Whole-Earth Structure and Plate Tectonics

Jyr-Ching Hu, Department of GeosciencesNational Taiwan University

Landsat-7 ETM+ image

www.environmentalgraffiti.com

Iranian Zagros Mountains: they make up Iran and Iraq’s largest mountain range and were formed by the collision of the Eurasian and Arabic plates.

Basic Plate Kinematics (基本的板塊運動學)

• Plate Kinematics: Description of the rates and direction of plate motion on the surface of the Earth.

• Spherical Geometry (球面幾何): Description of plate motion is essentially a geometric exercises, because the motion takes places on the surface of a sphere.

Basic Plate Kinematics: Basic assumptions

1. Earth is a sphere. In reality, the Earth is slightly flattened at the poles (the Earth’s radius at the pole is about 20 km less than it is at the equator)

2. The circumference of the Earth remains constant through time. This assumption implies that the Earth neither expands nor contracts, and thus that the amount of seafloor spreading worldwide is equivalent to the amount of subduction worldwide.

Note: this assumption does not require that the rate of subduction on one side of a specific plate be the same as the rate of spreading on the other side of that plate.

Basic Plate Kinematics: Basic assumptions

3. Plates are internally rigid. It meaning that all motiontakes place at plate boundaries.

Note: It is not completely valid because continental platesdo deform internally, but the error in plate motion calculations resulting from this assumption is less than a few percent

Absolute and Relative Reference Frames (絕對性的參考座標相對性的參考座標)

• Absolute reference frame: We describe plate motions with respect to a fixed point in the Earth’s interior.

• Relative reference frame: We describe plate motions with respect to another.

Relative Plate VelocityDescribing plate velocity

Absolute Reference Frame

Velocities of plates A and B in different reference frame

MOR: Mid-ocean ridge

Absolute Plate Velocity: The Hawaiian-Emperor hot-spot tracks

Mantle plumes (地函熱柱) appear to be independent of plate boundaries, they can be used as the “fixed” reference pointsfor calculating absolute plate velocities

Absolute Plate Velocity: The Hawaiian-Emperor hot-spot tracks

1. The hot-spot frame of reference gives a reasonable approximation of absolute plate velocity, but it is not perfect because hot spots actually do move with respect to one another.

2. The velocity of hot-spot movement is an order of magnitude less than the velocity of plate movement, so the error in absolute plate motion based on the hot-spot reference frame is only a few percent.

Direction and rates in mm/y of plate motion

Convergent: Pairs of inward-pointing arrowsDivergent: Paris of outward-pointing arrows

Euler pole (尤拉極)

• Euler pole (尤拉極): In plate kinematic calculations, the Earth is considered to be a sphere, so such a movement is described by a rotation at a specified angular velocityaround an imaginary axis that passes through the center of the earth.

• Note that Euler poles are merely geometric elementsand that they are not related to the Earth’s geographic poles.

Euler pole (尤拉極)

• Instantaneous Euler pole (瞬時尤拉極): Used to describe relative motion between two plates at an instant in geological time.

• Finite Euler pole (有限尤拉極): Used to describe total relative plate motion over a long period of geological time.

Describing the motion of plates on the Earth’s surface

Latitudes and longitude around the Euler pole are small circlesand great circles.

The motion of a plate between time 1 and time 2 is a rotation ω around the Euler axis.

The linear velocity V is measured on the surface of the Earth

Describing the motion of plates on the Earth’s surface

Transform faults are small circles (latitudes of rotation) relative to the Euler pole.

Describing the motion of plates on the Earth’s surface

Note that spreading velocity and rate of slip along the transform faults increasing with increasing distance away from the Euler pole.

Projection looking down on the Euler pole

Using Vectors to Describe Relative Plate Velocity

A B iv r= Ω ×

siniv r θ=

A B kωΩ =

Two plates, A and B, that are moving with respect to each other

A B iv r= Ω ×

ω: angular velocity;k: unit vector parallel to the rotation pole

v: linear velocity;ri: radius vector

地心

Using Vectors to Describe Relative Plate Velocity

A B iv r= Ω ×

地心

As you get closer to the Euler pole, the value of q becomes progressively smaller, and at the pole itself, θ = 0ο.

Linear velocity increases as the angle θ increases. ri is the radius vector to a point on the Earth’s surface. Since θ2 > θ1, V2 > V1.

Closure relationship (閉合關係) and vector circuit (向量迴路)

A C A B B CΩ = Ω + Ω

. .Africa Pacific Africa S America S America Nasca Nasca PacificΩ = Ω + Ω + Ω

Because the relative velocity between two plates can be described by a vector, plate velocity calculations obey the closure relationship:

We can the relative velocity of two plates even if they do not share a common boundary.

