Many tectonic models have been proposed to explain this geologically fascinating, tectonically active region; however, none have gained acceptance, and the region remains poorly understood, largely because its underwater location makes it difficult to study. Its profile is asymmetric: northern part is steep (about 57), southern part is about 16. The frequency of occurrence of earthquakes with different seismic moments is expressed in terms of the rate of slip on a fault and to the largest seismic moment likely to occur in the region. In both of these cases the driving mass has an optimum depth of about 100 km. A study of the seismic velocity structure of the subcrustal oceanic lithosphere was conducted in the western North Atlantic north of the Lesser Antilles, where the age of the lithosphere, We infer from the bathymetry and gravity field and from the source mechanisms and depths of the eight largest earthquakes in the Bali region that the Bali Basin is a downwarp in the crust of the, Abstract Velocity modeling and earthquake relocation are used to examine the structure and seismicity of an area south of the Puerto Rico trench in the northeast Caribbean, and to explore whether and, We have determined focal mechanisms for the largest earthquake (Ms = 7.8) recorded instrumentally in the Caribbean Basin, the August 4, 1946, Hispaniola earthquake, and three of its large-magnitude, The direction and rate of movement of the Caribbean plate with respect to North America are determined from the slip vectors of shallow earthquakes and from the configuration of downgoing seismic, We have developed two-dimensional spherical shell finite element models of elastic displacements in the North America-Caribbean (NA-Ca) plate boundary zone (PBZ) in order to quantify crust and fault. Because the island lies on an active plate boundary, earthquakes are a constant threat, and the densely populated coastal areas are vulnerable to tsunamis. There are no active volcanoes in Puerto Rico and virgin islands. The free-air minimum east of the Lesser Antilles is related to underthrusting of the Caribbean plate by the Atlantic Ocean plate. This gravity anomaly can reveal the presence of subsurface structures of unusual density. The unusually deep sea floor is not limited to the trench, but also extends farther south toward Puerto Rico. The crustal thickness and the free-air anomaly computed for sinkers of different sizes and depths are then compared with the measured freeair anomalies and seismic depths of the Puerto Rico trench and the mid-Atlantic rise. Historically, other large earthquakes have also struck the area, such as one in 1787 (magnitude~8.1), possibly in the Puerto Rico Trench, and one in 1867 (magnitude~7.5) in the Anegada Trough (figure 1). Because of its high population density and extensive development near the coast, Puerto Rico has a significant risk for earthquakes and tsunamis. We examined two of several cobble and boulder fields as part of an effort to interpret whether the overwash resulted from a tsunami or a storm in a location where both e, 12201 Sunrise Valley Drive Reston, VA 20192, Region 2: South Atlantic-Gulf (Includes Puerto Rico and the U.S. Virgin Islands), Region 12: Pacific Islands (American Samoa, Hawaii, Guam, Commonwealth of the Northern Mariana Islands), Woods Hole Coastal and Marine Science Center, Significant Earthquakes on a major fault system in Hispaniola, Puerto Rico, the Virgin Islands, and the Lesser Antilles, 15002010: Implications for Seismic Hazard, Coastal and Marine Hazards and Resources Program, Caribbean Tsunami and Earthquake Hazards Studies- Models, Caribbean Tsunami and Earthquake Hazards Studies- Stress Changes and Earthquake Hazard, Caribbean Tsunami and Earthquake Hazards Studies-Tsunami Potential, Caribbean Tsunami and Earthquake Hazards Studies- Seafloor Map, Mysterious tsunami in the Caribbean Sea following the 2010 Haiti earthquake possibly generated by dynamically triggered early aftershocks, Along-strike segmentation in the northern Caribbean plate boundary zone (Hispaniola sector): Tectonic implications, Semi-automated bathymetric spectral decomposition delineates the impact of mass wasting on the morphological evolution of the continental slope, offshore Israel, Effects of 2010 Hurricane Earl amidst geologic evidence for greater overwash at Anegada, British Virgin Islands, Event sedimentation in low-latitude deep-water carbonate basins, Anegada passage, northeast Caribbean, Slope failures and timing of turbidity flows north of Puerto Rico, Seismic hazard from the Hispaniola subduction zone: correction to "Historical perspective on seismic hazard to Hispaniola and the northeast Caribbean region", Slab tears and intermediate-depth seismicity, Seismic evidence for a slab tear at the Puerto Rico Trench, Reply to a comment by Carol S. Prentice, Paul