A New FiniteElement Model of the Hayward Fault

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A New Finite-Element Model of the Hayward Fault

• Michael Barall USGS Menlo Park and Invisible
  Software Inc.Northern California Earthquake
  Hazards Program Workshop, January 2006

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Web Version

• Slides with yellow backgrounds, like this one,
  were not part of the original oral presentation.
  We added them to the PowerPoint file on our web
  site, www.FaultMod.com, to make the file easier
  to understand for readers who did not hear the
  oral presentation.
• The next slide acknowledges the many people at
  USGS who have contributed to this effort.

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Acknowledgements

• Brad Aagaard, Thomas Brocher, James Dieterich,
  Russell Graymer, Ruth Harris, Robert Jachens,
  Patricia McCrory, Andrew Michael, Diane Moore,
  Geoffrey Phelps, David Ponce, Robert Simpson,
  William Stuart, Carl Wentworth.

4
Goals

• This project has two goals. The first goal is to
  create a finite-element model of the Hayward
  fault that includes both the 3D distribution of
  rock properties and the 3D fault geometry. Well
  be using new 3D data sets from USGS, that make it
  possible for the first time to construct such a
  model.
• The second goal is to test and demonstrate the
  capabilities of the FAULTMOD software. FAULTMOD
  is a new open-source 3D finite element program.
  It was developed for USGS, and is designed
  specifically for earthquake modeling.

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Goal Create a finite-element model that includes
the 3D distribution of rock properties and the 3D
fault geometry.

• Use the latest 3D data sets from USGS
• Hayward 3D geologic map.
• Bay Area 3D geologic map.
• Bay Area 3D velocity model.

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FAULTMOD Software

• Open-source finite-element software developed for
  USGS.
• Designed specifically for earthquake modeling.
• Web site www.FaultMod.com.

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Outline

• Finite-element mesh.
• Geologic and physical property data.
• 3D fault geometry.
• First calculation results.
• Future directions.

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Topography and Bathymetry

• The next slide shows our finite-element mesh,
  colored by elevation. Green and blue are below
  sea level, yellow and red are above sea level. In
  the center, you can see San Francisco Bay as a
  green lake, surrounded by the cities of San
  Francisco, Oakland, and San Jose.
• The coloring is the actual elevation of the top
  surface of the finite-element mesh. Its not just
  a topographic map overlaid on an image of the
  mesh. The image shows that we are using
  topographic and bathymetric data from USGS to
  form the upper surface of our mesh, and you can
  see that the meshs upper surface is a fairly
  good map of the Bay Area.

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Topography and Bathymetry
Oakland
San Francisco
San Jose
50 km
400 km
300 km
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Geologic Data
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Geologic Data

• Geologic data tells you what type of rock is
  present within the earth. We are using two truly
  remarkable 3D geologic data sets, both published
  by USGS in 2005.
• The next slide shows the Hayward 3D geologic map.
  It is a very detailed map that gives rock types
  within 10 km of the Hayward fault, down to a
  depth of 13 km. It also gives the 3D geometry of
  the fault surface.
• The second slide after this one shows the Bay
  Area 3D geologic map. It gives the distribution
  of rock types throughout the San Francisco Bay
  Area.

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Sources of Geologic DataHayward 3D Geologic Map
(Graymer et. al.)
This map gives rock types near the fault, and the
3D fault geometry. We use both pieces of
information.
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Sources of Geologic DataBay Area 3D Geologic
Map (Jachens et. al.)
This model gives rock types over the entire Bay
Area.
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Geologic Data in the Mesh

• The next slide shows how we are using geologic
  data to fill in the finite-element mesh. The
  central part (yellow) comes from the detailed
  Hayward 3D geologic map. Surrounding the central
  area (green) we use the much larger Bay Area 3D
  geologic map.
• Our mesh is so big that even the Bay Area map
  doesnt fill it, so the outer portion of the mesh
  (blue) is filled in using regional average
  properties. Finally, at depths below the geologic
  maps (red), we use a simple mantle model.