A C A B B CΩ = Ω + Ω

Determine the instantaneous Euler pole and the value of v at point P on the mid-Atlantic Ridge

between African and N. American plates1. Spreading direction: Transform fault describes a small circles around the Euler pole.2. Location of the Euler pole: A great circle drawn perpendicular to a transform fault must pass through the Euler pole .

3. Magnitude of v: The age of oceanic crust on the either side of point P.

4. We can not directly determine relative motion across a convergent boundary but we can do it by vector circuit.

Euler pole of plate motion

How to confirm the relative plate motion?Direction observation: Global Positioning System (GPS), or other

space geodesy such as VLBI (Very Long Baseline Interferometry, 特長基線干涉術) and SLR (Satellite Laser Ranging, 衛星雷射測距)

GPS定位基本觀念

GPS衛星測量乃利用GPS衛星發射之無線電訊號，以測定點位的三度空間座標之定位系統，基本上為距離的量測，即量測未知點（接收儀）與已知位置的衛星之間的瞬時距離 (即所謂後方交會的原理)，並依據差分法平差計算座標進行定位。

GPS定位基本觀念

Global Plate Motion Based on GPS Measurements

Chen Shu-YenDept. GeosciencesNTU

Data: gvel 1.1

VLBI (Very Long Baseline Interferometry)

VLBI是利用多座無線電天文望遠鏡同時追蹤外太空某一訊號發射源，記錄無線電磁波訊號。經由對電磁波的相關處理，可求得發射源至測站的時間差，進而解算出測站間之距離。 全球VLBI觀測站之天文望遠鏡都相隔數百，甚至數千公里。目前 全球有40多個VLBI站，大部份VLBI站都納入了國際VLBI服務局(ILS)的資料庫和處理中心。VLBI可以精密測定外太空無線電發射源之位置及地面VLBI站之位置的特性，可用來建立天球參考座標系與地球參考座標系。對於地球定向參數方面，如極移、自轉、歲差和章動，可確定地球參考座標系和天球參考座標系之間的轉換參數。除此之外，地球板塊運動也可藉由VLBI來進行測定。

http://cgsweb.moeacgs.gov.tw/result/Fault/web/teaching/geodetic/pb.htm

SLR (Satellite Laser Ranging)

SLR是利用極短的雷射波來量測衛星至地面之距離。先由地面測站向衛星傳送雷射波，經衛星反射至原測站，其時間差乘上光速，測得衛星與地面測站之距離。利用高精度的原子鐘進行測度，SLR進行數百公里甚至二萬公里的距離量度，其精度可達數厘米。衛星雷射測距儀分為固定式和流動是兩類。前者安裝在地面的固定測站上，後者可安裝在車輛上，具有高機動性。目前全球共有約50個SLR站。SLR技術有精度高之特性，目前仍是衛星定軌的重要技術，也是測定高程精度最高的一種衛星大地測量技術。對於確定地球質心之位置、地球定向參數及其時間變化，建立與維持地球參考框架，利用SLR技術均可達到高精度之成果。。

http://cgsweb.moeacgs.gov.tw/result/Fault/web/teaching/geodetic/pb.htm

Triple Junctions (三接點, 三叉點 )

Triple junction: The point where three plate boundaries meet.

We name specific types of triple junction by listing the plate boundaries that intersect. Ex., ridge-ridge-ridge and ridge-trench-transform triple junctions.

Stable triple junction: Can exist for a long time even though the location of triple junction changes.

Unstable triple junction: Must change rapidly to creat a new arrangement of plate boundaries.

Fig.2.45ab

W. W. Norton

Ridge-ridge-ridgeTriple junction

Trench-transform-transformTriple junction

Stable triple junction原來是transform-ridge-trench的三叉點，經過一段的地質時間，雖然三叉點的位置改變了，但三個板塊相交接的邊界性質仍然是transform-ridge-trench的三叉點。

Plate-driving Forces (板塊運動的驅動力)

Convection-cell Model(對流胞模式): 地幔內部的對流作用驅動板塊的運動。 板塊之所以會運動是因為地幔內部的對流作用。在剖面上，地幔內部對流的軌跡是以中洋脊為對稱軸線的兩個橢圓形。