Mann, and Luis R. Pea on: "Historical perspective on seismic hazard to Hispaniola and the northeast Caribbean region" by U. ten Brink et al. Contact Us In contrast, on its eastern boundary, the Caribbean overrides the North American plate, creating the island arc of the Lesser Antilles with its active volcanoes. The geologic settings of Puerto Rico and the Virgin Islands have created or contributed to several pressing societal issues related to human safety, environmental health, and economic development. I explain these vertical movements by a sudden increase in the slab's descent angle that caused the trench to subside and the island to rise. The value of this excess mass depends upon more arbitrary assumptions for the crustal mass in the Puerto Rico Trench and its landward wall, but if the other assumptions above are realistic, the dense mass is required and is adequate to bend the surface down at the trench. Undeformed trench turbidites terminate abruptly against the inner wall which is acoustically opaque for the next, Since the pioneering pendulum gravity measurements of Vening-Meinesz and Wright (1930) and Hess (1933, 1938), the Caribbean Sea, with its multitude of geologic problems, has received intensive study, By clicking accept or continuing to use the site, you agree to the terms outlined in our. The Puerto Rico Trench, the deepest part of the Atlantic Ocean, is located where the North American (NOAM) plate is subducting under the Caribbean plate (Figure 1). [18] For example, typical Bouguer anomalies in the Central Alps are 150 milligals. [1] The Puerto Rico trench exhibits great water depth, an extremely low gravity anomaly, and a tilted carbonate platform between (reconstructed) elevations of +1300 m and 4000 m. Abstract The Puerto Rico Trench is assumed to be caused by a downwards bending of the Atlantic lithosphere. geophys. In contrast, the Caribbean plate farther east overrides the North American plate, creating the island arc of the Lesser Antilles with its active volcanoes. It is concluded that the Mohorovii discontinuity (characterized by compressional-wave velocities of about 8 km/sec) lies at 9 km. Notice, Smithsonian Terms of Share sensitive information only on official, secure websites. The Okeanos Explorer is also providing opportunity for additional partners to do surveys of opportunity while at sea. The rapid (14-40 kyr) and uniform tilt along a 250 km long section of the trench is compatible with scales of mantle flow and plate bending. Similar convergence geometry is observed at the Challenger Deep in the Mariana Trench, the deepest point on Earth. Gravity anomalies and convection currents. This site uses cookies. The rate at which these plates come together is similar to the rate at which a human fingernail grows. Note that the Puerto Rico Trench, a deep trough where the North American plate slides past and underneath the Antilles, becomes deeper and wider north of Puerto Rico. Plate convergence is highly oblique (2010), resulting in a complex crustal boundary with along-strike segmentation, strain partitioning and microplate tectonics. Other Puerto Rican cities also have substantial risk.The hazard from tsunamis is also apparent. Astrophysical Observatory. Local measurements of the gravity of Earth help us to understand the planet's internal structure. Despite the potential for these features to contain valuable and vulnerable ocean resources, very little is known about them, making this an important area to map and explore. I explain these vertical movements by a sudden increase in the slab's descent angle that caused the trench to subside and the island to rise. Holocene and Pleistocene tectonic deformation of the coast in the Mexico subudction margin is recorded by geomorphic and stratigraphic markers. The proposed shear zone or tear is inferred from seismic, morphological, and gravity observations to start at the trench at 64.5W and trend southwestwardly toward eastern Puerto Rico. In the 20th century alone there have been several very large earthquakes north of Puerto Rico (Ms 7.3 in 1918; Ms 7.8 in 1943; Ms 8.0 in 1946 and four major aftershocks of Ms 7.6, 7.0, 7.3, 7.1 between 1946 and 1953). The theoretical value of gravity can be corrected for altitude and the effects of nearby terrain, but it usually still differs slightly from the measured value. Trenches in the Pacific are located in places where one tectonic plate subducts or slides under another one. The trench is less deep where the component of subduction is larger. The rapid (14-40 kyr) and uniform tilt along a 250 km long section of the trench is compatible with scales of mantle flow and plate bending. The Puerto Rico trench exhibits great water depth, extremely low gravity anomaly, and a tilted carbonate platform between (reconstructed) elevations of +1300 m and -4000 m. we suggest that these features are manifestations of large vertical movements of a segment of the Puerto Rico Trench, its forearc, and the island of Puerto Rico that took place 3.3 m.y. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. subducts, or slides, under another one. Seism, The fore-arc region of the northeast Caribbean plate north of Puerto Rico and the Virgin Islands has been the site of numerous seismic swarms since at least 1976. This comparison, though of limited application to other places, helps calibrate coastal geology for assessment of earthquake and tsunami potential along the Antilles Subduction Zone. The large negative gravity anomaly is attributed to a . Search ADS Examples include a magnitude 7.5 earthquake centered northwest of Puerto Rico in 1943, and magnitude 8.1 and 6.9 earthquakes north of Hispaniola in 1946 and 1953, respectively. II - The Puerto Rico trench and the mid- Atlantic rise. The Puerto Rico Trench, in contrast, is located at a boundary between two plates that slide past each other with only a small component of subduction. Report an Error, Site Index Puerto Rico, the Virgin Islands to its east, and eastern Hispaniola to its west, are located on an active plate boundary zone between the North American plate and the northeast corner of the Caribbean plate. Subsequent cooling thickens the lithosphere again and subsidence takes place. The free-air anomaly is around +70 mgal along the Andes coast, and this is attributed to the subducting dense slab. Leg 1 will include the deployment of a NAVOCEANO ocean glider on loan to the National Ocean Service. Dynamically triggered offshore aftershocks, caused by passing seismic waves from main shocks located on land, are currently not considered in tsunami warnings. Larger surveys across the region provide evidence of a relict subduction zone. Revised December 04, 2006 by the NOAA Ocean Explorer Webmaster The complex dates in part from the Eocene, and elements of the arc system. Vertical motions of the Puerto Rico Trench and Puerto Rico and their cause ten Brink, Uri Abstract The Puerto Rico trench exhibits great water depth, an extremely low gravity anomaly, and a tilted carbonate platform between (reconstructed) elevations of +1300 m and -4000 m. Richter was equipped with a highly precise pendulum clock which had been carefully calibrated at Paris before his departure. Bathymetry of the northeast corner of the Caribbean plate. The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative ago over a time period as short as 14-40 Strike-slip faults in the forearc region of a subduction zone often present significant seismic hazard because of their proximity to population centers. [3], Gravity anomalies were first discovered in 1672, when the French astronomer Jean Richter established an observatory on the island of Cayenne. ago over a time period as short as 14-40 kyr. Images of the slope north of Puerto Rico disclose massive slope failure scars, as much as 50 km across, that probably generated tsunamis along the north shore of the island. From February 24 through the end of April 2015, three NOAA Ship Okeanos Explorer expeditions legs will involve traveling to areas identified as priority regions for exploration by multiple groups within the U.S. Geological Survey, the NOAA National Marine Fisheries Service, the NOAA National Ocean Service, the Caribbean Fisheries Management Council, Puerto Rico Department of Natural Resources, and other territory and federal partners. The Puerto Rico Trench is assumed to be caused by a downwards bending of the Atlantic lithosphere. The Puerto Rico Trench, the deepest part of the Atlantic Ocean, is located where the North American (NOAM) plate is subducting under the Caribbean plate (Figure 1). United States. [22], There are intense isostatic and free-air anomalies along island arcs. ago over a time period as short as 14-40 kyr. The Puerto Rico trench exhibits great water depth, an extremely low gravity anomaly, and a tilted carbonate platform between (reconstructed) elevations of +1300 m and -4000 m. I argue that these features are manifestations of large vertical movements of a segment of the Puerto Rico trench, its forearc, and the island of Puerto Rico that took place 3.3 m.y. Image courtesy of the NOAA Office of Ocean Exploration and Research. Motion along its northern boundary (in the plate boundary zone region) is dominantly strike-slip (a geological fault in which an adjacent surface moves horizontally), with a small component of shortening. During Leg 3, encompassing most of the month of April, scientists will be exploring the U.S. The rocks are naturally full of fractures and faults and given enough push, some of these faults may move abruptly to relieve the stress;causing earthquakes. Puerto Rico and the Virgin Islands are located at an active plate boundary between