A HighResolution Finite Element Model of the Hayward Fault

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A High-Resolution Finite Element Model of the
Hayward Fault

• Michael BarallInvisible Software, Inc., and
  USGS
• Robert SimpsonUSGS
• William Stuart
• USGS
• 4th Annual Northern California Earthquake Hazards
  WorkshopUSGS, Menlo Park, CaliforniaJanuary 2007

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Research Objectives

• To understand seismicity on the Hayward Fault
  using 3D geology and physics based models.
• In particular, to explore how rock properties and
  3D fault geometry could affect locations of
  locked patches, segment boundaries, and
  earthquakes.

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Finite Element Mesh

• (One of the several versions used.)
• Smallest cells are cubes 625 meters on a side.
• Total of about 850,000 cells, all quadratic
  hexahedra.
• Mesh resolves rock units in Hayward 3D geologic
  model.

100
km
400 km
300 km

• Rock properties imported from
• Hayward geologic model (Graymer et al.)
• Bay Area geologic model (Jachens et al.)
• Bay Area velocity model (Brocher et al.)

10 km
Point Pinole
Fremont
San Leandro Gabbro (green area)
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Fault Surface
San Leandro Gabbro (brown)
Point Pinole
Fremont
10 km

• Colors denote shear wave velocity, red fast,
  blue slow.
• Purple dots are seismicity, and white curves are
  proposed locked patches (Waldhauser and
  Ellsworth).

Rock Units with Low Vs (green)
West side of fault
San Leandro Gabbro (brown)
Point Pinole
10 km
Fremont

• Smallest cells are 625 meters across.
• Mesh resolves rock units in Hayward geologic
  model, and proposed locked patches.

Rock Unit with Low Vs (green)
East side of fault
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Normal Stress on Fault, Due to Rock Properties
Point Pinole
Fremont
10 km
Extent of San Leandro Gabbro
Model driven by far-field shear distortion.Blue
Clamping (compression)Red Unclamping
(tension)Purple dots SeismicityWhite curves
Waldhauser and Ellsworth
proposed locked patches
Rates 10 30 of shear stress 700
2000 Pascal/year
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Normal Stress, due to Rock Properties, with
Detachment Layer
Point Pinole
Fremont
10 km
Extent of San Leandro Gabbro
Horizontal detachment layer at 15 km depth.Model
driven by far-field shear distortion. Blue
Clamping (compression)Red Unclamping
(tension)Purple dots SeismicityWhite curves
Schmidt et al. proposed
locked patches
Rates 10 30 of shear stress 700
2000 Pascal/year
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Shear Stress on Fault, Due to Rock Properties
Point Pinole
Fremont
10 km
Extent of San Leandro Gabbro
Model driven by far-field shear distortion. Blue
Low shear stressRed High shear stressPurple
dots SeismicityWhite curves Waldhauser and
Ellsworth proposed
locked patches
Stressing rate 7000 Pascal/year
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Warping of Fault Surface, Due to Rock Properties
Point Pinole
Fremont
10 km
Extent of San Leandro Gabbro
Model driven by far-field shear distortion. Blue
Toward viewer (westward)Red Away from viewer
(eastward)Purple dots SeismicityWhite curves
Waldhauser and Ellsworth
proposed locked patches
Rates 1 of fault slip 0.1 mm/year
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Morphing Process

• (Separates the effects of rock properties and 3D
  fault geometry.)
• Original Curved-Fault Model
• Fault is a curved 3D surface.
• Mesh curves to follow the shape of the fault.

• Morphed Planar-Fault Model
• Fault is a vertical plane.
• Mesh is rectilinear.
• Entire geologic model is gently distorted to
  obtain a planar fault.
• Rock units remain on correct side of fault, with
  size and shape preserved as much as possible.

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Comparison of Results from Curved-Fault and
Planar-Fault Models
10 km
Curved fault, with actual Hayward fault 3D
geometry.Stresses are due to rock properties and
fault geometry.Red unclamping, blue
clamping. Detachment layer at 15 km.
10 km
Morphed planar fault.Stresses are due to rock
properties only.Red unclamping, blue
clamping. Detachment layer at 15 km.
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Sample Entry fromInclusion Catalog

• Purpose Develop intuition about how material
  heterogeneity affects stresses on the fault.
• Inclusion has higher stiffness than surrounding
  material.
• Vary the shape and position of the inclusion.
• Vary how the model is driven
• Regional shear distortion.
• Horizontal screw dislocation at depth.
• Vertical edge dislocation.
• Regional compression.

West side of fault
East side of fault
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Sample Results fromInclusion Catalog

• Catalog can be viewed in a web browser.
• Browse catalog to explore how idealized rock
  units affect a fault, under various conditions.

Normal stress on fault planeBlue clamping,
red unclamping.
Shear stress on fault planeBlue low, red
high.
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Research Plans for 2007

• Compare numerical results to observational data
• Seismicity, fault creep, geodetic, and InSAR
  data.
• Extend model southward toward the Calaveras
  fault
• Geometry becomes more complex and interesting.
• Perform dynamic rupture calculations
• Can the model suggest fault segment boundaries?
• www.FaultMod.com