Ridge-push and Slab-pull

Forces

依對流胞模式，板塊之所以會運動，是因為軟流圈的對流作用施加剪應力於板塊的底部，因而牽引板塊的底部，使板塊跟著軟流圈的流動而流動。但這個模式結果還是被拋棄掉，因為雖然地幔確實有對流的現象，但是卻無法畫出全球性對流胞的分佈情形，來解釋現在的板塊邊界的幾何型態。隨後計算的結果，認為從中洋脊中心往兩側的推力(ridge push)與聚合型板塊邊界拉扯板塊的拉力(slab pull)是帶動板塊運動的兩種主要力量。

Simplified diagram illustrating the forces acting on a plate

下沈板塊的拉力地幔的抵抗力

大陸板塊的抵抗力

分離板塊的推力

轉型斷層的抵抗力

海洋板塊底部被軟流圈的流動所牽引的力

從中洋脊中心往兩側的推力(ridge push) 中洋脊中心會產生往兩側的推力(ridge push)，是因為中洋

脊的高度要比兩側的海洋平原高出很多。因此中洋脊的位能要比海洋平原高。這高出來的位能會轉換成向海洋平原方向推擠的力量。

板塊被拉往聚合邊界方向的拉力(slab pull)離開中洋脊的海洋板塊會變得越來越冷而越厚(板塊底部的界面是以12800C的等溫線作為岩石圈與軟流圈的分界)，使得浮力變小而往下沈沒，一旦板塊向下沈沒到地幔時，海洋板塊上層的玄武岩會產生相變而轉變成更緊密的榴輝岩(ecologite)，其向下沈沒的力量越大，因而拉動淺部的板塊一起往下沈沒。

The Supercontinent Cycle: Wilson cycleWilson cycle：一個海洋盆地因為裂谷作用而形成，海底擴張作用使海洋盆地擴張，海洋板塊的隱沒作用則使這個海洋盆地逐漸地關閉，大陸碰撞使海洋盆地消失而結合成一個超大型大陸。這一個超大型大陸又再度地因為裂谷作用而開張成為海洋盆地，接之而來的海底擴張作用使海洋盆地擴張，海洋板塊的隱沒作用則使這個海洋盆地逐漸地關閉，大陸碰撞使得海洋盆地消失而形成一個超大型大陸。

這種海洋盆地因為裂谷作用而開張，因為海底擴張作用而擴大，因為板塊聚合作用而關閉，因為大陸碰撞作用形成超大型大陸而消失，再度因為裂谷作用而再度開張的循環作用，稱為威爾森循環(Wilson cycle)。

Stages in the supercontinent cycle

(a)大陸之間做相對的運動，漸漸地集合在一個地幔熱流下沈地帶的上面。

(b)超大型大陸形成之後，底下的地幔重新組合成一個大規模的對流。

(c)超大型大陸底下熱流開始往上湧升，使超大型大陸弱化。最後，發生裂谷作用，超大型大陸分裂成小型的大陸。

Supercontinents

• Pangaea: Formed by the end of Paleozoic (~250 Ma), only to disperse in the Mosozoic.

• Rodinia: Formed at the end of the Precambrian (1.1 Ga) only to disperse at about 900 Ma.

• Panotia: Formed at the dispersion of Rodinia, which itself broke up about 600 Ma (at the beginning of the Paleozoic).

HomeworkPresent-Day Relative and Absolute Plate Motion Calculators from University of Tokyo, Ocean Research Institute:

Plate motion calculation

Plate model: NUVEL-1, NUVEL-1A, NNR-NUVEL-1, NNR-NUVEL-1A, HS3-NUVEL-1AMoving Plate: Philippines, Fixed plate: Eurasia

http://ofgs.ori.u-tokyo.ac.jp/~okino/platecalc_new.html

http://ofgs.ori.u-tokyo.ac.jp/

Relative Plate motions

Relative plate motions are indicated by:1. orientation of transform faults (these make small circles

centred on the pole of relative motion of the two plates)(pole of rotation is found by constructing great circles at right angles to the trends of the transform faults, and finding their intersection)

2. variation in spreading ratethe velocity of motion between to plate is maximum at 90° from the Euler Pole, and decreases to 0 at the Euler Pole by cos φ (latitude)

3. magnetic stripes – provide both rate and direction4. earthquake focal mechanism solutions – give relative

direction of movement (but not rate)5. actual direct measurements (surveying, GPS surveying).

NUVEL-1 (Northwesern University VELocity): Global Relative Plate Motion

Model• 277 spreading rates, 121 transform directions,

724 earthquake slip vectors from around the world

• To find motion of 12 Major plates: • Some motions are derived using data from other

plates by plate circuit closure.• Used to describe average plate motions over the

past 3 million years and compare them to shorter-term motions from earthquake and space geodesy.