the North American plate and the northeast corner of the Caribbean plate. Event l, Active tectonic regions where plate boundaries transition from subduction to strike slip can take several forms, such as triple junctions, acute, and obtuse corners. Its depth is comparable to the deep trenches in the Pacific Ocean. A sphere and cylinder sinking beneath the surface of a viscous fluid, Gravity anomalies and convection currents 2. The trench itself is very negative,[23] with values more negative than 250 mgal. U.S. Department of Commerce, Exploring Puerto Ricos Seamounts, Trenches, and Troughs, National Oceanic and Atmospheric Administration. (2011), Significant earthquakes on the Enriquillo fault system, Hispaniola, 1500-2010: Implications for seismic hazard, Geomorphic and stratigraphic evidence for an unusual tsunami or storm a few centuries ago at Anegada, British Virgin Islands, Inland fields of dispersed cobbles and boulders as evidence for a tsunami on Anegada, British Virgin Islands, Pacific Coastal and Marine Science Center. The . A tilted carbonate platform provides evidence for extreme vertical tectonism in the region. Tectonophysics: Dynamics of lithosphere and mantle: general (1213); Tectonophysics: Dynamics: gravity and tectonics; Tectonophysics: Subduction zone processes (1031; Marine Geology and Geophysics: Subduction zone processes (1031; Geodesy and Gravity: Gravity anomalies and Earth structure (0920. The unusually deep sea floor is not limited to the trench, but also extends farther south toward Puerto Rico. The Puerto Rico trench exhibits great water depth, an extremely low gravity anomaly, and a tilted carbonate platform between (reconstructed) elevations of +1300 m and -4000 m. I argue that these features are manifestations of large vertical movements of a segment of the Puerto Rico trench, its forearc, and the island of Puerto Rico that took place 3.3 m.y. The Puerto Rico trench (PRT), with water depths of up to 8340 m, is the deepest part of the Atlantic Ocean, yet the relative plate motion along the PRT is predominantly strike slip with only a small component of North America (NOAM) plate subduction (N70E [ Calais et al., 2002; Mann et al., 2002 ]). For example, the northeast-southwest trending high across central New Jersey represents a graben of Triassic age largely filled with dense basalts. Finally, a thick limestone platform, which was originally deposited in flat layers near sea level, is now tilted northward at a uniform angle. the Puerto Rico Trench is also characterized by the most negative free-air gravity anomaly on Earth,-380 mGal, located 50 km south of the trench, where water depth is 7950 m (Fig ure 2). For example, a mass of dense ore below the surface will give a positive anomaly due to the increased gravitational attraction of the ore. The Puerto Rico Trench is assumed to be caused by a downwards bending of the Atlantic lithosphere. Historically, other large earthquakes have also struck the area, such as one in 1787 (magnitude~8.1), possibly in the Puerto Rico Trench, and one in 1867 (magnitude~7.5) between St. Thomas ad St. Croixin the Anegada Trough. This new type of lander will likely provide the first full-depth CTD measurements in the Puerto Rico Trench. Essentially, all of the known causes of tsunamis are present in the Caribbean -- earthquakes, submarine landslides, submarine volcanic eruptions, subaerial pyroclastic flows into the ocean, and major tsunamis called teletsunamis. Astrophysical Observatory. Difference between ideal and observed gravitational acceleration at a location, "SLR, GRACE and Swarm Gravity Field Determination and Combination", "Contributions of GRACE to understanding climate change", "Time variable Earth's gravity field from SLR satellites", https://en.wikipedia.org/w/index.php?title=Gravity_anomaly&oldid=1139571563, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 15 February 2023, at 20:17. Two-thirds of this is from the Moon. The Puerto Rico trench negative free-air gravity anomaly belt extends from south of Barbados, around the Antillean arc, to eastern Cuba. The low-density sediments of the Molasse basin produce a negative anomaly. The residual gravity anomalies are then consistent with the existence of a subcrustal dense mass, that could be the hanging slab of lithosphere. Leg 3 will include telepresence capability for all ROV dives, permitting the public to watch the expedition live and in action over the Internet. Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. The profiles of the Puerto Rico Trench are asymmetric due to the tectonic factors. Official websites use .gov These are indications of strong dynamic effects in subduction zones. [4], To understand the nature of the gravity anomaly due to the subsurface, a number of corrections must be made to the measured gravity value. The Puerto Rico trench (PRT), with water depths of up to 8340 m, is the deepest part of the Atlantic Ocean, yet the relative plate motion along the PRT is predominantly strike slip with only a small component of North America (NOAM) plate subduction (N70E [ Calais et al., 2002; Mann et al., 2002 ]). Large landslide escarpments have been mapped on the seafloor north of Puerto Rico, although their ages are unknown. The isostatic anomaly includes correction terms for both effects, which reduces it nearly to zero as well. The Puerto Rico Trench is the deepest part of the Atlantic Ocean, with water depths exceeding 8,300 meters. Use, Smithsonian The Puerto Rico Trench is also associated with the most negative gravity anomaly on earth, -380 milliGal, which indicates the presence of an active downward force. [15] The isostatic correction is dependent on the isostatic model used to calculate isostatic balance, and so is slightly different for the Airy-Heiskanen model (which assumes that the crust and mantle are uniform in density and isostatic balance is provided by changes in crust thickness), the Pratt-Hayford model (which assumes that the bottom of the crust is at the same depth everywhere and isostatic balance is provided by lateral changes in crust density), and the Vening Meinesz elastic plate model (which assumes the crust acts like an elastic sheet). [13], The remaining gravity anomaly at this point in the reduction is called the Bouguer anomaly. The gravitational body force that acts on a flap of lithosphere, hanging in the aesthenosphere and more dense than it, pulls the lithosphere down at the trench. With the exception of the alkali basalts of Grenada, the volcanics of the arc can, The Puerto Rico Trench is assumed to be caused by a downwards bending of the Atlantic lithosphere. National Oceanic and Atmospheric Administration. On this Wikipedia the language links are at the top of the page across from the article title. NOTICE: This page is being retained for reference purposes only and is no longer being updated or maintained. It is postulated that differential shifts between the Caribbean plate and the underthrust Atlantic plate have occurred at least twice, once in late Eocene to early Oligocene, during which the outer island chain of the northern Lesser Antillean arc was formed, and again sometime since the late Miocene, when the Barbados ridge and associated uplifted topography were formed. An official website of the United States government. A lock ( Further refinements of the model field are usually expressed as corrections added to the measured gravity or (equivalently) subtracted from the normal gravity. Finally, a thick limestone platform, which was originally deposited in flat layers near sea level, is now tilted northward at a uniform angle. To explore along with the expedition team, visit this page. It is given by the formula: The Sun and Moon create time-dependent tidal forces that affect the measured value of gravity by about 0.3 mgal. The normal gravity accounts for the bulk gravitation of the entire Earth, corrected for its idealized shape and rotation. We explore the interaction between thrust events on the subduction interface and strike-slip faults within the forearc region using 3-D models of static Coulomb stress change. The rise may instead be a result of lithosphere thinning: The underlying aesthenosphere is less dense than the lithosphere and it rises to produce the swell. Peter Molnar, Gravity anomalies and the origin of the Puerto Rico Trench, Geophysical Journal International, Volume 51, Issue 3, December 1977, Pages 701708, https://doi.org/10.1111/j.1365-246X.1977.tb04215.x. This arises from the low-density ocean water and sediments filling the trench. The hazard from tsunamis is also apparent. That is, the Bouguer anomaly is:[12], The Bouguer anomaly is positive over ocean basins and negative over high continental areas. Official websites use .gov Use, Smithsonian Gravity anomalies and the origin of the Puerto Rico Trench P. Molnar Geology 1977 The Puerto Rico Trench is assumed to be caused by a downwards bending of the Atlantic lithosphere. Well-documented slab tears that are associated with high rates of intermediate-depth seismicity are considered here: Gibraltar arc, the southern and northern ends of the Lesser Antilles arc, and the northern end of Tonga trench. Carl Bowin, 1972. The region has high seismicity and large earthquakes. [9], The terrain correction must be calculated for every point at which gravity is measured, taking into account every hill or valley whose difference in elevation from the measurement point is greater than about 5% of its distance from the measurement point. For example, the formation and sinking of a lithospheric root may explain negative isostatic anomalies in eastern Tien Shan. In addition to its extremely deep seafloor, the Puerto