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Sources of Geologic Data
Hayward 3D Geologic Map
Bay Area 3D Geologic Map
Regional Averages
Mantle Model
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Physical Property Data
17
Physical Properties

• Physical properties tell you the actual behavior
  of the rock. This information is needed to run
  the finite-element simulations. Initially we are
  assuming elastic properties, but the FAULTMOD
  software also permits the use of viscoelastic and
  plastic rheologies.
• Our physical property data comes from the Bay
  Area 3D velocity model, another remarkable data
  set published by USGS in 2005. It gives the
  physical properties as a function of rock type
  and depth.

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Sources of Physical Property DataBay Area 3D
Velocity Model (Brocher et. al.)
This model assigns rock properties based on rock
type and depth, for the Bay Area.
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Physical Property Data

• The next five slides show you the distribution of
  physical properties in the finite-element mesh,
  which results from combining the geologic data
  and property data. The data includes S-wave
  velocity, S-wave attenuation, P-wave velocity,
  P-wave attenuation, and rock density.
• The images illustrate the wealth of data that is
  available in the 3D data sets from USGS.

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Physical Property Data S-Wave Velocity
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Physical Property Data S-Wave Attenuation
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Physical Property Data P-Wave Velocity
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Physical Property Data P-Wave Attenuation
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Physical Property Data Rock Density
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3D Fault Geometry
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Fault Surface

• The next slide shows the location of the fault
  surface within the finite-element mesh. The red
  line is the model fault. Note that it runs right
  under the city of Oakland.
• The actual Hayward fault lies in the central
  portion of the mesh, where its shape is
  determined by the Hayward 3D geologic map.
• For modeling purposes, we extended the fault
  straight north and south for the entire 400 km
  length of the model. Below 13 km depth, which is
  the lower limit of the Hayward 3D geologic map,
  we extended the fault straight down to the bottom
  of the mesh.

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Fault Surface
Oakland
San Francisco
San Jose
50 km
400 km
300 km
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Fault Surface Faces

• The next two slides show the east and west faces
  of the fault surface, inside the model. The
  curved section in the center lies in and below
  the Hayward 3D geologic map. The upper portion of
  the fault surface dips to the east.
• The surface is colored according to the S-wave
  velocity of the adjacent rock. If you look
  carefully, you can see that the coloring is
  different on the two sides of the fault. The
  software is able to display different colors on
  opposite sides of the surface, to indicate the
  rock properties on each side.

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Fault Surface East Face
400 km
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Fault Surface West Face
400 km
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Morphing the Mesh
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Morphing the Mesh

• The next seven slides illustrate how we produce a
  mesh with a curved fault surface. It is done by
  morphing. We start with an ideal mesh, which is
  a simple rectilinear mesh with a straight
  vertical fault. Then we gently distort the entire
  mesh, to produce the desired curved and dipping
  fault surface.
• The following slides show horizontal slices of
  the mesh. The first slide shows a slice of the
  ideal mesh, with a straight fault. Succeeding
  slides show slices of the final mesh, at six
  different depths ranging from 0 to 12.5 km. In
  each slice, the fault is curved according to the
  Hayward 3D geologic map at the corresponding
  depth.

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Morphing the Mesh (continued)

• The mesh in each slice is distorted to
  accommodate the shape of the fault. Notice that
  the gentle distortion is distributed throughout
  the mesh.
• If you page through the slides in sequence, you
  can see that the fault overall moves to the east
  as you view increasing depths. This generates the
  eastward dip of the fault surface.
• These horizontal slices are connected together to
  produce the final 3D mesh. Below 12.5 km depth,
  the shape of the fault is kept constant.
• The topography on the top surface of the mesh is
  also produced by morphing, but in this case the
  distortion is vertical rather than horizontal.

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Ideal Mesh

• All cells are squares.
• Fault is a straight line.

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Morphed Mesh,Depth 0.0 km

• Distort the entire mesh to produce the fault
  trace.
• Each layer of the mesh has a different trace.
• In successive layers, fault trace shifts to the
  east, creating eastward dip.