DeMets et al., 1990, GJI

PH-EU relative plate motion estimated at 23oN 122oE

Rotation pole Linear velocity Ref. Lat. Long. ω(o/Ma) V. (mm/yr) Azi. (o)

1. 44.50 150.62 1.200 70.7 309 Seno, 19772. 48.20 157.00 1.090 73.7 309 Seno et al., 19933. 47.30 154.40 1.060 68.2 310 Seno et al., 19874. 38.80 142.00 1.950 83.8 314 Huchon, 19865. 37.00 141.00 1.600 65.3 315 Ranken et al., 19846. 48.26 162.45 1.227 105.0 321 Minster & Jordan, 1979

Hu et al., Tectonophysics, 1996

GPS Velocity Field of Taiwan-Luzon Area

Seno et al.,1993

Motion of the Philippine Sea plate consistent with the NUVEL-1A model

Solid star: Chase, 1978;Open square: Minister & Jordan, 1978;Open triangle: Karig, 1975;Plus sign: Huchon, 1986;Solid triangle: Ranke et al., 1984;Open diamond: Seno et al., 1977;Solid diamond: Seno et al., 1993;Solid circle: Zang et al., 2002 (Nuvel-1)

Euler vectors of some plate pairs

Plate pair Lat. of pole (oN) Lon. of pole (oE) Rotation rate (deg Myr-1)--------------------------- ---------------------------- --------------------------------

A B A B A BN-1 N-1A N-1 N-1A N-1 N-1A

-------------------------------------------------------------------------------------------------------------PH-PA 2.38 -0.11 -1.24 -44.34 -43.85 -45.81 0.961 0.964 1.000EU-PH 46.99 46.67 48.23 159.83 158.90 156.97 1.020 1.035 1.085CR-PH 5.00 6.20 6.24 135.10 134.20 134.09 0.300 0.400 0.700PA-CR -5.71 -4.18 -10.13 135.91 137.52 134.43 0.665 0.568 0.309--------------------------------------------------------------------------------------------------------------

N-1: NUVEL-1N-1A: NUVEL-1AA: Zang et al., 2002B: Seno et al., 1993

PH: PhilippineEU: EurasiaCR: CarolinePA: Pacific

Motion of the Philippine Sea plate consistent with the NUVEL-1A model

Whole-Earth Structure and Plate TectonicsBasic Plate Kinematics (基本的板塊運動學)Basic Plate Kinematics: Basic assumptions Basic Plate Kinematics: Basic assumptions Absolute and Relative Reference Frames (絕對性的參考座標相對性的參考座標)Relative Plate VelocityVelocities of plates A and B in different reference frameAbsolute Plate Velocity: The Hawaiian-Emperor hot-spot tracksAbsolute Plate Velocity: The Hawaiian-Emperor hot-spot tracksDirection and rates in mm/y of plate motionEuler pole (尤拉極)Euler pole (尤拉極)Describing the motion of plates on the Earth’s surfaceDescribing the motion of plates on the Earth’s surfaceDescribing the motion of plates on the Earth’s surfaceUsing Vectors to Describe Relative Plate VelocityUsing Vectors to Describe Relative Plate VelocityClosure relationship (閉合關係) and vector circuit (向量迴路)Determine the instantaneous Euler pole and the value of v at point P on the mid-Atlantic Ridge between African and N. AmericanEuler pole of plate motion How to confirm the relative plate motion?GPS定位基本觀念GPS定位基本觀念Global Plate Motion Based on GPS MeasurementsVLBI (Very Long Baseline Interferometry)SLR (Satellite Laser Ranging)Triple Junctions (三接點, 三叉點 )Fig.2.45abStable triple junctionPlate-driving Forces (板塊運動的驅動力)Ridge-push and Slab-pull ForcesSimplified diagram illustrating the forces acting on a plate從中洋脊中心往兩側的推力(ridge push) � 中洋脊中心會產生往兩側的推力(ridge push)，是因為中洋脊的高度要比兩側的海洋平原高出很多。因此中洋脊的位能要比海洋平原高。這高出來的位能會轉換成向海洋平原方向推擠的力量。��板塊被拉往The Supercontinent Cycle: Wilson cycleStages in the supercontinent cycleSupercontinentsHomeworkPlate motion calculationRelative Plate motionsNUVEL-1 (Northwesern University VELocity): Global Relative Plate Motion Model PH-EU relative plate motion estimated at 23oN 122oEGPS Velocity Field of Taiwan-Luzon AreaMotion of the Philippine Sea plate consistent with the NUVEL-1A modelEuler vectors of some plate pairsMotion of the Philippine Sea plate consistent with the NUVEL-1A model