Delphine Fitzenz, Generalization of a 3-dimensional fault interaction
model including tectonics, fluids, and stress transfer, 2002, PhD thesis,
Swiss Federal Institute of Technology. Thesis advisor S. A. Miller.
Summary of the principal results
We developed and used a set of modular, flexible, physics-based forward
fault models as a tool to investigate the dominant physical and chemical
processes at work in the earthquake process. The results of this study form
the foundation for developing time-forward mechanistic assessment of seismic
hazard for large-scale potentially destructive fault systems.
From semi-forward stress transfer to a fluid-controlled forward model
We developed a stress transfer model using the analytical solutions giving
the internal displacement field due to a finite dislocation in an elastic
half-space in the framework of the stress transfer theory. Using the slip
distribution inverted for the Izmit earthquake, we investigated how the main
event changed the proximity to failure on the surrounding optimally oriented
planes. We also compared maps of volumetric strain and Coulomb failure stress
changes with the aftershock distribution and the location of the hypocenter
of the Ducze earthquake which stroke four months later. The latter was in
a zone of increased proximity to failure. However, no significant conclusion
could be drawn about what drives aftershocks, namely because of the limited
knowledge on the regional stress and on the pore pressure state, and due
to the lack of reliably relocated aftershocks. The complexity of the stress
transfer patterns near the fault, reflecting both the changes in fault strike
and the heterogeneity of the slip on the main fault, defined regions of enhanced
proximity to failure (or the opposite) on the scale of the error on the
aftershock location.
The limits of this semi-forward study pointed to the need for a forward
3-dimensional fluid-controlled fault model, in which the local stress tensor
is determined by both the tectonic loading and the seismicity. The pore
pressure is monitored and fault interaction can be investigated. The construction
and simulation results of such a model was presented in Chapter 2. Although
the model leads to slip and stress distributions and seismicity statistics
in general agreement with observation, the development of pore pressure compartments
and the significant role of poroelastic effects in fault interaction pointed
to the need for better constrained fault hydraulics.
Rheology and hydraulics of fault zones
A model fault having properties of a ductile fault core was considered
and shear creep and ductile compaction were introduced in the 3-D forward
model (Chapter 3). We showed the development of weak overpressured faults
as a result of ductile compaction and small-scale coseismic pore pressure
redistribution, whether the fluid compressibility is pressure dependent or
kept constant. Because many faults exhibit creep slip, which are not purported
to be weak or overpressured, we propose two alternative mechanisms to regulate
the pore pressure cycle in fault zones. The first one is related to the
role of the highly permeable damage zone (Tanaka et al, 2001) and the second
relates to the in-plane pore pressure redistribution length-scale. Because
such hypotheses have to be tested against data, we built a regional model.
Regional model
Chapter 4 shows first results from a regional model of the transpressional
San Andreas Fault near the Big Bend (California). To avoid cell-size effects
in the pore pressure distribution, we computed and introduced a 2-dimensional
finite difference algorithm that calculates the diffusion of fluid pressure
during interseismic periods. We present the choice of the boundary conditions
(tectonics) and the evolved stress maps and tectonic regimes around the model
fault system due to the pore pressure and stress state and to seismic and
aseismic slip on the two specified faults. Small-scale seismicity-induced
stress perturbations develop near the model faults. Maps of $R$ show complex
distribution of the relative magnitude of the principal stresses. The hypothesis
of homogeneous stress used in focal mechanism inversions is therefore to
be handled with care in tectonically active regions exhibiting a bend in the
plate boundary. Maps of Coulomb failure stress, maximum shear stress, and
optimal orientation for failures calculated with the evolved 3-dimensional
local stress tensor show the advantage of the forward approach compared to
the stress triggering approach.
Methodological aspects
The earthquake process involves processes spanning over 21 orders of magnitude
in time and 15 orders of magnitude in space. It is studied by laboratory
experiments (e.g., short nucleation process experiments or long deformation
experiments, from microseconds to days and from micrometers to meters), field
measurements and geophysics (e.g., structural geology, fault mapping, plate
boundary, mantle convection, earthquakes, from milliseconds to million years
and from micrometers to thousand kilometers), and space-borne observations
(e.g., coseismic surface deformation, subsidence, erosion, long-term surface
strain rates, from seconds to years and from millimeters to thousands of kilometers).
Forward modeling earthquake generation on interacting faults including large-scale
tectonics and a detailed handling of fault zone hydraulics is therefore a
difficult task.
The quasi-static approach
We considered the problem of earthquake mechanics from a tectonic scale
while keeping small-scale processes intact. We made significant approximations
to simplify the physics, while ensuring that these approximations had substantial
supporting evidence. The advantage of the quasi-static approach shown here
is utilizing analytic solutions for the internal displacement field due to
slip on a model subfault. This guarantees accuracy of the solutions along
with other significant advantages. There is no need for a 3-dimensional mesh
covering the model space; the exact displacement (and subsequent stress)
field on a subfault is calculated directly from the dislocation that causes
the perturbation and does not require the convergence of a numerical method
(e.g., finite elements) on a series of nodes linking the perturbation to the
observation point. This saves considerable computation time and also gives
more freedom in the choice of the model geometry and the range of spatial
scales considered. Thus, the tectonic loading is applied on dislocation planes
much larger than the model faults (e.g. 800 km long, to avoid lateral boundary
effects) whereas the stresses are monitored on 2 km long subfaults and creep
slip is calculated using the tens of centimeter wide fault zone width. Note
that in principle, the subfault size can be reduced (or alternatively, the
resolution can be increased), but this results in the usual compromise between
resolution and computation time.
A modular, flexible tool
The computer code is made of a series of modules articulated within a
main fault interaction loop and synchronized namely through the time step
calculation. After the definition of the initial conditions, a module calculates
the time step required to reach failure on exactly one subfault. Once slip
on a subfault is initiated, the subsequent rupture is controlled by the
physics of a propagating elastic dislocation. Other modules include in-plane
fluid diffusion, slip calculation to get the assumed stress drop, pore pressure
redistribution, strain redistribution and stress calculation. Other processes
that have to be incorporated depend mainly on the drained vs undrained assumptions.
For instance, pore pressure redistribution occurs only once the system is
in stress equilibrium, and porosity is updated for frictional dilatancy before
pore pressure redistribution. This occurs because although
fluids do not fill the new porosity instantaneously, we consider that
pore pressure aids the propagation of the cracks responsible for the increase
in porosity. This structure is very convenient both to test different approaches
(e.g., different pore pressure redistribution methods, different boundary
conditions in terms of pore pressure, see differences between Chapter 2 and
Chapter 3) and to easily add modules.
Perspectives
The results of this thesis form a basis for many future directions in
modeling the earthquake process, with the long-term goal of building physics-based,
real-time self-learning models that describe the physics of major active
faults. Such models can be tailored to particular tectonic regimes and fault
systems that pose a major seismic risk (e.g., the North Anatolian Fault near
Istanbul, the San Andreas fault at Parkfield, the Nojima Fault near Kobe),
and of intraplate deformation in particularly sensitive densely populated
areas. A number of future developments and studies are necessary before achieving
this goal, and some of these are discussed below.
See the thesis text for more!
If you have ideas or comments, please contact me at fitzenz@usgs.gov.