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Morphed Mesh,Depth 2.5 km

• Distort the entire mesh to produce the fault
  trace.
• Each layer of the mesh has a different trace.
• In successive layers, fault trace shifts to the
  east, creating eastward dip.

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Morphed Mesh,Depth 5.0 km

• Distort the entire mesh to produce the fault
  trace.
• Each layer of the mesh has a different trace.
• In successive layers, fault trace shifts to the
  east, creating eastward dip.

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Morphed Mesh,Depth 7.5 km

• Distort the entire mesh to produce the fault
  trace.
• Each layer of the mesh has a different trace.
• In successive layers, fault trace shifts to the
  east, creating eastward dip.

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Morphed Mesh,Depth 10.0 km

• Distort the entire mesh to produce the fault
  trace.
• Each layer of the mesh has a different trace.
• In successive layers, fault trace shifts to the
  east, creating eastward dip.

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Morphed Mesh,Depth 12.5 km

• Distort the entire mesh to produce the fault
  trace.
• Each layer of the mesh has a different trace.
• In successive layers, fault trace shifts to the
  east, creating eastward dip.

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First CalculationFrictionless Fault Slip
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Frictionless Fault Slip

• For our first calculation, we allowed the entire
  fault to slip without friction. Tectonic driving
  forces were applied to the east and west borders
  of the mesh. Then, the FAULTMOD software
  calculated the resulting displacements and
  stresses throughout the mesh.
• If the fault were straight, the two sides would
  slide past each other without distortion or
  stress. But the model fault is curved, and so the
  fault geometry induces distortions and stresses
  as the two sides try to slide past each other.

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Calculated Vertical Displacement

• The next two slides show the calculated vertical
  displacement at the Earths surface, for
  frictionless fault slip. Red denotes upward
  displacement and blue denotes downward
  displacement. You can see that they form an
  interesting pattern. The FAULTMOD software also
  allows viewing displacements and stresses inside
  the mesh.
• We did the calculation twice. The first slide
  shows the results for a non-uniform rheology
  based on USGS 3D data. The second slide shows the
  results for a uniform rheology. Although there
  are some differences between the two slides,
  overall they are very similar. This demonstrates
  that, for this calculation, fault geometry is
  more important than rheology.

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Calculated Vertical Displacement
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Calculated Vertical Displacement Uniform
Rheology
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Calculated Perpendicular Displacement

• The next two slides show the calculated
  displacement at the Earths surface,
  perpendicular to the fault, for frictionless
  fault slip. Red denotes eastward displacement and
  blue denotes westward displacement.
• The first slide shows the results for a
  non-uniform rheology based on USGS 3D data. The
  second slide shows the results for a uniform
  rheology. Although there are some differences
  between the two slides, overall they are very
  similar. So once again, for this calculation,
  fault geometry is more important than rheology.

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Calculated Displacement Perpendicular to Fault
48
Calculated Displacement Perpendicular to Fault
Uniform Rheology
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Calculated Fault Slip

• The next two slides show the calculated slip on
  the fault surface, for frictionless fault slip.
  Red denotes maximum slip and blue denotes minimum
  slip. Maximum slip occurs along the straight
  sections at the north and south, and minimum slip
  occurs where the fault is most sharply curved.
  This is consistent with the idea that fault
  curvature impedes slip.
• The first slide shows the results for a
  non-uniform rheology based on USGS 3D data. The
  second slide shows the results for a uniform
  rheology. Although there are some differences
  between the two slides, overall they are very
  similar. So once again, for this calculation,
  fault geometry is more important than rheology.

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Calculated Fault Slip
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Calculated Fault Slip Uniform Rheology
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Future Directions

• The final slide lists some scientific questions
  that we plan to investigate with the model.

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Future Directions

• What are the effects and relative importance of
  fault geometry and non-uniform physical
  properties?
• Can the model account for the observed creep
  rates and geodetic observations along the Hayward
  fault?
• What are the effects of introducing locked
  patches and friction on the fault?
• Can aseismic slip on parts of the fault surface
  create patterns of deformation or concentrations
  of stress that are consistent with observations?