The generation of the first order stress field

caused by plate tectonics

Jasmaria Wojatschke

TU Bergakademie Freiberg, Institut für Geologie, Bernhard-v.-Cotta Str. 2, 09599 Freiberg,

Germany

Abstract. This paper is supposed to give an overview about the world stress field,

related data and the idea of its origin by relative plate motion. The World Stress

Map project summarizes the collected data from all over the world and developed

a system to categorize them. Another important model which is often used for

modeling plate motions is the NUVEL including the Euler poles. Wdowinski

(1998) developed a theory by using this to existing models to explain the first or-

der stress field with a strong correlation to the observed data. That the theory also

works within difficult conditions should be illustrated by the modeled Australian

stress field (Reynolds et al. 2002).

Introduction

The intraplate stress fields result from forces acting on the lithosphere and there-

fore contain information about the dynamics such as driving mechanism (Richard-

son 1992). So the theory of plate tectonics has provided the geodynamic frame-

work. The main idea is that the lithosphere can be divided in a finite number of

rigid plates moving relative to each other (relative plate motion) with each plate

having their own velocity to the geographic coordinates as reference system (abso-

lute plate motion). Since no real material is absolutely rigid, the applicability of

the theory is limited by this fact (Wdowinski 1998, Stein & Sella 2002). Neverthe-

less on plate interior regions the theory can be successfully applied; only the plate

boundary regions are characterized by significant intraplate deformation and non

rigid behavior (Wdowinski 1998).

The plate boundary forces are the principle controlling factors inducing the first

order stress field beside buoyancy forces which arise from density variation be-

tween mid-ocean ridge and plate interiors (ridge push). By modeling the intraplate

2 Jasmaria Wojatschke

stress field the ridge push forces could play an important role, e.g. for North and

South America (Richardson 1992; Wdowinski 1998).

The data used for modeling the direction of relative plate motion and analyzing

stress patterns, are taken from the WSM database and the visualized cards (Fig.1)

and the NUVEL-1a model by DeMets 1994. All of the stress data files from the

WSM project are available at the project’s web site at HUhttp://www.world-stress-

map-orgUH.

The World Stress Map Project

The World Stress Map (WSM) project is an effort to collect and interpret date on

the orientation and the relative magnitude of the present-day in situ tectonic stress

field with a focus on the intraplate stress field (Zoback 1992). The Complexities

within and along plate boundaries are well known (Zoback 1992).

Today the WSM project is a collaboration of academia, industry and govern-

mental organizations (Heidbach et al. 2007). The project was first initiated in

1986 and under the supervision of the International Lithosphere Program (Zoback

1992) and since 1995 it is a research project of the Heidelberg Academy of

Science and Humanities and is located at the Geophysical Institute of the Univer-

sity Karlsruhe (TH) in Germany (Sperner et al. 2003; Heidbach et al. 2007).

To sample data the following sources are used: Earthquakes and borehole brea-

kouts are the most sources for the incoming data. Other possibilities are drilling-

induced fractures and geological observation data (Sperner et al. 2003; Zoback

1992).

The data has a standardized quality ranking scheme for making them compara-

ble on a world wide scale. With A the highest quality is marked and E for the low-

est, whereas only the reliable data quality from A to C should be used in further

investigations (Sperner et al. 2003). First it was introduced by Zoback (1992) and

refined and extended in Sperner et al. (2003). In these two papers stress indicators

were explained and corresponding evaluation criteria are summarized. An over-

view about the distribution of data record is given in Fig.2. The information you

can get out of the database are the following: Orientation of SH (maximum hori-

The generation of the first order stress field caused by plate tectonics 3

zontal compression), the quality of the orientation, method, location and depth of

measurement, the tectonic stress regime and the source of measurement (Heidbach

et al. 2007).

Fig.1: Release of the World Stress Map (WSM 2008) showing only the data with quality rank A-C.

Lines show the orientation of the maximum horizontal compression (SH); different symbols represent

different data types; different symbol sizes characterize different data qualities; different colors and fil-

lings indicate different stress regimes (red/unfilled, normal faulting (NF); green/half-filled, strike-slip

faulting; (SS); blue/filled, thrust faulting (TF); black, unknown (U)). Sperner et al. 2003

Fig.2: Distribution of data records according to (a) data quantity (n = 15969), (b) data type (only A-C,

n = 12.046) and (c) tectonic stress regime (only A-C). (n – number of data) (Heidbach et al. 2005)

4 Jasmaria Wojatschke

The NUVEL-1a (Northwestern University VELocity model)

The model NUVEL-1 gives information about the angular velocity of the plates.