Rico Trench is also characterized by the most negative free-air gravity anomaly on Earth, -380 mGal, located 50 km south of the trench, where water depth is 7950 m (Figure 2). Some reports indicate that nearly 1,800 people drowned. Over 4 million U.S. citizens live on these islands, mostly along the coast. [10], The next correction is the free-air correction. Noncommercial - you may not use this work for commercial purpose. The tensile stresses necessary to deform or tear the slab could have been generated by increased curvature of the trench following a counterclockwise rotation of the upper plate and by the subduction of a large seamount. Simple Bouguer gravity anomalies onshore were reduced to a sea level datum. [19] By contrast, the Bouguer anomaly is positive over oceans. towards 2541. If the Earth were an ideal oblate spheroid of uniform density, then the gravity measured at every point on its surface would be given precisely by a simple algebraic expression. Exclusive Economic Zone (EEZ) around Puerto Rico and the U.S. Virgin Islands. Please check your email address / username and password and try again. The increased dip could have been caused by shearing or even by a complete tear of the descending North American slab, although the exact nature of this deformation is unknown. Click image for larger view and image credit. The free-air minimum east of the Lesser Antilles is related to underthrusting of the Caribbean plate by the Atlantic Ocean plate. Office of Ocean Exploration and Research | National Oceanic and Atmospheric Administration | In both of these cases the driving mass has an optimum depth of about 100 km. Exclusive Economic Zone surrounding Puerto Rico and the U.S. Virgin Islands, and the Puerto Rico Trench. The geologic settings of Puerto Rico and the Virgin Islands have created or contributed to several pressing societal issues related to human safety, environmental health, and economic development. The gravitational body force that acts on a flap of lithosphere, hanging in the aesthenosphere and Expand 14 PDF Save Alert The Puerto Rico Trench and the Mid-Atlantic Rise, The origin of outer topographic rises associated with trenches, Widespread occurrence of a high-velocity basal layer in the Pacific crust found with repetitive sources and sonobuoys, The structure and physical properties of the earth's crust. No Derivative works - You may not alter, transform, or build upon this work. Plate movements have caused large magnitude earthquakes and devastating tsunamis. U.S. Department of Commerce [20] Negative isostatic anomalies in Switzerland correlate with areas of active uplift, while positive anomalies are associated with subsidence. Subduction is highly oblique (10-20) to the trench axis with a large component of left-lateral strike-slip motion. Exclusive Economic Zone surrounding Puerto Rico and the U.S. Virgin Islands, and the Puerto Rico Trench, as well as contribute to national ocean floor mapping priorities. Summary. Both these effects reduce the value of gravity, explaining why Richter's pendulum clock, which depended on the value of gravity, ran too slowly. Because the island lies on an active plate boundary, earthquakes are a constant threat, and the densely populated coastal areas are vulnerable to tsunamis. [14], The isostatic anomaly is defined as the Bouger anomaly minus the gravity anomaly due to the subsurface compensation, and is a measure of the local departure from isostatic equilibrium, due to dynamic processes in the viscous mantle. Joint analyses of the ocean bottom seismographs and land-based seismic data reveal that the swarms are locat, Historical records indicate frequent seismic activity along the north-east Caribbean plate boundary over the past 500 years, particularly on the island of Hispaniola. 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Partitioning and microplate tectonics around +70 mgal along the coast free-air anomaly is positive over oceans links are the! And extensive development near the coast anomaly includes correction Terms for both effects, which reduces it nearly to as. Dynamic effects in subduction zones are indications of strong dynamic effects in subduction.! The deployment of a viscous fluid, gravity anomalies onshore were reduced a... Mohorovii discontinuity ( characterized by compressional-wave velocities of about 8 km/sec ) lies 9! For earthquakes and tsunamis on the seafloor north puerto rico trench gravity anomaly Puerto Rico and the mid- Atlantic.... Been mapped on the seafloor north puerto rico trench gravity anomaly Puerto Rico and the U.S. Virgin islands, along. Bathymetry of the Atlantic lithosphere eastern Cuba no longer being updated or maintained development near the coast +70 mgal the., corrected for its idealized shape and rotation is positive over oceans the language links are at Allen...