Relative Motion Estimation Research Articles

Pacific‐Farallon relative motion 42‐59 Ma determined from magnetic and tectonic data from the Southern Austral Islands

We have used recently collected magnetic profiles and high resolution multibeam bathymetry data near the southern Austral Islands in French Polynesia to constrain the relative motion of the Pacific and Farallon plates between chron 25 and chron 18 (42–59 Ma). A change in plate motion at about chron 21 (50 Ma), which reoriented spreading direction in the area by 10‐12° clockwise was apparently accommodated by a southward propagating rift which transferred 160 km of Pacific crust to the Farallon plate, the outer pseudofault of which is preserved as the Adventure Trough. These new constraints significantly revise previous estimates of Pacific‐Farallon relative motion at the crucial time period encompassing the bend in the Hawaiian‐Emperor chain, believed to represent an abrupt change in the absolute motion of the Pacific plate. Disrupted lithosphere at the Adventure Trough has apparently been a preferred site for later midplate volcanic activity.

A GPS estimate of relative motion between North and South America

GPS velocity data are used to estimate the Euler vector describing rigid body motion of North America relative to South America. Assuming the boundary between the North and South American plates is located near the Fifteen Twenty fracture zone in the equatorial Atlantic, the Euler vector predicts extension across the Royal Trough up to 1 mm/yr, and convergence across the Barracuda Ridge at about 2 mm/yr, in agreement with geological estimates averaged over tens of millions of years. Further west, convergence between North and South America at rates up to 8 mm/yr may contribute to deformation of the Caribbean plate along its southwest boundary with South America.

Mid‐Cretaceous paleomagnetic results from Marie Byrd Land, West Antarctica: A test of post‐100 Ma relative motion between East and West Antarctica

As part of the tripartite, United States ‐ United Kingdom ‐ New Zealand, 1990–1991 South Pacific Rim International Tectonics Expedition, oriented samples were collected for paleomagnetic analysis from mid‐Cretaceous (circa 100 Ma) intrusive rocks at sampling localities across 350 km of the Ruppert and Hobbs Coast area of Marie Byrd Land, West Antarctica. Paleomagnetic results are presented along with several lines of evidence, including a positive tilt test based on the attitude of circa 117 Ma volcanic rocks that the circa 100 Ma rocks intrude, which argue that these results are a representative estimate of the mid‐Cretaceous magnetic field in Marie Byrd Land (MBL). The new circa 100 Ma mean south pole (224.1°E/75.7°S, A95 = 3.8°, N = 19 site means) is concordant with other West Antarctic results of similar age implying that at least Marie Byrd Land, Thurston Island and the Antarctic Peninsula have not experienced any paleomagnetically resolvable relative motion since the mid‐Cretaceous. However, the poles from these Pacific‐bordering blocks of West Antarctica are significantly offset from a synthetic apparent polar wander path that was produced for the East Antarctic craton, implying relative movement between East Antarctica and Pacific West Antarctica since about 100 Ma. Though the paleomagnetic estimate for east‐west Antarctic relative motion may be reconciled with geologic estimates for extension in the Ross Sea at the extremes of the error envelope, the best paleomagnetic estimate of relative motion suggests a larger amount of total extension between East and West Antarctica (MBL) than previously suspected. Both estimates call for several hundreds of kilometers of post‐100 Ma displacement between East Antarctica and the Pacific‐bordering blocks of West Antarctica.

GPS measurement of relative motion of the Cocos and Caribbean Plates and strain accumulation across the Middle America Trench

Global Positioning System (GPS) measurements in 1988 and 1991 on Cocos Island (Cocos plate), San Andres Island (Caribbean plate), and Liberia (Caribbean plate, mainland Costa Rica) provide an estimate of relative motion between the Cocos and Caribbean plates. The data for Cocos and San Andres Islands, both located more than 400 km from the Middle America Trench, define a velocity that is equivalent within two standard errors (7 mm/yr rate, 5 degrees azimuth) to the NUVEL‐1 plate motion model. The data for Liberia, 120 km from the trench, define a velocity that is similar in azimuth but substantially different in rate from NUVEL‐1. The discrepancy can be explained with a simple model of elastic strain accumulation with a subduction zone that is locked to a relatively shallow (20±5 km) depth.

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.

Relative Motion of Two Points during an Earthquake

The results are discussed of experiments to test the adequancy of various approximate methods of estimating relative motion. The methods considered were characterized by the follwing: (a) the relative displacement is twice the maximum ground displacement; (b) the relative displacement is no greater than the maximum positive displacement minus the maximum negative displacement; approximation of the relative motion by an equation (given); (b) the propagation of body and surface waves through an elastic medium and the evaluation of expressions for relative motion and strains in various directions; (e) if the motion consisted of a single sinusoid, the maximum displacement would occur when b/c (distance between two points of earthquake motion; time lag between the motion of the two points) is exactly one-half the period of the wave. Direct calculations from accelerograms from 3 earthquakes showed that: method (a) is very conservative for all b/c; method (b) provides a reasonable upper value of R, it is very conservative for b/c, and use of the displacement, dm alone is inadequate; method (c) without the acceleration terms and method (d) provide a conservative but reasonable estimate of relative motion when it is less than dm; method (e) severely underestimates the possible relative motions.

Sonobuoy and teleseismic study of Gulf of California transform fault earthquake sequences

abstract Sonobuoys have been used in the study of two Gulf of California transform fault aftershock sequences. Uncertainties in epicentral locations are no larger than navigational uncertainties. The first local study of an oceanic transform fault aftershock sequence followed a M S = 5.5 event on March 25, 1973. The sonobuoy data suggest that the main event did not lie along the main transform fault scarp. Surface-wave radiation patterns and a P -wave fault-plane solution give a strike of 327, about 20 different from local bathymetric trends. Subsidiary faulting near a locked transform fault, perhaps a result of local tectonic complication, is a possible explanation for this difference. The second study followed a M S = 6.3 event on May 31, 1974. Sonobuoy data limit the aftershock zone to be about 25 km long, trending approximately parallel to local bathymetric features. All earthquakes located with sonobuoys were shallow. Arrival times limit the depths to be less than 7 km, and when good depth control is present, depths were 3 to 5 km. The calculated stress drop for the March 25, 1973 event is 8 to 30 bars. The historic seismic slip rate along Gulf of California transform faults has been estimated from the published seismicity to be 6.1 to 3.7 cm/yr, assuming fault thicknesses of 3 to 5 km, respectively, in good agreement with estimates of Pacific-American relative plate motion from geologic and geodetic methods. One 240-km section of transform fault appears to have been locked since about 1955, accumulating strain for a large earthquake. The good agreement between the calculated slip rate and the geologic and geodetic estimates supports the sonobuoy-based observation that the earthquake generating zone is very thin, perhaps only 3 to 5 km thick.

Conjecture on the visual estimation of relative radial motion.

THE ability to estimate accurately the time interval until the juncture of an observer with an object moving with relative radial velocity towards the observer seems to be highly developed in humans and many animals. In many practical situations, of probable importance for survival, it is not the distance of the object from the observer which is of interest, nor is it the velocity of the object, but rather the ratio of the two, which gives the time taken by the object to reach the observer. The importance of this parameter has certainly been renewed in the age of the motor car. The popularity of ball games may be partly due to the exercise of this faculty otherwise dormant in a sedentary era.