The information was taken from marine magnetic anomalies across spreading cen-

ters. But observations by geodetic space measurement suggested that the age of

geomagnetic reversals are systematically too young (DeMets et al. 1994). Due to

the fact the predicted velocities for the different plates are too fast (Stein & Sella

2002). That is the reason why the NUVEL-1 needed a recalibration which is called

NUVEL-1a (DeMets et al. 1994).

In the NUVEL-1a also the Poles of Rotation (PoR) are given (Wdowinski

1998), which can be defined in relation to the associated plates by using e.g. the

transform plate boundaries along the mid ocean ridges (MOR). The orthogonal

lines on the different segments should intersect in one point, the PoR or Euler

pole. This geometrical idea works because the transform faults describe small cir-

cles with respect to the pole (Fig.3).

A theory of intraplate tectonics (first order stress field cause by relative plate motion)

Shimon Wdowinski’s article focuses on the intraplate regions, where intern defor-

mation is negligible. It’s different in plate boundary regions, where intraplate de-

formation is significant and the assumption of rigid behavior can’t be utilized. In

his study he tries to develop a framework for calculating regional scale elastic de-

formation in both regions. (The width of the deforming plate boundary can vary

from a few hundred meters up to thousands of kilometers.)

The forces which arise from relative motion of neighboring plates induce forces

lying along the direction of the relative plate motion. There are three different

types of forces occurring at boundaries which are the following (Fig.4): (1) inward

directed forces occur at convergent plate boundaries (subduction and collision)

and along MOR where the ridge push acts, (2) outward forces appearing along di-

vergent plate boundaries (continental rifts) and at (3) transform faults tangential

forces are present. For the described boundary type the force or rather the dis-

The generation of the first order stress field caused by plate tectonics 5

placement are regarded with respect to the plate interior. The stress field varies

with time in magnitude by accumulating strain during interseismic stages and re-

leases during earthquakes. Only the MOR can be seen as to be constant over time

in its magnitude.

The theory Wdowinski uses, is based on the spherical geometry. With this in-

strument he is going to explain the intraplate displacement, strain and stress test-

ing it against the data of the WSM.

Fig.3 (left): Determination of the Euler pole for a MOR by using the transform faults following a small

circle with respect to the pole. (Kearey et al. 2009)

Fig.4 (left): Schematic illustration of the deformable plate P with the different boundaries following

the direction of relative plate motion (dotted lines, small circles) with respect to the adjacent plates.

PoR is marked by a solid triangle. (Wdowinski 1998)

The coordinate system has its origin in the earth center and the PoR for each

plate boundary can be described by colatitudinal and azimuthal coordinates (θ, φ).

For the inward and outward boundaries the displacement decreases linearly along

the small circles, but for transform boundaries the displacement decline along

great circles from equator to the pole. For the inward displacement the maximum

horizontal stress lies along small circles and in case of the outward displacement

along great circles (Fig.5). It is different for the tangential displacement; the max-

6 Jasmaria Wojatschke

imum horizontal stress follows a 45° loxodrome which is depending on the left- or

right-lateral displacement clockwise or counterclockwise (Fig.5 & 6). Referring to

the latter the prediction for the maximum horizontal stress is located with respect

to the PoR in an angle of 45°, 90°, 135° or 180°. This prediction Wdowinski tested

by using the Euler pole of the NUVEL-1a model against the observed stress data

from the WSM project. And his assumption worked out very well.

Fig.5 (left): Predicted directions of maximum and minimum horizontal stress for the different plate

boundaries. Solid triangle show the PoR. (Wdowinski 1998)

Fig.6 (right): Spherical coordinate presentation of the Earth viewed from an oblique angel (a, c) and

from the pole of rotation (b, d). Small circles are presented by thin dotted lines, great circles by thin

solid lines, clockwise 45° loxodromes by thick solid lines and counterclockwise 45° loxodromes by

dashed lines. (Wdowinski 1998)

Australia’s regional intraplate stress field as an evidence example for the theory of relative plate motion

Reynolds, Coblentz and Hillis (2002) modeled with the finite element analysis

(FEM) the intraplate stress field in the Indo-Australian plate (IAP). This passage

should show their work and the good fit to the above explained theory of intraplate

tectonics by Wdowinski.

The generation of the first order stress field caused by plate tectonics 7

The stress field in the IAP was for a long time difficult to explain because of

the variety of different plate boundaries (Fig.7). Along the northern and eastern

boundaries island arc, subduction and collisional zones are represented. The

southwestern border only consists of the mid-ocean ridge as boundary typ. Besides

in contrast to some other plates (e.g. North- and South America), the maximum

horizontal stress orientation in Australia does not correlate with the absolute plate

motion, which is NNE for the IAP. So another approach to explain the stress field

was necessary.

