abhijit gangopadhyay and pradeep talwani institute for geophysics university of texas at austin

Localized Stress Concentration: Localized Stress Concentration: A PossibleA Possible

Cause of Current Seismicity in Cause of Current Seismicity in New Madrid and Charleston New Madrid and Charleston

Seismic ZonesSeismic Zones

Abhijit Gangopadhyay and Pradeep TalwaniAbhijit Gangopadhyay and Pradeep TalwaniInstitute for GeophysicsInstitute for Geophysics

University of Texas at AustinUniversity of Texas at AustinDepartment of Geological SciencesDepartment of Geological Sciences

University of South CarolinaUniversity of South Carolina

STRATEGYSTRATEGY

Multi-Step Analyze and synthesize global data

Develop simple mechanical models

Models wherein stress perturbation occurs in upper crust

GLOBAL SURVEY GLOBAL SURVEY (Gangopadhyay and Talwani, (Gangopadhyay and Talwani, 2003)2003)

Johnston (1994)

(1)(3)

(2)(1)(1)

(1)

(1)

(3)

(2)

(1)(1) (1)

(3)

(1) (1)

(4)

(5)(3)

(3)

(1)

•39 Earthquakes•20 Continental Intraplate Regions

•12 Rifted, 8 Non-Rifted

Spatial Association with Stress Spatial Association with Stress ConcentratorsConcentrators

Intersecting faults and bendsIntersecting faults and bends• 8 out of 12 cases in rifts8 out of 12 cases in rifts• 5 out of 8 cases in non-rifted regions5 out of 8 cases in non-rifted regions

Buried plutonsBuried plutons• 6 out of 8 cases in rifts6 out of 8 cases in rifts• 5 out of 8 cases in non-rifted regions5 out of 8 cases in non-rifted regions

Rift pillowsRift pillows• 4 cases4 cases

Testable HypothesisTestable Hypothesis

Observed spatial association

Causal association

Intraplate earthquakes occur due to a localized stress build-up in response to plate tectonic

forces, in the vicinity of stress concentrator/s, such as intersecting faults, buried plutons, rift

pillows located in a pre-existing zone of weakness

SIMPLE MECHANICAL SIMPLE MECHANICAL MODELSMODELS

Distinct Element Method : UDEC & 3DECDistinct Element Method : UDEC & 3DEC Structural Framework in a Block Model Structural Framework in a Block Model

(Deformable)(Deformable) Faults treated as DiscontinuitiesFaults treated as Discontinuities Constant Strain Triangular ZonesConstant Strain Triangular Zones Elastic Properties based on Known Elastic Properties based on Known

Geology (Densities and Elastic properties Geology (Densities and Elastic properties of blocks, Stiffnesses, Cohesion, and of blocks, Stiffnesses, Cohesion, and Friction for faults)Friction for faults)

Tectonic Loading along STectonic Loading along SHmaxHmax

Resultant patterns of stresses, strains, Resultant patterns of stresses, strains, and displacementsand displacements

Summary of 2-D Model for Summary of 2-D Model for NMSZNMSZ

(Gangopadhyay et al., 2004)(Gangopadhyay et al., 2004)

A

B

P

Q N

Y

M

Need for 3-D ModelsNeed for 3-D Models

o 2-D Models do not show uplift

o 3-D Models are more realistic with respect to Fault Geometry

3-D Model for NMSZ (using 3DEC)3-D Model for NMSZ (using 3DEC)[Gangopadhyay and Talwani, 2006 (In [Gangopadhyay and Talwani, 2006 (In

Revision, JGR)]Revision, JGR)]

Max. Shear Stress along Max. Shear Stress along BFZBFZ

Max. Shear Stress along Max. Shear Stress along RFRF

Max. Shear Stress along BL & Max. Shear Stress along BL & NMNFNMNF

Movement along BFZ, BL, Movement along BFZ, BL, NMNFNMNF

Vertical Movement along Vertical Movement along RFRF

Max. Shear Stress Vs. Max. Shear Stress Vs. Seismicity in DepthSeismicity in Depth

Seismogenic Intersecting FaultsSeismogenic Intersecting Faults(Gangopadhyay and Talwani, 2007)(Gangopadhyay and Talwani, 2007)

SUMMARYSUMMARY

Spatial Association of Continental Spatial Association of Continental Intraplate Seismicity with Stress Intraplate Seismicity with Stress Concentrators such as:Concentrators such as:• Intersecting FaultsIntersecting Faults

Based on 2-D and 3-D Mechanical Based on 2-D and 3-D Mechanical Models:Models:• Stress Concentration due to Stress Concentration due to

Intersecting Faults explains current Intersecting Faults explains current seismicity and tectonic features in seismicity and tectonic features in NMSZNMSZ

THE FINAL ANSWER!THE FINAL ANSWER!

A Cause of Continental Intraplate Seismicity may be Localized Stress Concentration due to Stress

Concentrators such as Intersecting Faults (favorably oriented) in response to Plate

Tectonic Forces, and simple models involving these stress concentrators can explain the

seismicity in NMSZ

RESERVE SLIDESRESERVE SLIDES

UDEC/3DEC Computation UDEC/3DEC Computation CycleCycle

Rounding Concept – Avoiding Rounding Concept – Avoiding SingularitiesSingularities

Elastic Properties Elastic Properties (NMSZ)(NMSZ)

Blocks pertainin

g to

Bulk Modulus

(GPa)

Shear Modulus

(GPa)

Density(kg/m3)

Reelfoot rift

47.28 28.48 2690

Missouri Batholith

57.66 34.74 2705

Outside of rift

58.61 35.32 2750

Joints Friction Angle(deg)

Normal Stiffness(GPa/m)

Shear Stiffness(GPa/m)

Cohesion(MPa)

BFZ, RF, NMNF, and BL

27 101 76 0

Margins of the Missouri Batholith

33 133 100 0.5

Rift boundary faults

27 101 76 0.5

Computational SequenceComputational Sequence

Calculations done at each grid pointCalculations done at each grid pointüi = (Fi)/m

Fi = FZ + FC + FL + FG

Contribution of internal stresses

in zones adjacent to grid

point

Contact forces for grid points along block boundary

External applied loads

Force due to gravity

Computational Sequence Computational Sequence (contd.)(contd.)

Acceleration at each grid pointAcceleration at each grid point• Finite difference form of Newton’s Finite difference form of Newton’s

second law of motionsecond law of motionm[Vi(t + Δt/2) - Vi(t – Δt/2)]/t = Fi(t)

For each time stepFor each time step• Strains and rotations computedStrains and rotations computed

ij = ½ (Vi,j + Vj,i)ij = ½ (Vi,j - Vj,i)

Computational sequence Computational sequence (contd.)(contd.)

Constitutive equations for blocks appliedConstitutive equations for blocks appliedij = 2ij + kkij

where, = k – (2/3) Failure criteria for faults appliedFailure criteria for faults applied

S C + ntan

where, n = - knun

S = - kSuS

3-D Model for MPSSZ (using 3-D Model for MPSSZ (using 3DEC)3DEC)

[Gangopadhyay and Talwani, 2006 (In [Gangopadhyay and Talwani, 2006 (In Revision, JGR)]Revision, JGR)]

Shear Stress along Shear Stress along WF(N)WF(N)

Shear Stress along SBFShear Stress along SBF

Shear Stress along WF(S)Shear Stress along WF(S)

Movement along WF(N) and Movement along WF(N) and WF(S)WF(S)

Vertical Movement along Vertical Movement along SBFSBF

Shear Stress Vs. Seismicity Shear Stress Vs. Seismicity in Depthin Depth