of volcanism, be they dynamic as in the hot spot/plume models or passive as in models of propagating lithospheric fractures. If it is accepted that these volcanic sources trace the motion of the lithosphere over the mantle and thus define the “absolute” frame of reference for plate movement, Pacific plate motion may be fixed to the geometry and volcanic migration rates of French Polynesia. This allows calculation of the absolute motion of all other plates, providing an accurate relative motion model is known (Minster et al., 1974). Such a calculation predicts that Africa is virtually stationary and that the Mid-Atlantic Ridge and East Pacific Rise are moving slowly to the west.

Marine magnetic anomalies as related to plate tectonics

During the last 4 years, preliminary or revised analyses of magnetic lineations have been published for all the major ocean basins. These results are graphically summarized in the global lineation and geologic age maps of Pitman et al. [1974] and have also been incorporated in the bibliography for this section. Using magnetic, bathymetric, and seismic data and different mathematical techniques, Chase [1972] and B. Minster et al. (personal communication, 1974) determined models of the instantaneous relative motion of major rigid crustal plates. In addition to describing the relative motion of 11 major plates, the Minster et al. model also suggests that there has been no relative movement between various hot spots during the last 10 m.y.