Fig.7: Indo-Australian plate with the boundaries and their forces used for modeling. The large solid ar-

rows represent ridge push and the smaller ones boundary traction forces. The open arrows show vari-

ous buoyancy forces, whereas none of them are drawn to scale. The opposing arrows were able to ap-

ply both tension and compression during the modeling. The northwestern part was neglected for the

model because of not having a big influence on the stress field of continental Australia.

H – Himalaya; S – Sumatra Trench; J – Java Trench; B – Banda Arc; NG – New Guinea; SM – Solo-

mon Trench; NH – New Hebrides; TK – Tonga-Kermadec Trench; NZ – New Zealand; SNZ – south of

New Zealand; MOR – mid-ocean ridge; LHR – Lord Howe Rise; cb – collisional boundary; sz – sub-

duction zone; ia – island arc. (Reynolds et al. 2002)

8 Jasmaria Wojatschke

With the increase of data in the WSM project over the years it is possible to de-

fine 16 provinces where the orientation of stress is broadly consistent, but only

twelve of them are important for the model (Fig.8 & 9). On each province a

weight was given having a factor for how consistent the orientation data are with-

in. Beside the FEM is modeling the whole IAP, only the observed continental

stress field was used to constrain the model. The great distance of other stress

fields to the central point of the study Australia makes this instance possible. How

the modeling was done and which parameters were used can be read in the paper

and is not for any interest at this point.

The two described forces driving the tectonic stress, mentioned above, were

used for the modeling, boundary traction and buoyancy forces.

Fig.8: Release of the Australian Stress Map (WSM 2008) showing only the data with quality rank A-C.

The generation of the first order stress field caused by plate tectonics 9

During modeling the stress field following observations could be made: In gen-

eral all provinces are dominated by reverse fault conditions which describe the ob-

served stress orientations perfectly. Tensional forces associated with back arc

spreading are not transmitted into the plate interior and the slap-pull forces of the

subduction zones along the IAP only control a second order stress field. Also the

buoyancy forces are not the major source for the induced stress field especially in

eastern Australia. By plotting the standard deviation and the differential horizontal

stress field it was good to see that the model fits very well excepting the eastern

Australia and a region southward (Fig.9). The deviations are easily explained by

an isotropic stress field where differences are induced by the various plate bounda-

ries. Hence not the tectonic forces dominate these regions but rather local sources

which produce a highly variable orientation of stress data. But this assumption

could not be proved by the model.

But except the southern and eastern region the stress field in Australia can be

explained by first order kinematics of relative plate motion.

Fig.9: The stress provinces used to constrain the predicted stress field and the best fitting stress model.

(Reynolds et al. 2002)

10 Jasmaria Wojatschke

Conclusion

The first order stress field can be very well explained with the theory of relative

plate motion. Horizontal forces appear in the direction of relative plate motion be-

tween adjacent plates and by buoyancy forces (ridge push). The simple spherical

geometry and the three different plate boundary types are the key. To the Pole of

Rotation the maximum horizontal stress direction can only lie on a small circle,

great circle or a 45° loxodromes. After testing the theory, the predicted and ob-

served stress field from the WSM data has shown a strong correlation. So it is a

good explanation for origin of the first order stress field.

By modeling the difficult intraplate stress field of Australia, the same approach

was done and the results could be simply explained with the theory of relative

plate motion.

References

DeMets, C. et al. (1994): Effect of recent revision to the geomagnetic reversal

time scale on estimates of current plate motions; Geophy. Res. Letters Vol.21

No.20

Heidbach, O. et al. (2005): Plate boundary forces are not enough: Second- and

third-order stress patterns highlighted in the World Stress Map database; Tectonics

Vol. 26

Kearey, P., Klepeis, K.A. & Vine F.J. (2009): Global Tectonics; Wiley-

Blackwell Puplishing, Oxford; 3rd

edition

Stein, S. & Sella, G.F. (2002): Plate Boundary Zones: Concept and Approaches;

Plate Boundary Zones – Geodynamics Series Vol. 30, edited by S. Stein & J.T.

Freymueller, American Geophysical Union, Washington D.C.

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World Stress Map project; New Insights into Structural Interpretation and Model-

ling, edited by D.A. Nieuwland, Geological Society, London; Special Publica-

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The generation of the first order stress field caused by plate tectonics 11

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element modeling; J. Geophy. Res., 107(B7)

Richardson, R.M. (1992): Ridge Forces, Absolute Plate Motions, and Intraplate

Stress Field; J. Geophys. Res., 97(B8), pp. 11,739-11,748

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103(B3), pp. 5037-5059

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